How to vary a variable in a system of ODE's?

Question

Danny Helwegen 2021-3-6

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/764831-how-to-vary-a-variable-in-a-system-of-ode-s

评论： Star Strider 2021-3-6

Hello everybody,

I want to make a plot where I from where I can find and show the best value for a parameter. In order to do this I have to vary a variable in my system of ODE's (here a simplified example from the Matlab site). In the lines of codes below I show the set of ODE's, here Tau is the variable that I want to vary. In other words, I want solutions for a system where Tau = 1, Tau = 2, Tau = 3, etc. I tried to do this using a for-loop but it doesn't seems to be working as only the first two columns are calculated and the last ones remain their inital values. Does somebody have a smart solution?

function dpdt = Tester(t,p,val)
dpdt = zeros(2*val,1);
delta = 0.02;
beta = 0.01;
    for tau = 1:1:val
    dpdt(1) = tau * p(1) .* (1 - beta*p(2));
    dpdt(2) = tau * p(2) .* (-1 + delta*p(1));
    end
end

And the solution script is given below:

tspan = [0 15]
val = 2;
[t,p] = ode45(@Tester,tspan,[5 5 50 50],[],val);
plot(t,p)
title('Predator/Prey Populations Over Time')
xlabel('t')
ylabel('Population')
legend('Prey','Predators')

Thanks in advance for your help.

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Star Strider 2021-3-6

2
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/764831-how-to-vary-a-variable-in-a-system-of-ode-s#answer_640686

在 MATLAB Online 中打开

Try this slightly changed version of your code:

function dpdt = Tester(t,p,tau)
dpdt = zeros(2,1);
delta = 0.02;
beta = 0.01;
dpdt(1) = tau * p(1) .* (1 - beta*p(2));
dpdt(2) = tau * p(2) .* (-1 + delta*p(1));
end
tspan = linspace(0, 15, 150);
Tau = 1:5;
for k = 1:numel(Tau)
    [t,p{k}] = ode45(@(t,p)Tester(t,p,Tau(k)),tspan,[5 50]);
end
Np = numel(Tau);
figure
for k = 1:Np
    subplot(Np,1,k)
    plot(t,p{k})
    title(sprintf('Predator/Prey Populations Over Time \\tau = %d',Tau(k)))
    xlabel('t')
    ylabel('Population')
    legend('Prey','Predators', 'Location','EastOutside')
end
pos = get(gcf,'Position');
set(gcf,'Position',pos+[0 -200 0 200])