• No se han encontrado resultados

Vista de Simulación basada en SMA de sistemas originalmente representados con EDO

N/A
N/A
Protected

Academic year: 2023

Share "Vista de Simulación basada en SMA de sistemas originalmente representados con EDO"

Copied!
11
0
0

Texto completo

(1)

© 2011 CEA. Publicado por Elsevier España, S.L. Todos los derechos reservados doi:10.1016/j.riai.2011.09.011

6LPXODFLyQEDVDGDHQ60$GHVLVWHPDVRULJLQDOPHQWHUHSUHVHQWDGRVFRQ

('2 

(NDLW]=XOXHWD*XHUUHURD $VLHU*RQ]iOH]*RQ]iOH]E-RVH0DQXHO/RSH]*XHGHD,VLGUR&DOYR*RUGLOORD

D'HSDUWDPHQWRGH,QJHQLHUtDGH6LVWHPDV\$XWRPiWLFD(8,QJHQLHUtDGH9LWRULD*DVWHL]&1LHYHV&DQRQž9LWRULD*DVWHL](VSDxD

E7HFQDOLD5HVHDUFK ,QQRYDWLRQ3DUTXH7HFQROyJLFRGHÈODYD&$OEHUW(LQVWHLQQ0LxDQR ÈODYD (VSDxD





5HVXPHQ

(QHOSUHVHQWHWUDEDMRVHH[SRQHXQDPHWRGRORJtDSDUDPRGHODUPHGLDQWHXQ6LVWHPD0XOWL$JHQWH 60$ VLVWHPDVELROyJLFRV\

ILVLROyJLFRV GLQiPLFRV FRQ YDULDEOHV FXDQWLILFDGDV GLVFUHWDV FRPR HO FUHFLPLHQWR \ GHFUHFLPLHQWR GH SREODFLRQHV R HO PRGHODGR

HSLGHPLROyJLFRGHHQIHUPHGDGHV6HPXHVWUDXQSURFHGLPLHQWRSDUDWUDQVIRUPDUXQVLVWHPDGH(FXDFLRQHV'LIHUHQFLDOHV2UGLQDULDV

('2  TXHPRGHODXQHQWRUQRGHIRUPDFRUUHFWD HQXQ60$HTXLYDOHQWHPHGLDQWHXQHVTXHPDEDVDGRHQHOPpWRGRGH0RQWH

&DUOR6HXWLOL]DXQFDVRSUiFWLFRIXQGDPHQWDGRHQXQPRGHORPDWHPiWLFRGH/HXFHPLD0LHORLGH&UyQLFD /0& SDUDFRPSDUDUOD

PHWRGRORJtD EDVDGD HQ DJHQWHV FRQ HO PRGHODGR WUDGLFLRQDO EDVDGR HQ XQ VLVWHPD GH ('2 6H UHDOL]D XQD VLPXODFLyQ FRQ FDGD

PRGHOR 60$ \ ('2  \ VH FRPSDUD ORV UHVXOWDGRV REWHQLGRV FRQ DPEDV PHWRGRORJtDV &RS\ULJKW ‹ &($ 3XEOLFDGR SRU

(OVHYLHU(VSDxD6/7RGRVORVGHUHFKRVUHVHUYDGRV

3DODEUDV&ODYH

(FXDFLRQHVGLIHUHQFLDOHVPRGHOREDVDGRHQDJHQWHV0RQWH&DUOR



 

$XWRUHQFRUUHVSRQGHQFLD

&RUUHRVHOHFWUyQLFRVHNDLW]]XOXHWD#HKXHV (=XOXHWD 

DVLHUJRQ]DOH]#WHFQDOLDFRP $*OH]*OH] 

MPORSH]#HKXHV -0/RSH]*XHGH LVLGURFDOYR#HKXHV ,&DOYR*RUGLOOR 

 ,1752'8&&,Ï1

(Q HVWH WUDEDMR VH SURSRQH XQ QXHYR HQIRTXH HQ HO

PRGHODGR GHVLVWHPDV ELROyJLFRV GLQiPLFRV FRQ YDULDEOHV

FXDQWLILFDGDV GLVFUHWDV (VWRV PRGHORV GLQiPLFRV VH DMXVWDQ

SULQFLSDOPHQWH D XQD JUDQ FDQWLGDG GH VLVWHPDV GH WLSR

ELROyJLFR \ ILVLROyJLFR FRPR HO PRGHODGR GH SREODFLRQHV

0XUUD\ D  R HO PRGHODGR GH HQIHUPHGDGHV

HSLGHPLROyJLFDV 0XUUD\E 



3DUDHOPRGHODGRGHORVVLVWHPDVELROyJLFRVGLQiPLFRVVH

XVDQGLIHUHQWHVWpFQLFDVPDWHPiWLFDV 9DQ'HQ%HUJ

6KRQNZLOHUHWDO%UDXHUHWDO (QWUHODVPiV

GHVWDFDGDV HVWiQ ODV HFXDFLRQHV GLIHUHQFLDOHV RUGLQDULDV

('2  ODV HFXDFLRQHV HQ GHULYDGDV SDUFLDOHV \ PRGHORV

EDVDGRV HQ SURFHVRV HVWRFiVWLFRV :RGDU] DQG .RPDURYD

 'HHVWDVWpFQLFDVGHPRGHODGRHOSUHVHQWHWUDEDMRVH

FHQWUDHQHOPRGHODGRFRQ('2



(Q HVWH WUDEDMR VH SODQWHD XQ QXHYR HQIRTXH SDUD HO

PRGHODGR GH HVWRV VLVWHPDV EDVDGR HQ XQ 6LVWHPD 0XOWL

$JHQWH 60$  \ VH H[SRQH XQD PHWRGRORJtD SDUD

FRQVWUXLUOR D SDUWLU GH XQ FRQMXQWR GH ('2V TXH PRGHODQ

FRUUHFWDPHQWHHOHQWRUQR



$VLPLVPRVHSUHVHQWDXQFDVRSUiFWLFRTXHFRPSDUDORV

UHVXOWDGRV REWHQLGRV FRQ HVWRV GRV PRGHODGRV 60$ \

VLVWHPD GH ('2 (O FDVR SUiFWLFR VH EDVD HQ XQ PRGHOR

PDWHPiWLFR GH /HXFHPLD 0LHORLGH &UyQLFD 3DYyQ 0RUiQ

HWDO 

 Introducción

(2)

/DSUREOHPiWLFDGHOPRGHODGRFRQHFXDFLRQHV

GLIHUHQFLDOHV

([LVWH XQD DPSOLD ELEOLRJUDItD TXH WUDWD HO WHPD GHO

PRGHODGRGHVLVWHPDVELROyJLFRVGLQiPLFRVFRQHFXDFLRQHV

GLIHUHQFLDOHV (Q %DVVH DQG 8EH]LR   VH PRGHOD XQ

VLVWHPDGHHFXDFLRQHVHQGHULYDGDVSDUFLDOHVTXHJRELHUQD

OD FLQpWLFD GH XQD SREODFLyQ GH FpOXODV \ OD GHQVLGDG GH

pVWDVHQGHWHUPLQDGDVIDVHVGHOFLFORGHODGLYLVLyQFHOXODU

(Q 6SHQFHU HW DO    VH DQDOL]D XQ PRGHOR GH ('2

TXHH[SORUDHOHTXLOLEULRHQWUHODDQJLRJpQHVLVODVWDVDVGH

PXHUWH FHOXODU ODV PXWDFLRQHV JHQpWLFDV \ ODV WDVDV GH

UHSURGXFFLyQHQHOGHVDUUROORGHOFiQFHU2WURV PRGHODGRV

PDWHPiWLFRV GH FpOXODV WXPRUDOHV FRQ HFXDFLRQHV

GLIHUHQFLDOHV SXHGHQ FRQVXOWDUVH HQ 1DJ\ 

%XQLPRYLFK0HQGUD]LWVN\ HW DO  6]\PDQVND HW DO

 



([LVWHQ XQD VHULH GH IDFWRUHV TXH KDFHQ TXH ODV

HFXDFLRQHVGLIHUHQFLDOHVQRVHPXHVWUHQORVXILFLHQWHPHQWH

DGHFXDGDVSDUDPRGHODUHVWHWLSRGHVLVWHPDV

• 8Q PRGHOR EDVDGR HQ HFXDFLRQHV GLIHUHQFLDOHV

GHVFULEH HO VLVWHPD GH IRUPD GHWHUPLQLVWD PHGLDQWH

YDORUHVSURPHGLRGHODVYDULDEOHVGHHVWDGR(OPRGHOR

VyOR FRQVLGHUD HO FRPSRUWDPLHQWR PHGLR GH WRGRV ORV

LQGLYLGXRV VLQ WHQHU HQ FXHQWD OD YDULDQ]D GH OD

SREODFLyQ ‘NVHQGDO 

• (Q HO PRGHODGR GH SREODFLRQHV \ GH HQIHUPHGDGHV

HSLGHPLROyJLFDV H[LVWH XQD DOHDWRULHGDG H[SOLFDGD HQ

SDUWHSRUHOIHQyPHQRItVLFRGHOHIHFWRGHOPRYLPLHQWR

EURZQLDQR /HZLV DQG 3XOq   3RU HMHPSOR ODV

SREODFLRQHV GH EDFWHULDV *XDQJODL HW DO   \ GH

DQLPDOHV +RUQH HW DO   HVWiQ LQIOXLGRV

IXHUWHPHQWH SRU HVWH HIHFWR 'H KHFKR OD GLVWULEXFLyQ

HVSDFLDO GH ORV HOHPHQWRV TXH FRQIRUPDQ HO PRGHOR

LQIOX\H QRWDEOHPHQWH HQ VX HYROXFLyQ FXHVWLyQ pVWD

TXH QR VH FRQWHPSOD IiFLOPHQWH HQ ODV HFXDFLRQHV

GLIHUHQFLDOHV RUGLQDULDV \ TXH VH SXHGH SODQWHDU FRQ

QDWXUDOLGDGHQQXHVWURHQIRTXH

• /DV HFXDFLRQHV GLIHUHQFLDOHV RUGLQDULDV VRQ

GHWHUPLQLVWDVSRUWDQWRSDUDXQDVPLVPDVFRQGLFLRQHV

LQLFLDOHV OD VROXFLyQ VLHPSUH HV OD PLVPD $JDUZDO

DQG25HJDQ 

• ([LVWH OD SRVLELOLGDG GH TXH HQ XQ LQVWDQWH GH WLHPSR

DOJXQD YDULDEOH GH HVWDGR GHO PRGHOR GH ('2 Gp XQ

UHVXOWDGR QHJDWLYR 6L VH PRGHOD SREODFLRQHV R

HQIHUPHGDGHV HSLGHPLROyJLFDV HVWD VLWXDFLyQ QR HV

FRUUHFWD \D TXH QR WLHQH VHQWLGR TXH OD FDQWLGDG GH

FpOXODV TXH H[LVWHQ HQ XQ PRPHQWR GHWHUPLQDGR VHD

QHJDWLYD

• 8QVLVWHPDGH('2XVDODVYDULDEOHVGHHVWDGRGHQWUR

GHO UDQJR GH ORV Q~PHURV UHDOHV 0RGHODU GH HVWD

PDQHUD SREODFLRQHV R HQIHUPHGDGHV HSLGHPLROyJLFDV

QR HV UHDOLVWD SRUTXH ODV YDULDEOHV GLQiPLFDV VRQ

GLVFUHWDV 3RU HMHPSOR VL PRGHODPRV SREODFLRQHV GH

FpOXODV QR HV UHDOLVWD TXH HO Q~PHUR GH FpOXODV VHD

IUDFFLRQDULR

• (QRFDVLRQHVHOPRGHODGRFRQHFXDFLRQHVGLIHUHQFLDOHV

KDFHTXHHOFRQMXQWRGHHFXDFLRQHVVHDPX\FRPSOHMR

\ SUHVHQWHQ XQ HOHYDGR Q~PHUR GH SDUiPHWURV TXH

GHEHQVHUFDOFXODGRVRDMXVWDGRV/DLGHQWLILFDFLyQGH

ORV YDORUHV GH HVWRV SDUiPHWURV QR UHVXOWD VHQFLOOD GH

UHDOL]DUHQJHQHUDO

7UDEDMRVUHODFLRQDGRV

&RPR VH KD H[SOLFDGR H[LVWH DPSOLD ELEOLRJUDItD TXH

WUDWD HO PRGHODGR GH VLVWHPDV ELROyJLFRV FRQ ('2 SHUR

WDPELpQ H[LVWHQ WUDEDMRV TXH PRGHODQ VLVWHPDV ELROyJLFRV

XVDQGRWpFQLFDVEDVDGDVHQDJHQWHV %HQMDPLQHWDO

5HGRXHWDO 



$OJXQRV WUDEDMRV SURSRQHQ PRGHORV KtEULGRV GH

VLPXODFLyQ HQ ORV TXH XWLOL]DQ GH IRUPD FRPELQDGD

VLVWHPDV EDVDGRV HQ DJHQWHV \ HFXDFLRQHV GLIHUHQFLDOHV

*XRHWDO%DQHUMHHDQG0RVHV 



/D QRYHGDG GH HVWH WUDEDMR UHVLGH HQ OD GLVHxR GH XQD

PHWRGRORJtD JHQHUDO SDUD WUDQVIRUPDU XQ VLVWHPD GH ('2

HQ XQ 60$ HTXLYDOHQWH \ HQ OD FRPSDUDFLyQ GH ORV GRV

PRGHORV PHGLDQWH XQ FDVR SUiFWLFR EDVDGR HQ XQ PRGHOR

PDWHPiWLFR GH /HXFHPLD 0LHORLGH &UyQLFD (O PRGHOR

60$ SURSXHVWR SHUPLWH GHVFULELU HQ WpUPLQRV HVWDGtVWLFRV

HYHQWRV WDQ UHOHYDQWHV FRPR OD H[WLQFLyQ GH XQD

GHWHUPLQDGDSREODFLyQGHFpOXODVTXHSXHGHQGHVHQFDGHQDU

XQDSDWRORJtD



 $548,7(&785$

/DDUTXLWHFWXUDJHQpULFDHTXLYDOHQWHDXQ VLVWHPD('2

GDGRTXHVHSURSRQHVHEDVDHQXQPRGHOR0XOWL$JHQWHR

60$ TXH VH FRQVWUX\H D SDUWLU GH GLFKR VLVWHPD ('2 6H

FRQVLGHUD SDUD VLPSOLILFDU HO GHVDUUROOR TXH WRGDV ODV

HFXDFLRQHVGLIHUHQFLDOHVVRQ('2GHSULPHURUGHQ



(Q SULPHU OXJDU DVXPLPRV TXH VH SDUWH GH XQ PRGHOR

FRQ XQ VLVWHPD GH XQD R YDULDV ('2V TXH GHVFULEHQ

FRUUHFWDPHQWH HO FRPSRUWDPLHQWR PHGLR GH XQ VLVWHPD

ELROyJLFRFRQYDULDEOHVFXDQWLILFDGDVGLVFUHWDV



(



    SDUD



)  

L

L Q

G[ I [ [ [ W L Q

GW = =

  



$ SDUWLU GH HVWH PRGHOR GH HFXDFLRQHV GLIHUHQFLDOHV VH

FRQVWUX\H XQ 60$ 8Q 60$ HV XQ VLVWHPD GH P~OWLSOHV

DJHQWHV DXWyQRPRV TXH LQWHUDFFLRQDQ HQWUH Vt \ FRQ HO

HQWRUQREXVFDQGRVDWLVIDFHUFDGDXQRVXVSURSLRVREMHWLYRV

:RROGULGJH 



(OPRGHOR0XOWL$JHQWHPiVVHQFLOOR\TXHUHSURGXFHHO

FRPSRUWDPLHQWR GH XQ PRGHOR FRQ ('2V HVWi FRPSXHVWR

Arquitectura

(3)

SRUWUHVHOHPHQWRVORVDJHQWHVHOHQWRUQR \ODVGLIHUHQWHV

FRQH[LRQHV $ FRQWLQXDFLyQ VH GHVFULEH HQ GHWDOOH FDGD

HOHPHQWRGHGLFKRPRGHOR



$JHQWHV

8Q DJHQWH HV XQD HQWLGDG GH VRIWZDUH VLWXDGR HQ XQ

HQWRUQR YLUWXDOFDSD]GHDFWXDUFRPXQLFDUVHUHSURGXFLUVH

\ HQ JHQHUDO WHQHU XQ FRPSRUWDPLHQWR DXWyQRPR 8Q

DJHQWH HQ IXQFLyQ GH ODV SHUFHSFLRQHV \ GH VXV UHFXUVRV

LQWHUDFFLRQD FRQ HO HQWRUQR \ FRQ RWURV DJHQWHV )HUEHU

 



(Q OD ILJXUD  SXHGH YHUVH HO HVTXHPD TXH VLJXH XQ

DJHQWH HQ FDGD LWHUDFLyQ 3ULPHUR SHUFLEH OXHJR GHFLGH \

SRUXOWLPRDFW~D





)LJXUD3URFHVRTXHVLJXHFDGDDJHQWHHQFDGDLWHUDFLyQ



(QODDUTXLWHFWXUDEDVDGDHQDJHQWHVTXHVHSURSRQHODV

YDULDEOHVGHHVWDGRGHOVLVWHPDGH('2GHODHFXDFLyQ   QRFRUUHVSRQGHQGLUHFWDPHQWHFRQDJHQWHVVLQRFRQJUXSRV

GHHVSHFLHVGHODVLJXLHQWHPDQHUD

• (OQ~PHURGHHVSHFLHVGLIHUHQWHVGH$JHQWHVGHO60$

FRUUHVSRQGHDOQ~PHURGHYDULDEOHVGHHVWDGRµQ¶HQHO

VLVWHPDGH('2

• /DVXPDGHOQ~PHURGHLQGLYLGXRVGHFDGDHVSHFLHHQ

HO 60$ FRUUHVSRQGH D ODV YDULDEOHV GH HVWDGR GHO

VLVWHPDGH('2µ[[«[Q¶



3HUFHSFLyQ

&DGDDJHQWHUHFLEHHQFDGDLWHUDFLyQXQDVHULHGHGDWRV

TXHVRQUHFRJLGRVGHOHQWRUQRDXQTXHGH IRUPDLQGLUHFWD

SXHGHQVHUGDWRVTXHSURYLHQHQGHRWURVDJHQWHV



3DUD WUDQVIRUPDU HO VLVWHPD GH ('2 HQ XQ 60$ FDGD

DJHQWH SHUFLEH GHO HQWRUQR HO Q~PHUR GH DJHQWHV TXH

H[LVWHQGHFDGDHVSHFLH



'HFLVLyQ

(Q IXQFLyQ GH ODV SHUFHSFLRQHV FDGD DJHQWH WRPD XQDV

GHFLVLRQHV (VWDV GHFLVLRQHV VH WRPDQ HQ IXQFLyQ GH ODV

SUREDELOLGDGHV GH VXV PiTXLQDV GH HVWDGRV LQWHUQD TXH

SXHGHWHQHURQRPHPRULD 3DUXQDNDQG%UXHFNQHU 

/D WRPD GH GHFLVLRQHV HV OD SDUWH FHQWUDO GH VX

FRPSRUWDPLHQWR



&DGDDJHQWHWLHQHDOPHQRVGRVPiTXLQDVGHHVWDGRVFRQ

SUREDELOLGDGHV GH WUDQVLFLyQ HQWUH ORV HVWDGRV /DV

PiTXLQDV GH HVWDGRV VRQ GHSHQGLHQWHV GHO Q~PHUR GH

DJHQWHV GH FDGD HVSHFLH \ GHO WLHPSR (VWDV GRV PiTXLQDV

GH HVWDGRV VRQ GHQRPLQDGDV µ9LYLU0RULU¶ \ µ5HSURGXFLU

$ERUWDU¶



3XHGHQ DxDGLUVH RWUDV PiTXLQDV GH HVWDGRV VLQ

HPEDUJRHOFDVRPiVVLPSOHTXHVHGHWDOODDFRQWLQXDFLyQ

HVFRQHVWDVGRVPiTXLQDVGHHVWDGRV

0iTXLQDGHHVWDGRVµ9LYLU0RULU¶

/D PiTXLQD GH HVWDGRV µ9LYLU0RULU¶ HVWi GHILQLGD SRU

GRVHVWDGRVµ9LYR¶\µ0XHUWR¶

6LXQDJHQWHSDVDDXQHVWDGRµ0XHUWR¶HVWHDJHQWHVH

HOLPLQD \ GHVDSDUHFH /D SUREDELOLGDG GH TXH XQ

DJHQWH GH OD HVSHFLH µL¶ SDVH DO HVWDGR µ0XHUWR¶ VH

UHSUHVHQWDSRUµ3LP¶

6L XQ DJHQWH HVWi HQ HO HVWDGR µ9LYR¶ H[LVWH \ SXHGH

GHVSOD]DUVHSRUHOHQWRUQR/DSUREDELOLGDGGHTXHXQ

DJHQWHGHODHVSHFLHµL¶SHUPDQH]FDHQHOHVWDGRµ9LYR¶

VHUHSUHVHQWDSRUµ3LY¶\VHFDOFXODFRPR









SDUD  

L Y L P

3 = − 3 L = Q

  



(Q OD ILJXUD  SXHGH YHUVH ORV GRV HVWDGRV \ ODV

SUREDELOLGDGHV GH WUDQVLFLyQ (O HVWDGR µ0XHUWR¶ HV XQ

HVWDGRDEVRUEHQWHGHOFXDOHODJHQWHQRSXHGHVDOLU



 )LJXUD0iTXLQDGHHVWDGRVµ9LYLU0RULU¶



0iTXLQDGHHVWDGRVµ5HSURGXFLU$ERUWDU¶

/D VHJXQGD PiTXLQD GH HVWDGRV µ5HSURGXFLU$ERUWDU¶

WLHQHGRVHVWDGRVµ5HSURGXFH¶\µ$ERUWR¶

• 8QDJHQWHSXHGHJHQHUDUDSDUWLUGHVtPLVPRXQQXHYR

DJHQWH D HVWH HVWDGR OR OODPDPRV µ5HSURGXFH¶ /D

SUREDELOLGDGGHTXHXQDJHQWHGHODHVSHFLHµL¶HVWpHQ

HOHVWDGRµ5HSURGXFH¶VHUHSUHVHQWDSRUµ3LU¶

• 6LXQDJHQWHQRJHQHUDRWURDJHQWHDSDUWLUGHVLPLVPR

HVWi HQ HO HVWDGR µ$ERUWR¶ /D SUREDELOLGDG GHTXH XQ

DJHQWH GH OD HVSHFLH µL¶ HVWp HQ HO HVWDGR µ$ERUWR¶ VH

UHSUHVHQWDSRUµ3LD¶\VHFDOFXODFRPR









SDUD  

L D L U

3 = − 3 L = Q

  

(4)

$FFLRQHV

/DV DFFLRQHV UHSUHVHQWDQ ODV GHFLVLRQHV TXH WRPD XQ

DJHQWH EDViQGRVH HQ HO HVWDGR HQ HO TXH VH HQFXHQWUD (O

FDVR PiV VLPSOH OR FRPSRQH XQ DJHQWH TXH UHDOL]D ODV

DFFLRQHV GH ODV PiTXLQDV GH HVWDGRV µ9LYLU0RULU¶ \

µ5HSURGXFLU$ERUWDU¶



 )LJXUD0iTXLQDGHHVWDGRVµ5HSURGXFLU$ERUWDU¶



6L XQ DJHQWH SHUPDQHFH HQ HO HVWDGR µ9LYR¶ GH OD

PiTXLQD GH HVWDGRV µ9LYLU0RULU¶ UHDOL]D OD DFFLyQ GH

GHVSOD]DUVHSRUHOHQWRUQR/RVDJHQWHVVHGHVSOD]DQSRUHO

HQWRUQR GHVFULELHQGR GLIHUHQWHV WUD\HFWRULDV HVSDFLDOHV $

FDGD HVSHFLH GH DJHQWH VH OH SXHGH DVLJQDU XQ WLSR GH

PRYLPLHQWR FDUDFWHUtVWLFR (O PRYLPLHQWR EURZQLDQR

GHVFULEH GH IRUPD UHDOLVWD ODV WUD\HFWRULDV GH HOHPHQWRV

ELROyJLFRVR ILVLROyJLFRV /HZLVDQG3XOq*XDQJODL

HWDO+RUQHHWDO 



6L XQ DJHQWH SDVD DO HVWDGR µ5HSURGXFH¶ JHQHUD D XQ

QXHYRDJHQWHGHODPLVPDHVSHFLHTXHVHSRVLFLRQDGHQWUR

GHOHQWRUQRHQXQDXELFDFLyQPX\FHUFDQDDODJHQWHTXHOR

KDFUHDGR



(QWRUQR

/DVHQWUDGDVTXHXQDJHQWHUHFLEHSURYLHQHQGHOHQWRUQR

\GHOPLVPRPRGRODVVDOLGDVTXHXQDJHQWHSURGXFHYDQDO

HQWRUQR



(O PRGHODGR GHO HQWRUQR SXHGH VHU UHSUHVHQWDGR

PHGLDQWHXQDPDOODGHFHOGDVHQODTXHHQFDGDFHOGDSXHGH

KDEHUXQDJHQWH8QDFHOGDHVXQD]RQDGHOLPLWDGDGHVGHOD

FXDOFDGDDJHQWHSXHGHSHUFLELUODVHQWUDGDVGHOHQWRUQR \

UHDOL]DUDFFLRQHV :H\QVHWDO:H\QVHWDO 

6HFRQVLGHUDTXHHQXQDPLVPDFHOGDQRSXHGHH[LVWLUPiV

GHXQDJHQWH



&RQH[LRQHV

/DLQWHUDFFLyQHQWUHORVDJHQWHVSULQFLSDOPHQWHVHSXHGH

GDU PHGLDQWH  PHFDQLVPRV (O SULPHUR GH HOORV HV OD

FRPXQLFDFLyQGLUHFWDHQWUHORVDJHQWHVORTXHSHUPLWHXQD

LQWHUDFFLyQGLUHFWDHQWUHHOORV(OVHJXQGRPHFDQLVPRHVD

WUDYpVGHOHQWRUQR(VWDWpFQLFDVHEDVDHQTXHORVDJHQWHV

SXHGDQ PRGLILFDU VX HQWRUQR \ TXH ORV GHPiV DJHQWHV

GHWHFWHQ HVD PRGLILFDFLyQ GiQGRVH DVt XQD LQWHUDFFLyQ

LQGLUHFWD



(QQXHVWURPRGHORVHKDFRQVLGHUDGRTXHODLQIRUPDFLyQ

QHFHVDULDSDUDODHYROXFLyQGHOVLVWHPDVHDQODVSREODFLRQHV

WRWDOHV GH FDGD WLSR GH DJHQWH R HVSHFLH TXH VH GDQ HQ HO

HQWRUQR



0RGHODGRGHOWLHPSR

(OWLHPSRVHPRGHODGHIRUPDGLVFUHWD\HYROXFLRQDFRQ

UHVSHFWRDXQLQFUHPHQWRGHWLHPSR(QHO60$WRGRVORV

DJHQWHV DFW~DQ H LQWHUDFW~DQ DO PLVPR WLHPSR FRQ UHVSHWR

DOSULQFLSLRGHFDXVDOLGDG )LDQ\RHWDO 



 352%$%,/,'$'(6'(75$16,&,Ï1

,QLFLDOPHQWH HV QHFHVDULR WUDQVIRUPDU XQD HFXDFLyQ

GLIHUHQFLDO FRQWLQXD HQ XQD HFXDFLyQ HQ GLIHUHQFLDV 3RU

VLPSOLFLGDGVHUHDOL]DODDSUR[LPDFLyQPHGLDQWHGLIHUHQFLDV

ILQLWDVSRUHOPpWRGRGH(XOHU



(Q OD HFXDFLyQ   VH SUHVHQWD XQD DSUR[LPDFLyQ SRU

GLIHUHQFLDV ILQLWDV GH XQ FRQMXQWR GH µQ¶ HFXDFLRQHV

GLIHUHQFLDOHV RUGLQDULDV TXH GHILQHQ FRUUHFWDPHQWH HO

FRPSRUWDPLHQWRGHXQVLVWHPDFXDOTXLHUD



(



    SDUD



)  

L L

L Q

[ G[

I [ [ [ W L Q

W GW

Δ ≈ = =

Δ



 



6RQSRVLEOHVRWUDVDSUR[LPDFLRQHVHQGLIHUHQFLDVILQLWDV

EDVDGDV HQ HVTXHPDV GH LQWHJUDFLyQ GH HFXDFLRQHV

GLIHUHQFLDOHV WDOHV FRPR 5XQJH.XWWD $ SHVDU GH HVWR

~OWLPR ORV DXWRUHV QR KDQ DSUHFLDGR GLIHUHQFLDV

VLJQLILFDWLYDV HQ ORV UHVXOWDGRV \ FRQFOXVLRQHV REWHQLGDV

FRQODVVLPXODFLRQHVGHORVPRGHORV('2\60$



3RURWURODGRSDUDHOFiOFXORGHODVSUREDELOLGDGHVGHODV

PiTXLQDV GH HVWDGRV GH FDGD DJHQWH HQ FDGD LWHUDFLyQ VH

XWLOL]DXQHVTXHPDGH0RQWH&DUOR



8QPRGHOREDVDGRHQXQHVTXHPDGH0RQWH&DUORHVXQ

PRGHORTXHVHEDVDHQXQJHQHUDGRUGHQ~PHURVDOHDWRULRV

FRQ XQD GHWHUPLQDGD GLVWULEXFLyQ SDUD UHDOL]DU XQD

SUHYLVLyQHVWLPDFLyQRDQiOLVLV )LVKPDQ 



(O JHQHUDGRU GH Q~PHURV DOHDWRULRV TXH VH XWLOL]D SDUD

VLPXODU HO 60$ SURSXHVWR SRU ORV DXWRUHV GHYXHOYH

Q~PHURV SVHXGR DOHDWRULRV FRQ XQD GLVWULEXFLyQ XQLIRUPH

Probabilidades de transición

(5)

HQ HO LQWHUYDOR > @ +DFLHQGR XVR GH HVWH JHQHUDGRU VH

ORJUD FUHDU ORV HYHQWRV FRQ ODV SUREDELOLGDGHV TXH

FRUUHVSRQGHQDFDGDDJHQWHHQXQLQVWDQWHGDGR



(Q ODV VHFFLRQHV VLJXLHQWHV VH DQDOL]D HO PRGHOR PXOWL

DJHQWH SURSXHVWR 3DUD FRQVWUXLU HO 60$ VH SDUWH GHO

VLVWHPDGH('2GHILQLGRHQODHFXDFLyQ  



3UREDELOLGDGHVVLµ¦L [«[QW ¶

6L µ¦L [« [Q W   ¶ QLQJ~Q DJHQWH VH UHSURGXFH HQ

HVH LQVWDQWH GH WLHPSR µW¶ 3RU WDQWR ORV ~QLFRV HYHQWRV

SRVLEOHV VRQ OD VXSHUYLYHQFLD R OD PXHUWH GH XQ DJHQWH

PHGLDQWHODPiTXLQDGHHVWDGRVµ9LYLU0RULU¶



/DV SUREDELOLGDGHV GH WUDQVLFLyQ GH OD PiTXLQD GH

HVWDGRV µ9LYLU0RULU¶ VRQ GHILQLGDV FRPR XQ SURFHVR

ELQRPLDO GDGR TXH ORV DJHQWHV SXHGHQ HVWDU HQ HO HVWDGR

µ9LYR¶ R SXHGHQ SDVDU DO HVWDGR DEVRUEHQWH µ0XHUWR¶ FRQ

XQDSUREDELOLGDGGDGD



( ) (

 

)

L

L L P 0L



L P [ 0L L

L

* 0 [ 3 3

0

§ ·

= ¨ ¸ ⋅ ⋅ −

© ¹

  

SDUD

L =   Q

GRQGH

µ0L¶HVHOQ~PHURGHDJHQWHVGHODHVSHFLHµL¶TXHPXHUHQ

HQHOVLJXLHQWHLQVWDQWHGHWLHPSR

µ[L¶HVHOQ~PHURWRWDOGHDJHQWHVGHODHVSHFLHµL¶HQXQ

LQVWDQWHGHWLHPSRµW¶

µ3LP¶ HV OD SUREDELOLGDG GH PXHUWH GH XQ DJHQWH GH OD

HVSHFLHµL¶HQHOVLJXLHQWHLQVWDQWHGHWLHPSR

µ* 0L ¶HVODSUREDELOLGDGGHTXHµ0L¶DJHQWHVPXHUDQHQ

HOVLJXLHQWHLQVWDQWHGHWLHPSR



(OYDORUPHGLRGHOQ~PHURGHDJHQWHVTXHPXHUHQHQHO

VLJXLHQWH LQVWDQWH GH WLHPSR VLJXH XQD GLVWULEXFLyQ

ELQRPLDO /D HVSHUDQ]D PDWHPiWLFD R YDORU HVSHUDGR µ0L¶

HV



( 0 ( )

L

= ⋅ [ 3

L L P

SDUD L =   Q

  



/D HVSHUDQ]D PDWHPiWLFD R YDORU HVSHUDGR GH µ0L¶ HV

LJXDODOYDORUPHGLRGHOQ~PHURGHDJHQWHVGHODHVSHFLHµL¶

TXH PXHUHQ HQWUH ORV LQVWDQWHV µW¶ \ µWǻW¶ \ D OD YH] HV

LJXDO DO YDORU DEVROXWR GHO GHFUHPHQWR GH OD YDULDEOH GH

HVWDGRµ[L¶GHODHFXDFLyQGLIHUHQFLDO(PSOHDQGR    \

 VHREWLHQH

 

( ) (



  



) 

SDUD  

L L P L L Q

[ 3 ( 0 I [ [ [ W W

L Q

⋅ = = ⋅ Δ

=

  



(PSOHDQGR  \GHVSHMDQGRµ3LP¶VHREWLHQH



(

 

)



  



SDUD  

L Q

L P

L

I [ [ [ W W

3 [

L Q

= ⋅Δ

=

  



(PSOHDQGR  \  VHFDOFXODHOYDORUGHµ3LY¶



(

 

)



   

 

SDUD  

L Q

L Y

L

I [ [ [ W W

3 [

L Q

= − Δ

=

   



(QODVHFXDFLRQHV  \  VHFXPSOHVLHPSUHTXHµ[L•

¶ SRUTXH ODV SUREDELOLGDGHVµ3LP¶ \ µ3LY¶ VH DSOLFDQ D ORV

DJHQWHV GH OD HVSHFLH µL¶ \ QR HV SRVLEOH XWLOL]DU HVWDV

SUREDELOLGDGHVVLQRH[LVWHDOPHQRVXQDJHQWHGHODHVSHFLH

µL¶DOTXHDVLJQiUVHODV



3UREDELOLGDGHVVLµ¦L [«[QW !¶

6L µ¦L [« [Q W  ! ¶ QLQJ~Q DJHQWH PXHUH HQ HVH

LQVWDQWH GH WLHPSR µW¶ 3RU WDQWR ORV ~QLFRV HYHQWRV

SRVLEOHV VRQ OD VXSHUYLYHQFLD R OD UHSURGXFFLyQ GH XQ

DJHQWH PHGLDQWH OD PiTXLQD GH HVWDGRV µ5HSURGXFLU

$ERUWDU¶



/DV SUREDELOLGDGHV GH WUDQVLFLyQ GH OD PiTXLQD GH

HVWDGRV µ5HSURGXFLU$ERUWDU¶ VRQ GHILQLGDV WDPELpQ FRPR

XQSURFHVRELQRPLDOSRUTXHORVDJHQWHVSXHGHQHVWDUHQHO

HVWDGR µ5HSURGXFH¶ R HQ HO HVWDGR µ$ERUWR¶ FRQ XQD

SUREDELOLGDGGHWUDQVLFLyQ



( ) ( )

L L U 5L



U [ 5L L

L

* 5 [ 3 3

5

§ ·

= ¨ ¸ ⋅ ⋅ −

© ¹

   

SDUD

L =   Q

GRQGH

µ5L¶HVHOQ~PHURGHDJHQWHVGHODHVSHFLHµL¶TXHQDFHQHQ

HOVLJXLHQWHLQVWDQWHGHWLHPSR

µ[L¶HVHOQ~PHURWRWDOGHDJHQWHVGHODHVSHFLHµL¶HQXQ

LQVWDQWHGHWLHPSRµW¶

µ3LU¶HVODSUREDELOLGDGGHTXHXQDJHQWHGHODHVSHFLHµL¶

PXHUDHQHOVLJXLHQWHLQVWDQWHGHWLHPSR

µ* 5L ¶ HV OD SUREDELOLGDG GH TXH µ5L¶ DJHQWHV VH

UHSURGX]FDQHQHVHLQVWDQWHGHWLHPSR



(O YDORU PHGLR GHO Q~PHUR GH DJHQWHV TXH QDFHQ HQ HO

VLJXLHQWH LQVWDQWH GH WLHPSR VLJXH XQD GLVWULEXFLyQ

ELQRPLDO/DHVSHUDQ]DPDWHPiWLFDRYDORUHVSHUDGRGHµ5L¶

HV



( )

L L L U

 SDUD  

( 5 = ⋅ [ 3 L = Q

  



(6)

/D HVSHUDQ]D PDWHPiWLFD R YDORU HVSHUDGR GH µ5L¶ HV

LJXDODOYDORUPHGLRGHOQ~PHURGHDJHQWHVGHODHVSHFLHµL¶

TXH HQWUH ORV LQVWDQWHV µW¶ \ µWǻW¶ \ D OD YH] HV LJXDO DO

LQFUHPHQWRGHODYDULDEOHLQGHSHQGLHQWHµ[L¶GHODHFXDFLyQ

GLIHUHQFLDO(PSOHDQGR    \  VHREWLHQH

 

(



  



) 

SDUD  

L L U L Q

[ 3 I [ [ [ W W

L Q

⋅ = ⋅ Δ

=

   



(PSOHDQGR  \GHVSHMDQGRµ3LU¶VHREWLHQH



(

 

)



  



SDUD  

L Q

L U

L

I [ [ [ W W

3 [

L Q

= ⋅Δ

=

   



(PSOHDQGR  \  VHFDOFXODHOYDORUGHµ3LD¶



(

 

)



   

 

SDUD  

L Q

L D

L

I [ [ [ W W

3 [

L Q

= − Δ

=

   



(QODVHFXDFLRQHV  \  VHFXPSOHVLHPSUHTXHµ[L

•¶SRUTXHODVSUREDELOLGDGHVµ3LU¶\µ3LD¶VHDSOLFDQDORV

DJHQWHV GH OD HVSHFLH µL¶ \ QR HV SRVLEOH XWLOL]DU HVWDV

SUREDELOLGDGHV VL QR H[LVWH DO PHQRV XQ DJHQWH µL¶ DO TXH

DVLJQiUVHODV



3UREDELOLGDGHVVLµ¦L [«[QW  ¶

6Lµ¦L [«[QW  ¶QRVHSURGXFHQLQJXQDGHIXQFLyQ

QL QDFLPLHQWR VyOR VH SURGXFH XQ PRYLPLHQWR GH ORV

DJHQWHVSRUHOHQWRUQR/DVSUREDELOLGDGHVGHWUDQVLFLyQGH

ODVPiTXLQDVGHHVWDGRVTXHGDQ

/DPiTXLQDGHHVWDGRVµ9LYLU0RULU¶TXHGDµ3LY ¶

\µ3LP ¶

/DPiTXLQDGHHVWDGRVµ5HSURGXFLU$ERUWDU¶TXHGD

µ3LU ¶\µ3LD ¶



2WUDRSFLyQFXDQGRµ¦L [«[QW  ¶HVLQWURGXFLUXQ

FRPSRUWDPLHQWR DOHDWRULR DVLJQDQGR GLVWULEXFLRQHV GH

SUREDELOLGDGDORVSDUiPHWURVµ3LP¶\µ3LU¶DMXVWiQGRVHDOD

UHDOLGDG GHO VLVWHPD PRGHODGR (O FiOFXOR GH µ3LY¶ \ µ3LD¶

VHUHDOL]DXVDQGRODVHFXDFLRQHV  \  UHVSHFWLYDPHQWH



 02'(/2'(/0&0(',$17(60$

6H KD XWLOL]DGR XQ VLVWHPD GH ('2 TXH PRGHOD OD

/HXFHPLD 0LHORLGH &UyQLFD /0&  SDUD VHU FRPSDUDGR

FRQ HO 60$ /D /0& HV XQ FiQFHU TXH DIHFWD D XQ

GHWHUPLQDGRWLSRGHFpOXODVHQHOVLVWHPDLQPXQH



(OPRGHORGH('2HOHJLGRFRQVLVWHHQSREODFLRQHVGH

FpOXODV ODV FpOXODV 7 QDLYH ODV FpOXODV 7 DFWLYDGDV

HVSHFtILFDPHQWHSDUDOD/0&\ODVFpOXODVFDQFHUtJHQDVGH

/0&(OPRGHORGH/0&XWLOL]DGRHQHOSUHVHQWHWUDEDMR

FRQVXVSDUiPHWURV\FRQGLFLRQHVLQLFLDOHVGHODV('2HVWi

GHVFULWR HQ SURIXQGLGDG HQ 0RRUH DQG /L   $

FRQWLQXDFLyQVHPXHVWUDHOVLVWHPDGH('2HOHJLGR



PD[



OQ

Q

Q Q Q Q Q

H

Q Q Q H H

H H H H

F F F H

G7 &

V G 7 N 7

GW &

G7 & &

N 7 7

GW & &

G 7 & 7

&

G&

U & G & & 7

GW &

η

α α

η η

γ

γ

­ § ·

= − ⋅ − ⋅

° ¨ © + ¸ ¹

° ° § · § ·

° = ⋅ ⋅ ⋅ ¨ + ¸ + ⋅ ⋅ ¨ + ¸

® © ¹ © ¹

° − ⋅ − ⋅ ⋅

° ° § ·

= ⋅ ⋅ − ⋅ − ⋅ ⋅

° ¨ ¸

© ¹

¯

  

6LHQGR

µW¶UHSUHVHQWDHOWLHPSRPHGLGRHQGtDV

µ7Q¶ UHSUHVHQWD HO Q~PHUR GH µFpOXODV 7 QDLYH¶ QDLYH 7

FHOOV SRUPLFUROLWUR ȝO 

µ7H¶ UHSUHVHQWD HO Q~PHUR GH µFpOXODV 7 DFWLYDGDV

HVSHFtILFDPHQWHSDUDOD/0&¶SRUȝO

µ&¶ UHSUHVHQWD HO Q~PHUR GH µFpOXODV FDQFHUtJHQDV GH

/0&¶SRUȝO

/RVSDUiPHWURVGHOPRGHORHVWiQHVSHFLILFDGRVHQODWDEOD



&iOFXORGHODVSUREDELOLGDGHVGHOPRGHOR60$

HTXLYDOHQWH

/DV SUREDELOLGDGHV GH WUDQVLFLyQ GH ODV PiTXLQDV GH

HVWDGRV µ5HSURGXFLU$ERUWDU¶ \ µ9LYLU0RULU¶ VRQ

FDOFXODGDVSDUDODVHVSHFLHVGHDJHQWHV



0iTXLQDGHHVWDGRVµ5HSURGXFLU$ERUWDU¶

/DV SUREDELOLGDGHV GH WUDQVLFLyQ GH OD PiTXLQD GH

HVWDGRVµ5HSURGXFLU$ERUWDU¶GHODHVSHFLHGHFpOXODV µ7Q¶

VRQ





 

Q Q Q Q Q

U Q H

Q

&

V G 7 N 7

&

3 7 7 & W

7

η

§ § · ·

− ⋅ − ⋅

¨ ¨ © + ¸ ¹ ¸

© ¹

= ⋅Δ

 



D

  

Q H U

 

Q H

3 7 7 & = − 3 7 7 &

  



/DV SUREDELOLGDGHV GH WUDQVLFLyQ GH OD PiTXLQD GH

HVWDGRV µ5HSURGXFLU$ERUWDU¶ GH OD HVSHFLH GH FpOXODV µ7H¶

VRQ

Modelo de LMC mediante SMA

(7)





 



U Q H Q Q Q

H

H H H H H H

W &

3 7 7 & N 7

7 &

&

7 G 7 & 7

&

α η

α γ

η

§ § ·

= Δ ⋅ ¨ © ⋅ ⋅ ⋅ ¨ © + ¸ ¹

§ · ·

+ ⋅ ⋅ ¨ © + ¸ ¹ − ⋅ − ⋅ ⋅ ¸ ¹



  



D

  

Q H U

 

Q H

3 7 7 & = − 3 7 7 &

  



/DV SUREDELOLGDGHV GH WUDQVLFLyQ GH OD PiTXLQD GH

HVWDGRV µ5HSURGXFLU$ERUWDU¶ GH OD HVSHFLH GH FpOXODV µ&¶

VRQ



PD[



OQ  

F F F

U Q H

&

U & G & & 7

&

3 7 7 & W

&

§ ⋅ ⋅ § ¨ · ¸ − ⋅ − ⋅ ⋅ γ ·

¨ © ¹ ¸

© ¹

= ⋅Δ

 



D

  

Q H U

 

Q H

3 7 7 & = − 3 7 7 &

  



0iTXLQDGHHVWDGRVµ9LYLU0RULU¶

/DV SUREDELOLGDGHV GH WUDQVLFLyQ GH OD PiTXLQD GH

HVWDGRVµ9LYLU0RULU¶GHODHVSHFLHGHFpOXODVµ7Q¶VRQ





 

Q Q Q Q Q

P Q H

Q

&

V G 7 N 7

&

3 7 7 & W

7

η

§ § · ·

− ⋅ − ⋅

¨ ¨ © + ¸ ¹ ¸

© ¹

= ⋅Δ

 



Y

  

Q H P

 

Q H

3 7 7 & = − 3 7 7 &

  



/DV SUREDELOLGDGHV GH WUDQVLFLyQ GH OD PiTXLQD GH

HVWDGRVµ9LYLU0RULU¶GHODHVSHFLHGHFpOXODVµ7H¶VRQ





 



P Q H Q Q Q

H

H H H H H

W &

3 7 7 & N 7

7 &

&

7 G 7 & 7

&

α η

α γ

η

§ § ·

= Δ ⋅ ¨ © ⋅ ⋅ ⋅ ¨ © + ¸ ¹

§ · ·

+ ⋅ ⋅ ¨ © + ¸ ¹ − ⋅ − ⋅ ⋅ ¸ ¹

  



Y

  

Q H P

 

Q H

3 7 7 & = − 3 7 7 &

  



/DV SUREDELOLGDGHV GH WUDQVLFLyQ GH OD PiTXLQD GH

HVWDGRVµ9LYLU0RULU¶GHODHVSHFLHGHFpOXODVµ&¶VRQ



PD[



OQ  

F F F

P Q H

&

U & G & & 7

&

3 7 7 & W

&

§ ⋅ ⋅ §¨ ·¸− ⋅ − ⋅ ⋅

γ

·

¨ © ¹ ¸

© ¹

= ⋅ Δ

 



Y

  

Q H P

 

Q H

3 7 7 & = − 3 7 7 &

  



6LPXODFLyQ

/D VLPXODFLyQ GHO VLVWHPD GH ('2 \ GHO 60$ HV

UHDOL]DGD FRQ ORV VLJXLHQWHV SDUiPHWURV SURSXHVWRV SRU

0RRUHDQG/L 



7DEOD



/RVYDORUHVSDUDORVSDUiPHWURVGHODVLPXODFLyQ

3DUiPHWUR 'HVFULSFLyQ 9DORU 8QLGDGHV

µVQ¶ )XHQWHGHµ7Q¶  μFHOXODVO GtDV⋅ 

µGQ¶ ËQGLFHGHPRUWDOLGDG

GHµ7Q¶  GtDV µGH¶ ËQGLFHGHPRUWDOLGDG

GHµ7H¶  GtDV µGF¶ ËQGLFHGHPRUWDOLGDG

GHµ&¶  GtDV µNQ¶ 'LIHUHQFLDFLyQGHµ7Q¶  GtDV

µȘ¶ 0LFKDHOLV0HQWHQ  FHOXODVO

μ 

µĮQ¶ 3UROLIHUDFLyQµ7H¶  

µĮH¶ 5HFOXWDPLHQWRµ7H¶  GtDV

µ&PD[¶ µ&¶Pi[LPR  FHOXODVμO 

µUF¶ &UHFLPLHQWRGH&  GtDV

µȖH¶ 3HUGLGDGHµ7H¶GHELGR

D& 

O FHOXODV GtDV

μ



µȖF¶ 3HUGLGDGH&GHELGRD

µ7H¶ 

O FHOXODV GtDV

μ





/DV VLJXLHQWHV FRQGLFLRQHV LQLFLDOHV VRQ XVDGDV SDUD OD

VLPXODFLyQGHORVGRVPRGHORV 60$\VLVWHPDGH('2V 

 QDLYHV

 Q FpOXODV 7

7 μO

• =



(8)

     

 H FpOXODV 7 DFWLYDGDV HVSHFLILFDPHQWH SDUD OD /0&

7 μO

• = 

  

 FpOXODV FDQFHUtJHQDV GH /0&

&

μO

• = 



(O PRYLPLHQWR EURZQLDQR VH HOLJH SDUD HO

GHVSOD]DPLHQWRGHORVDJHQWHVSRUHOHQWRUQRSRUTXHHVXQ

PRGHOR ELROyJLFR GH XQD SREODFLyQ GH FpOXODV TXH

LQWHUDFW~DQ GHQWUR GH XQ IOXLGR VDQJXtQHR (Q HVWD

DSOLFDFLyQ VL ELHQ VH KDQ LQWURGXFLGR DJHQWHV PyYLOHV QR

VH KD FRQWHPSODGR ORV YDORUHV TXH FDGD DJHQWH SXHGH

REWHQHUDQLYHOORFDO3RUWDQWRODVSUREDELOLGDGHVGHPXHUWH

R UHSURGXFFLyQ GH ODV FpOXODV GH OD PLVPD HVSHFLH HQ XQ

GHWHUPLQDGR LQVWDQWH YDQ D VHU ODV PLVPDV

LQGHSHQGLHQWHPHQWH GH OD SRVLFLyQ TXH RFXSHQ HQ HO

HQWRUQR



 )LJXUD&RPSDUDWLYDHQWUHHO60$\HOVLVWHPDGH('2HQ

ODHYROXFLyQGHODVµFpOXODV7QDLYH¶



(QODILJXUDSXHGHREVHUYDUVHTXHHOPRGHORGH('2\

60$VHFRPSRUWDQGHIRUPDVLPLODUDOPRGHODUHOQ~PHUR

GHµFpOXODV7QDLYH¶



$O PRGHODU HO Q~PHUR GH µFpOXODV 7 DFWLYDGDV

HVSHFtILFDPHQWH SDUD OD /0&¶ HO 60$ \ HO PRGHOR GH

('2 VH FRPSRUWDQ GH IRUPD GLVWLQWD FRPR SXHGH

REVHUYDUVH HQ OD ILJXUD  6H PXHVWUD TXH HO LQWHUYDOR GH

WLHPSR HQWUH  \  GtDV SRUTXH HV HO LQWHUYDOR PiV

VLJQLILFDWLYR



(OPRGHORGH('2QRGHILQHFRQFODULGDGHOLQVWDQWHHQ

HO TXH ODV µFpOXODV 7 DFWLYDGDV HVSHFtILFDPHQWH SDUD OD

/0&¶VHH[WLQJXHQSRUTXHHVWDVFpOXODVWLHQGHQDFHURSHUR

VLQOOHJDUDDOFDQ]DUORHQQLQJ~QPRPHQWR





0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0

2 4 6 8 10 12 14 16 18

Tiempo en días Número de células T activadas específicamente para la LMC.

Sistema de EDO SMA

)LJXUD&RPSDUDWLYDHQWUHHO60$\HOVLVWHPDGH('2HQ

ODHYROXFLyQGHODVµFpOXODV7DFWLYDGDVHVSHFtILFDPHQWH

SDUDOD/0&¶



0 10 20 30 40 50 60 70 80 90

9000 9100 9200 9300 9400 9500 9600 9700 9800 9900 10000

Tiempo en días

Número de células cancerígenas de LMC

SMA

Sistema de EDO

)LJXUD&RPSDUDWLYDHQWUHHO60$\HOVLVWHPDGH('2HQ

ODHYROXFLyQGHODVµFpOXODVFDQFHUtJHQDVGH/0&¶



(O 60$ GHILQH FODUDPHQWH HO LQVWDQWH HQ HO TXH ODV

µFpOXODV 7 DFWLYDGDV HVSHFtILFDPHQWH SDUD OD /0&¶ VH

H[WLQJXHQ (Q HVWD VLPXODFLyQ HO LQVWDQWH HQ HO TXH VH

H[WLQJXHQ HVWi HQ WRUQR D ORV  GtDV FRPR SXHGH

DSUHFLDUVHHQODILJXUD



$O PRGHODU HO Q~PHUR GH µFpOXODV FDQFHUtJHQDV GH

/0&¶ HO PRGHOR GH ('2 \ 60$ QR VH FRPSRUWDQ GH OD

PLVPD IRUPD DXQTXH ORV GRV PRGHORV WLHQGHQ KDFLD HO

PLVPR SXQWR GH HTXLOLEULR WDO \ FRPR VH REVHUYD HQ OD

ILJXUD



(9)

(O GLIHUHQWH FRPSRUWDPLHQWR GH ORV PRGHORV VH H[SOLFD

SRUTXHHQHO60$ODVµFpOXODV7DFWLYDGDVHVSHFtILFDPHQWH

SDUD OD /0&¶ VH H[WLQJXHQ FRPSOHWDPHQWH HQ HO LQVWDQWH

GtDVPLHQWUDVTXHHQHOPRGHORGH('2HOQ~PHURGH

µFpOXODV7DFWLYDGDVHVSHFtILFDPHQWHSDUDOD/0&¶DSDUWLU

GHHVHLQVWDQWHHVXQQ~PHURIUDFFLRQDULRPHQRUTXHXQR



 352%$%,/,'$''((;7,1&,Ï1

(V LQWHUHVDQWH SRGHU GHGXFLU XQ LQWHUYDOR GH WLHPSR

HQWUH HO LQVWDQWH LQLFLDO \ XQ LQVWDQWH GH WLHPSR µ=L¶ HQ HO

FXDOVHSURGX]FDODH[WLQFLyQGHXQDHVSHFLHµL¶GHDJHQWHV

yFpOXODVFRQXQDSUREDELOLGDGGDGD



(Q HO DSDUWDGR  VH H[SOLFD XQ PpWRGR SDUD SRGHU

LGHQWLILFDUHOLQVWDQWHGHWLHPSRµ=L¶DSDUWLUGHXQFRQMXQWR

GH VLPXODFLRQHV GHO PRGHOR 60$ (Q HO DSDUWDGR  VH

H[SOLFDFyPRVHSXHGHREWHQHUHOWLHPSRGHH[WLQFLyQ µ=L¶

FRQ XQD SUREDELOLGDG GDGD D SDUWLU GH XQD GLVWULEXFLyQ GH

:HLEXOO DMXVWDGD FRQ ORV GDWRV REWHQLGRV HQ ODV

VLPXODFLRQHV



&iOFXORGHODGLVWULEXFLyQGHOWLHPSRGHH[WLQFLyQ

3ULPHUR HQ FDGD XQD GH ODV µP¶ VLPXODFLRQHV GHO

SURFHVRVHUHFRJHHOSULPHULQVWDQWHGHWLHPSRHQHOFXDOHO

Q~PHUR GH DJHQWHV GH OD HVSHFLH µL¶ HV LJXDO D FHUR 6H

REWLHQH GH HVWD PDQHUD XQ YHFWRU GH WLHPSRV µ%L¶ DO

UHDOL]DUVHODVµP¶VLPXODFLRQHV

 %L =

{

E EL LEL P

}

SDUDL= Q  



6HJXQGRVHFRQVWUX\HXQKLVWRJUDPDFRQORVYDORUHVGHO

YHFWRUµ%L¶3DUDHOORSULPHURVHGLVFUHWL]DHOWLHPSRHQµT¶

LQWHUYDORVGHWDPDxRµ4L¶





PD[ PLQ 

SDUD  

L P L P

L L L

L L

% %

4 L Q

T

= =

==

= =   



7HUFHURVHFODVLILFDQORVYDORUHVGHOYHFWRUµ%L¶GHQWUR

GH ORV LQWHUYDORV GH WLHPSR GLVFUHWL]DGRV REWHQLHQGR HO

GLDJUDPDGHODILJXUD



&XDUWR VH DMXVWD XQD GLVWULEXFLyQ :HLEXOO FRQ HVWRV

WLHPSRV GH H[WLQFLyQ REWHQLGRV HQ ODV VLPXODFLRQHV

UHDOL]DGDVSDUDSRGHUGHWHUPLQDUHOWLHPSRGHH[WLQFLyQGH

HVWDV FpOXODV FRQ XQD SUREDELOLGDG GDGD \D TXH HVWD

H[WLQFLyQGHWHUPLQDFXiQGRVHDOFDQ]DODHWDSDDJXGDGHOD

HQIHUPHGDG



&iOFXORGHOWLHPSRGHH[WLQFLyQFRQXQDSUREDELOLGDG

GDGD



0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

0 5 10 15 20 25 30 35 40 45 50

Tiempo en días

Número de simulaciones

)LJXUD  'LDJUDPD GH IUHFXHQFLDV GH µFpOXODV 7 DFWLYDGDV

HVSHFtILFDPHQWHSDUDOD/0&¶TXHVHKDQH[WLQJXLGRHQ

FDGDLQVWDQWHGHWLHPSR



(QHVWHFDVRSUiFWLFRGH/0&VHXVDXQDGLVWULEXFLyQGH

SUREDELOLGDG GH :HLEXOO SDUD GHVFULELU HO WLHPSR GH

H[WLQFLyQGHODVµFpOXODV7DFWLYDGDVHVSHFtILFDPHQWHSDUD

OD/0&¶ 0LOWRQDQG$UQROG 



/DIXQFLyQGHGHQVLGDGGHSUREDELOLGDGGH:HLEXOOHV



( )



3DUD    Z ] α β ]β Hα]β

α β

− ⋅

= ⋅ ⋅ ⋅

> >

  

 /DGLVWULEXFLyQDFXPXODGDGH:HLEXOOHV



( )

 ( )



 3DUD   

] = ] =

]

: ] α β ]β Hα β H α β

α β

= − ⋅ − ⋅

=

= ⋅ ⋅ ⋅ = −

> >

³

  

6H UHDOL]D XQD DSUR[LPDFLyQ GHO KLVWRJUDPD GH

IUHFXHQFLDV DFXPXODGDV PHGLDQWH OD GLVWULEXFLyQ GH

SUREDELOLGDGGH:HLEXOO  3DUDHVWRVHXWLOL]DXQDMXVWH

SRUPtQLPRVFXDGUDGRV :X'HWDO 



/DSUREDELOLGDGµǜ į ¶GHTXHXQDHVSHFLHµL¶GH

DJHQWHVVHH[WLQJDDQWHVGHXQWLHPSRµ=L¶HVWiGDGDSRU

 3 ]

[

L=L

]

= −    δ

  Probabilidad de extinción

(10)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Tiempo en días

Probabilidad

Distribución acumulada de Weibull Aproximación por minimos cuadrados

 )LJXUD  )XQFLyQ GH IUHFXHQFLDV DFXPXODGDV \ IXQFLyQ GH

DSUR[LPDFLyQSRUPtQLPRVFXDGUDGRV



8QDGLVWULEXFLyQGHSUREDELOLGDGµZL ] ¶FXPSOHTXH

( )



=L

L L

Z ] G]

δ

−∞

− = ³ ⋅

 

 

&RPELQDQGR ODV HFXDFLRQHV   \   \ GHVSHMDQGR

µ=L¶VHREWLHQHODHFXDFLyQ  



( )

β

α δ



OQ »¼ º

«¬ ª−

=

=

L



  



&RQVLGHUDQGR XQD SUREDELOLGDG GH  \ VXVWLWX\HQGR

ORV YDORUHV GH µĮ  ¶ \ µȕ  ¶ FDOFXODGRV FRQ

PtQLPRV FXDGUDGRV  HO WLHPSR GH H[WLQFLyQ GH ODV FpOXODV

GHODHVSHFLHµL¶REWHQLGRVLJXLHQGRHOPpWRGRH[SXHVWRHV

GHµ¶GtDV(VWHYDORUFRPRVHSXHGHDSUHFLDUHV

FRKHUHQWHFRQHOKLVWRJUDPDGHODILJXUD





 &21&/86,21(6

(Q HVWH WUDEDMR VH PXHVWUD OD PHWRGRORJtD SDUD

WUDQVIRUPDUXQVLVWHPDGH('2HQXQ60$HTXLYDOHQWH\

ODV YHQWDMDV GH PRGHODU VLVWHPDV ELROyJLFRV FRQ XQ VLVWHPD

EDVDGR HQ DJHQWHV /D SULPHUD YHQWDMD FRQVLVWH HQ TXH HO

PRGHOR 60$ FRQ XQ PLVPR HVWDGR LQLFLDO \ XQRV

SDUiPHWURV LGpQWLFRVQRSURSRUFLRQDHQFDGDUHDOL]DFLyQy

VLPXODFLyQ OD PLVPD VROXFLyQ (VWH FRPSRUWDPLHQWR

DOHDWRULRSHUPLWHFRPSUHQGHUPHMRUFyPRHVSRVLEOHTXHHQ

VLWXDFLRQHVHTXLYDOHQWHVHOFRPSRUWDPLHQWRGHXQSDFLHQWH

GLILHUDIXHUWHPHQWHGHODGHRWUR(QORVPRGHORV('2OD

VROXFLyQTXH VHREWLHQHDQWH XQ PLVPRHVWDGRLQLFLDO \XQ

PLVPR FRQMXQWR GH YDORUHV SDUD ORV SDUiPHWURV HV ~QLFD

(VWR KDFH TXH XQD VLWXDFLyQ FRQFUHWD VRODPHQWH SXHGD

GHVDUUROODUVHGHXQ~QLFRPRGR(VSRVLEOHTXHXQPRGHOR

('2 SUHVHQWH FRPSRUWDPLHQWRV PX\ GLIHUHQWHV FRQ

FRQGLFLRQHVLQLFLDOHVPX\VLPXODUHVTXHSHUPLWDQH[SOLFDU

SRU TXH SDFLHQWHV FRQ VLWXDFLRQHV HTXLYDOHQWHV WLHQHQ XQ

GHVDUUROORGHODHQIHUPHGDGGLIHUHQWH(VWDVFDUDFWHUtVWLFDV

VRQ SURSLDV GH VLVWHPDV FDyWLFRV R GH HFXDFLRQHV FRQ

VHQVLELOLGDG D ODV FRQGLFLRQHV LQLFLDOHV SHUR HO PRGHOR

WUDWDGRQRSUHVHQWDGLFKDVFDUDFWHUtVWLFDV



/D VHJXQGD YHQWDMD VHJ~Q VH PXHVWUD HQ HVWH WUDEDMR

FRQVLVWH HQ TXH HO 60$ PRGHOD SREODFLRQHV R

HQIHUPHGDGHVHSLGHPLROyJLFDVGHXQPRGRPiVUHDOLVWD\D

TXHFDGDYDULDEOHGHOVLVWHPDGH('2HTXLYDOHDO Q~PHUR

HQWHUR GH DJHQWHV GH HVD HVSHFLH 'H HVWD IRUPD HO 60$

PRGHOD ODV YDULDEOHV GH XQ PRGR GLVFUHWR \ GHQWUR GHO

UDQJR GH ORV Q~PHURV SRVLWLYRV (VWD FXHVWLyQ TXH SXHGH

SDUHFHU D SULPHUD YLVWD LUUHOHYDQWH VH PXHVWUD

HVSHFLDOPHQWH LPSRUWDQWH FXDQGR VH GHVHD GHWHUPLQDU OD

H[WLQFLyQ GH FLHUWDV SREODFLRQHV GH DJHQWHV R FpOXODV TXH

KDFHQTXHVHGHVHQFDGHQHQXQDVHULHGHSDWRORJtDVFRPRHV

HOFDVRGHOD/0&



/D WHUFHUD YHQWDMD FRQVLVWH HQ TXH D SHVDU GH TXH HO

SUREOHPDSURSXHVWRQRVHKDFRQWHPSODGRODLQIOXHQFLDGH

ODGLVWULEXFLyQHVSDFLDOGHORVDJHQWHVSRUVLPSOLFLGDGHQOD

H[SRVLFLyQ GHO PRGHOR UHVXOWD VHQFLOOR JHQHUDOL]DU HO

PRGHORSDUDTXHFRQWHPSOHHO PRYLPLHQWRGHORVDJHQWHV

(Q QXHVWUR FDVR HO 60$ PRGHOD SRU PHGLR GH XQD OH\

HVWRFiVWLFD R GLVWULEXFLyQ HVWDGtVWLFD ORV FDPELRV TXH VH

GDQHQODVSREODFLRQHVGHELGRDHVWDVLQWHUDFFLRQHVTXHVH

GDQHQWUHODVFpOXODVRSREODFLRQHVGHDJHQWHV



&RPRFXDUWDYHQWDMDFRQVLVWHHQTXHHVSRVLEOHHVWLPDU

OD SUREDELOLGDG GH FDGD SRVLEOH VROXFLyQ \ GDU OD

SUREDELOLGDG GH XQ HYHQWR FRQFUHWR \D TXH VH GLVSRQH GH

ODV SUREDELOLGDGHV GH WUDQVLFLyQ HQ FDGD LQVWDQWH (VWD

SURSLHGDG HV HVSHFLDOPHQWH LPSRUWDQWH FXDQGR VH TXLHUH

FRQRFHU OD SUREDELOLGDG GH HOLPLQDFLyQ FRPSOHWD GH ODV

FpOXODVGHXQWXPRUHQFRQFUHWRHQWUDWDPLHQWRVGHFiQFHU

(Q HO PRGHOR SODQWHDGR VH PXHVWUD FyPR HV SRVLEOH

SODQWHDU GH IRUPD QDWXUDO OD H[WLQFLyQ GH XQD GHWHUPLQDGD

SREODFLyQ GH DJHQWHV OR TXH SHUPLWH GHILQLU HQ WpUPLQRV

HVWDGtVWLFRV HO GHVDUUROOR GH XQD SDWRORJtD R GH VX SRVLEOH

FXUDFLyQ





(QJOLVK6XPPDU\

60$EDVHG VLPXODWLRQ RI V\VWHPV RULJLQDOO\

UHSUHVHQWHGZLWK('2



 Conclusiones

(11)

$EVWUDFW



,Q WKH SUHVHQW ZRUN D PHWKRGRORJ\ LV H[SRVHG WR PRGHO

XVLQJ D 0XOWL$JHQW 6\VWHP 0$6  ELRORJLFDO DQG

SK\VLRORJLFDO G\QDPLF V\VWHPV ZLWK GLVFUHWH TXDQWLILHG

YDULDEOHV VXFK DV JURZWK DQG GHFUHDVH RI SRSXODWLRQV RU

HSLGHPLRORJLFDOPRGHOOLQJRIGLVHDVH,WLVVKRZQDSURFHGXUH

WRWUDQVIRUPD2UGLQDU\'LIIHUHQWLDO(TXDWLRQVV\VWHP 2'(  WKDWPRGHOVWKHHQYLURQPHQWFRUUHFWO\ RQDQHTXLYDOHQW0$6

XVLQJ D VFKHPD EDVHG RQ 0RQWH &DUOR PHWKRG $ SUDFWLFDO

FDVH EDVHG RQ D PDWKHPDWLFDO PRGHO RI &KURQLF 0\HORLG

/HXNDHPLD &0/ LVXVHGWRFRPSDUHWKHPHWKRGRORJ\EDVHG

RQDJHQWVZLWKWKHWUDGLWLRQDOPRGHOEDVHGRQDQ2'(V\VWHP

$VLPXODWLRQIRUHDFKPRGHO 0$6DQG2'( LVH[HFXWHGDQG

WKHUHVXOWVREWDLQHGZLWKERWKPHWKRGRORJLHVDUHFRPSDUHG



.H\ZRUGV



'LIIHUHQWLDOHTXDWLRQ$JHQWEDVHGPRGHO0RQWH&DUOR



 5()(5(1&,$6

$JDUZDO5325HJDQ'([LVWHQFHDQG8QLTXHQHVVRI6ROXWLRQV

RI 6\VWHPV $Q LQWURGXFWLRQ WR RUGLQDU\ GLIIHUHQWLDO HTXDWLRQV

6SULQJHU1HZ<RUNSS

%DQHUMHH 6 0RVHV 0  $ +\EULG $JHQW %DVHG DQG 'LIIHUHQWLDO

(TXDWLRQ0RGHORI%RG\6L]H(IIHFWVRQ3DWKRJHQ5HSOLFDWLRQDQG

,PPXQH 6\VWHP 5HVSRQVH /HFWXUH 1RWHV LQ &RPSXWHU 6FLHQFH

SS

%DVVH % 8EH]LR 3  $ *HQHUDOLVHG $JH DQG 3KDVH6WUXFWXUHG

0RGHO RI +XPDQ 7XPRXU &HOO 3RSXODWLRQV %RWK 8QSHUWXUEHG DQG

([SRVHGWRD5DQJHRI&DQFHU7KHUDSLHV%XOOHWLQRI0DWKHPDWLFDO

%LRORJ\SS

%HQMDPLQ5-HDQ)UDQFRLV*)UDQFRLV%0XOWLDJHQWV\VWHPVLQ

HSLGHPLRORJ\DILUVWVWHSIRUFRPSXWDWLRQDOELRORJ\LQWKHVWXG\RI

YHFWRUERUQH GLVHDVH WUDQVPLVVLRQ %0& %,2,1)250$7,&6

  

%UDXHU ) &KDYH] & &  0DWKHPDWLFDO 0RGHOV LQ 3RSXODWLRQ

%LRORJ\DQG(SLGHPLRORJ\6SULQJHU9HUODJ

%XQLPRYLFK0HQGUD]LWVN\ 6 %\UQH + 6WRQH /  0DWKHPDWLFDO

0RGHO RI 3XOVHG ,PPXQRWKHUDS\ IRU 6XSHUILFLDO %ODGGHU &DQFHU

%XOOHWLQRI0DWKHPDWLFDO%LRORJ\SS

)HUEHU -  0XOWL$JHQW 6\VWHPV $Q ,QWURGXFWLRQ WR 'LVWULEXWHG

$UWLILFLDO,QWHOOLJHQFH$GGLVRQ:HVOH\3URIHVVLRQDO

)LDQ\R ( 7UHXLO -3 3HUULHU ( DQG 'HPD]HDX <  0XOWLDJHQW

$UFKLWHFWXUH ,QWHJUDWLQJ +HWHURJHQHRXV 0RGHOV RI '\QDPLFDO

3URFHVVHV7KH5HSUHVHQWDWLRQRI7LPH/HFWXUH1RWHVLQ&RPSXWHU

6FLHQFHSS

)LVKPDQ * 0RQWH &DUOR &RQFHSWVDOJRULWKPV DQGDSSOLFDWLRQV

6SULQJHU9HUODJ

*XDQJODL//LFN.RQJ7-D\;7$PSOLILHGHIIHFWRI%URZQLDQ

PRWLRQ LQ EDFWHULDO QHDUVXUIDFH VZLPPLQJ 3URFHHGLQJV RI WKH

1DWLRQDO $FDGHP\ RI 6FLHQFHV RI WKH 8QLWHG 6WDWHV RI $PHULFD

  SS

*XR = < 6ORRW 3 0 $ DQG 7D\ - &  $ K\EULG DJHQWEDVHG

DSSURDFK IRU PRGHOLQJ PLFURELRORJLFDO V\VWHPV -RXUQDO RI

7KHRUHWLFDO%LRORJ\  SS















+RUQH - 6 *DUWRQ ( 2 .URQH 6 0 /HZLV - 6  $QDO\]LQJ

DQLPDO PRYHPHQWV XVLQJ %URZQLDQ EULGJHV 3URFHHGLQJV RI WKH

1DWLRQDO$FDGHP\RI6FLHQFHVRIWKH8QLWHG6WDWHVRI$PHULFD

SS

/HZLV - 7 3XOq - 9  '\QDPLFDO WKHRULHV RI %URZQLDQ PRWLRQ

/HFWXUH1RWHVLQ3K\VLFV6SULQJHU%HUOLQ+HLGHOEHUJSS



0LOWRQ-6$UQROG-&'LVWULEXFLRQHVFRQWLQXDV3UREDELOLGDG\

(VWDGtVWLFD FRQ DSOLFDFLRQHV SDUD LQJHQLHUtD \ FLHQFLDV

FRPSXWDFLRQDOHV0FJUDZ+LOOSS

0RRUH + /L 1 .  $ PDWKHPDWLFDO PRGHO IRU FKURQLF

P\HORJHQRXV OHXNHPLD &0/  DQG 7 FHOO LQWHUDFWLRQ -RXUQDO RI

7KHRUHWLFDO%LRORJ\SS

0XUUD\ - ' D 0RGHOV IRU ,QWHUDFWLQJ 3RSXODWLRQV 0DWKHPDWLFDO

ELRORJ\6SULQJHU1HZ<RUNSS

0XUUD\-'E'\QDPLFVRI,QIHFWLRXV'LVHDVHV(SLGHPLF0RGHOV

DQG$,'60DWKHPDWLFDOELRORJ\6SULQJHU1HZ<RUNSS



1DJ\ - '   &RPSHWLWLRQ DQG QDWXUDO VHOHFWLRQ LQ D PDWKHPDWLFDO

PRGHORIFDQFHU%XOOHWLQRI0DWKHPDWLFDO%LRORJ\SS

‘NVHQGDO%  6WRFKDVWLFGLIIHUHQWLDOHTXDWLRQVDQLQWURGXFWLRQZLWK

DSSOLFDWLRQV6SULQJHU9HUODJ+HLGHOEHUJ1HZ<RUN

3DUXQDN + 9 ' %UXHFNQHU 6 $  3RO\DJHQWV 6LPXODWLRQ IRU

6XSSRUWLQJ $JHQWV 'HFLVLRQ 0DNLQJ 0XOWL$JHQW 6\VWHPV

6LPXODWLRQDQG$SSOLFDWLRQV&5&3UHVVSS

3DYyQ0RUiQ9+HUQiQGH]5DPtUH]30DUWtQH]$QWXxD*$JUDPRQWH

/ODQHV2-DLPH)DJXQGR-&%UDYR5HJXHLUR-/HXFHPLD

PLHORLGH FUyQLFD $FWXDOL]DFLyQ HQ &LWRJHQpWLFD \ %LRORJtD

0ROHFXODU 5HYLVWD &XEDQD GH +HPDWRORJtD ,QPXQRORJtD \

+HPRWHUDSLD  

5HGRX 3 .HUGHOR 6 /H * & 4XHUUHF * 5RGLQ 9 $EJUDOO -)

7LVVHDX-5HDFWLRQDJHQWV)LUVWPDWKHPDWLFDOYDOLGDWLRQRID

PXOWLDJHQW V\VWHP IRU G\QDPLFDO ELRFKHPLFDO NLQHWLFV /HFWXUH

1RWHVLQ&RPSXWHU6FLHQFH6SULQJHU%HUOLQ+HLGHOEHUJSS



6KRQNZLOHU 5 : +HURG -  0DWKHPDWLFDO %LRORJ\ $Q

,QWURGXFWLRQZLWK0DSOHDQG0DWODE6SULQJHU9HUODJ

6SHQFHU6/%HUU\PDQ0-*DUFtD-$$EERWW'$QRUGLQDU\

GLIIHUHQWLDO HTXDWLRQ PRGHO IRU WKH PXOWLVWHS WUDQVIRUPDWLRQ WR

FDQFHU-RXUQDORI7KHRUHWLFDO%LRORJ\SS

6]\PDĔVND = 8UEDĔVNL - 0DUFLQLDN&]RFKUD $  0DWKHPDWLFDO

PRGHOOLQJRIWKHLQIOXHQFHRIKHDWVKRFNSURWHLQVRQFDQFHULQYDVLRQ

RIWLVVXH-RXUQDORI0DWKHPDWLFDO%LRORJ\SS

9DQ 'HQ %HUJ +  0DWKHPDWLFDO %LRORJ\ RI ELRORJLFDO V\VWHPV

2[IRUG8QLYHUVLW\3UHVV

:H\QV ' 6FKHOIWKRXW . +ROYRHW 7  ([SORLWLQJ D 9LUWXDO

(QYLURQPHQWLQD5HDO:RUOG$SSOLFDWLRQ/HFWXUHQRWHVLQDUWLILFLDO

LQWHOOLJHQFHSS

:H\QV ' 3DUXQDN +9 0LFKHO ) +ROYRHW 7 )HUEHU - ' 

(QYLURQPHQWVIRU0XOWLDJHQW6\VWHPV6WDWHRIWKH$UWDQG5HVHDUFK

&KDOOHQJHV/HFWXUH1RWHVLQ&RPSXWHU6FLHQFHSS

:RGDU] ' .RPDURYD 1 /  0DWKHPDWLFDO PRGHOLQJ RI

WXPRULJHQHVLV  &RPSXWDWLRQDO %LRORJ\ 2I &DQFHU /HFWXUH 1RWHV

$QG0DWKHPDWLFDO0RGHOLQJ:RUOG6FLHQWLILF3XEOLVKLQJ&RPSDQ\

SS

:RROGULGJH0-,QWURGXFWLRQWR0XOWL$JHQW6\VWHPV-RKQ:LOH\

6RQV

:X'=KRX-/L<8QELDVHGHVWLPDWLRQRI:HLEXOOSDUDPHWHUV

ZLWKWKHOLQHDUUHJUHVVLRQPHWKRG-RXUQDORIWKH(XURSHDQ&HUDPLF

6RFLHW\SS



Referencias

Referencias

Documento similar

Por lo tanto, en base a su perfil de eficacia y seguridad, ofatumumab debe considerarse una alternativa de tratamiento para pacientes con EMRR o EMSP con enfermedad activa

The part I assessment is coordinated involving all MSCs and led by the RMS who prepares a draft assessment report, sends the request for information (RFI) with considerations,

El fenómeno del cuidado, emerge como necesidad la simbiosis entre el proceso de enfermería y su transcendencia en la investigación científica a través de la enfermería basada

En esta secci´on se lleva acabo la sincornizaci´on de la posici´on del eje de un servo motor en dos partes en la primer parte el motor es sincronizado con el oscilador propuesto 1 y

Little drawback of the proposed method is rather more time that is necessary to design a simulation model at initial stage of the manufacturing system

El capítulo 4, presenta el análisis realizado para la descripción del sistema para una cuerda vibrante, este análisis es presentado desde dos ópticas, una que representa el

Se presenta la simulación numérica de la descomposición espinodal de dos sistemas de aleación binarios Fe-Cr y Cu-Ni, basada en la solución de las ecuación diferencial de

La metodolog´ıa utilizada para estudiar el impacto de la re- configuraci´on de un sistema distribuido en tiempo real por medio de agentes consisti´o en tipificar un falla en