ODE solver: how to integrate a system with a vector of parameters?

Question

Uladzislau 2020-1-24

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链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/501780-ode-solver-how-to-integrate-a-system-with-a-vector-of-parameters

评论： Uladzislau 2020-1-24

Hello! I would like to ask how can I solve the system below for V varying from 1 to 1.2 with step 0.001? My aim is to plot bifurcation diagramm.

function [out] = chuaSmoothIris(~,in,alpha, beta, A, C, V)
x = in(1);
y = in(2);
z = in(3);
    xdot  = alpha*y - A*alpha*x^3 - C*alpha*x - V*alpha*x;
    ydot  = x - y + z;
    zdot  = -beta*y;
out = [xdot ydot zdot]';
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
t = [0 400];
y = [0.004 0 0];
alpha = 15.6;
beta   = 28; 
A      = 0.002;
C      = -1.3;
V = 1:0.001:1.2;
   [t,y] = ode45(@(t, y) chuaSmoothIris(t, y, alpha', beta', A', C', V'), t, y ); 

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Answer 1

J. Alex Lee 2020-1-24

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/501780-ode-solver-how-to-integrate-a-system-with-a-vector-of-parameters#answer_411799

Are you just looking for solving the ODE as many times as you have different values of V?

t = [0 400];
y = [0.004 0 0];
alpha = 15.6;
beta   = 28; 
A      = 0.002;
C      = -1.3;
V = 1:0.001:1.2;
for i = 1:length(V)
    [t,y] = ode45(@(t, y) chuaSmoothIris(t, y, alpha', beta', A', C', V(i)), t, y ); 
end

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J. Alex Lee 2020-1-24

Oops. It's because you are overwriting the variable y.

t = [0 400];
y0 = [0.004 0 0]; % give this a special name
alpha = 15.6;
beta   = 28; 
A      = 0.002;
C      = -1.3;
V = 1:0.001:1.2;
for i = 1:length(V)
    [t,y] = ode45(@(t, y) chuaSmoothIris(t, y, alpha', beta', A', C', V(i)), t, y0 ); 
end