how to modify code for distributed delay

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Muhammad 2024-8-16，18:58

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https://ww2.mathworks.cn/matlabcentral/answers/2145819-how-to-modify-code-for-distributed-delay

评论： Muhammad 2024-8-17，10:38

采纳的回答： Torsten

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I have a code, which gives a solution of a delay logistic equation with discrete delay.

tau = 1;

tspan = [0 20];

y0 = 0.5;

sol = dde23(@ddefunc, tau, y0, tspan);

% Plot the solution

figure;

plot(sol.x, sol.y, 'LineWidth', 2);

xlabel('Time (days)');

ylabel('Population');

legend('y');

% Define the delay differential equation

function g = ddefunc(t, y, Z)

r = 1.5;

y_tau = Z;

g = r * y * (1 - y_tau);

end

Now I want to modify my code for distributed delay as attached below.

Can someone guide me how to deal with distributed delay

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采纳的回答

Torsten 2024-8-16，19:06

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r = 1.5;

fun = @(t,x)[r*x(1)*(1-x(2));x(1)];

x0 = [0.5;0];

tspan = [0 20];

[t,x] = ode45(fun,tspan,x0);

plot(t,x(:,1))

grid on

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Torsten 2024-8-16，20:54

编辑：Torsten 2024-8-16，20:58

在 MATLAB Online 中打开

@Muhammad

This is the solution for equation (1.6) with r=1.5 and x(0) = 0.5.

If you have something different in mind, you must post it.

Note that the second equation

dy/dt = x, y(0) = 0

gives

y(t) = integral_{tau=0}^{tau=t} x(tau) dtau

as solution, thus the integral in (1.6).

Muhammad 2024-8-17，10:38

Thank you for your clear response!

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