Acerca de la introducción en Colombia de la figura del autor detrás de

Transversal Lyapunov exponents for the stability of synchronization correspond to eigen- vectors transversal to the synchronization subspace M. When all N − 1 transversal Lyapunov exponents are negative, an initial synchronization error converges to zero, yielding stable synchro- nization. The largest transversal Lyapunov exponentλ⊥shown in Figs. 3.3 and 3.8 was calculated from simulated time-series data of the variational equations (3.3) via the orbit separation algorithm [64] and the standard fourth-order explicit Runge-Kutta method of numerical integration.

3.10.3 MATLAB codes % phaseifferencePlotter m-file load onePeriodSherman; vv = onePeriodShermanSys; tt = onePeriodShermanTime; periodTime = tt(end);

69 maxIndex =length(tt); stepSize = 200; grid =1:stepSize:maxIndex; numberPoints =length(grid); disp(numberPoints); phaseDiff=zeros(1,numberPoints); v0=vv(1,:); g_in=0.0; eps =0.01; options=odeset(’AbsTol’,[1e-8,1e-10,1e-10,1e-8,1e-10,1e-10],... ’RelTol’,1e-10); options2=odeset(’AbsTol’,[1e-8,1e-10,1e-10,1e-8,1e-10,1e-10],... ’RelTol’,1e-10,’Events’,@crossUpEvent); parfor ii=1:numberPoints; disp(ii); v1=vv(grid(ii),:); vv0=[v0,v1]; [˜,v] = ode15s(@shermanCoupled,[0:0.01:4000],vv0,... options,g_in,eps); vv0=v(end,:); [t,v,te,ve,ie] = ode15s(@shermanCoupled,[0:0.1:100000],... vv0,options2,g_in,eps);

times1=te(ie==1); %jump ups for the 1-st cell times2=te(ie==2); %jump ups for the 2-nd cell if times1(end)>times2(end)

(times1(end)-times1(end-1)); else phaseDiff(ii)=(times1(end)-times2(end-1))/... (times1(end)-times1(end-1)); end disp(phaseDiff(ii)) end plot(grid/maxIndex,phaseDiff,’.’) saveas(gcf,’Bprc_morePoints.fig’)

71 % shermanPhase-a-la_Sajia close all clear all clc tic load onePeriodSherman; vv = onePeriodShermanSys; tt = onePeriodShermanTime; periodTime = tt(end); maxIndex =length(tt); stepSize = 200; grid =1:stepSize:maxIndex; numberPoints =length(grid); disp(numberPoints); g_in=0.01; eps =0.01; upLine=zeros(1,numberPoints); downLine=upLine; options=odeset(’AbsTol’,[1e-8,1e-10,1e-10,1e-8,1e-10,1e-10],... ’RelTol’,1e-10,’Events’,@crossUpEvent); k=0; d=1000; parfor k=1:numberPoints; disp(k); ii=grid(k);

v0=vv(ii,:); vUp=v0; vDown=v0; diff1=0; diff2=0; jj=ii;

while diff1<0.01 && abs(ii-jj)<22900; jj=jj+d;

v1=vv(mod(maxIndex+jj,maxIndex)+1,:); vUp=[v0,v1];

[t,v,te,ve,ie] = ode15s(@shermanCoupled,[0:0.1:100000],... vUp,options,g_in,eps);

times1=te(ie==1); %jump ups for the 1-st cell times2=te(ie==2); %jump ups for the 2-nd cell

diff1=min(abs([times2(end)-times1(end),times2(end)-... times1(end-1),times2(end-1)-times1(end),times2(end-1)... -times1(end-1)])/(times1(end)-times1(end-1)));

if diff1<0.01; upLine(k)=upLine(k)+d; end; end

jj=ii;

while diff2<0.01 && abs(ii-jj)<22900; jj=jj-d;

v2=vv(mod(maxIndex-jj,maxIndex)+1,:); vDown=[v0,v2];

[t,v,te,ve,ie] = ode15s(@shermanCoupled,[0:0.1:100000],... vDown,options,g_in,eps);

times1=te(ie==1); %jump ups for the 1-st cell times2=te(ie==2); %jump ups for the 2-nd cell

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diff2=min(abs([times2(end)-times1(end),times2(end)... -times1(end-1),times2(end-1)-times1(end),times2(end-1)... -times1(end-1)])/(times1(end)-times1(end-1)));

if diff2<0.01; downLine(k)=downLine(k)-d; end; end end figure(1) title(’First Approximation g=%’) plot(tt(grid)/periodTime,upLine/10/periodTime,’b’,tt(grid)/... periodTime,downLine/10/periodTime,’b’); toc

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