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bifurcation.m (1897, 2017-10-30)

# Bifurcation Bifurcation diagram calcullation for ODE-system. ### Input parameters: x_label - the paramter of the x label rhs_ext_fcn - handle of function with right hand side of extended ODE-system. This function must include RHS of ODE-system coupled with variational equation (n items of linearized systems, see Example). fcn_integrator - handle of ODE integrator function, for example: @ode45 tstart - start values of independent value (time t) stept - step on t-variable for Gram-Schmidt renormalization procedure. tend - finish value of time ystart - start point of trajectory of ODE system. y_dest - intercept quadrant cut_start - remove the previous transient state ### Output parameters: X - x label Y - the ordinate of the bifurcation diagram --- ## main bifur phase: clc;clear all;close all; tic; W1 = []; W2 = []; W3 = []; W4 = []; d =-1:0.01:1; N = length(d); matlabpool local 4 parfor i = 1:N % for i = 1:N fprintf('i = %d\n',i); [x,y]= bifurcation(d(i),@(t,y)JM1(t,y),@ode23,0,1e-2,1000,[1 0 0 d(i)],3,5000); W1 = [W1;x]; W2 = [W2;y]; [x,y]= bifurcation(d(i),@(t,y)JM1(t,y),@ode23,0,1e-2,1000,[-1 0 0 d(i)],3,5000); W3 = [W3;x]; W4 = [W4;y]; end save bifur matlabpool close toc; figure(1); plot(W1,W2,'b.','markersize',0.5); hold on plot(W3,W4,'r.','markersize',0.5); ## JM1 function dy=JM1(t,y) dy=zeros(3,1); a=0.6;c=2;a1=1;b1=0.1;b=1.3; dy(1)=abs(y(2))-b; dy(2)=(a1-b1*abs(y(4)))*y(3); dy(3)=abs(y(1))-y(2)-a*y(3)-c; dy(4)=y(3);

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