Problems with ODE system using ode45

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Dennis 2019-11-13

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编辑： Dennis 2019-11-13

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I would like to solve (and then plot the solution of) the Ordinary Differential Equation system

with initial conditions

Note that one needs to choose

in order to make sense of the equations for

. My first attempt is to choose them constantly such that

I tried to implement this system in Matlab.

First, I wrote the function myODE for the right hand side of the system; then I tried to used ode45. The code can be seen below.

Unfortunately, there seems to be a mistake because the plot only shows the initial conditions and, moreover, the time range is from -1 to 1 (see the following image) which is not what I would like to plot.

Where is the mistake in my code?

Can you help me, please?

function dxdt = myODE(t,x,lambda,mu,y0,y4) % 
% y0 = leftmost outer neighbour (constant)
% y4 = rightmost outer neighbour (constant)
dxdt = [exp(lambda*(x(2)-x(1)))+exp(mu*(x(1)-y0)); ...
exp(lambda*(x(3)-x(2)))+exp(mu*(x(2)-x(1))); ...
exp(lambda*(y4-x(3))+exp(x(3)-x(2)))];
%%%%% Next: Try to use ode45:
%%% arbitrary choice of lambda, mu, y0 and y4 just for testing the code
 lambda=1;
 mu=1;
 y0=0;
 y4=50; 
 % initial conditions: y_1=5, y_2=10, y_3=15
 % consider 100 time steps
[t,X] = ode45(@(t,x) myODE(t,x,lambda,mu,y0,y4),[0 100], [5; 10; 15]);
% plot x_1=X(1), x(2)=X(2), x(3)=X(3) against t
 
plot(t,X(:,1),'-o',t,X(:,2),'-o',t,X(:,3),'-o')
xlabel('Time t');
ylabel('Solution x');
legend('x_1','x_2','x_3')