Direction field and phase potrait
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Hello, I need to draw a direction field and sketch phase potrait for this differential equation:
dL/dA = (-0.5L+0.0001AL)/2A(1-0.0001A)-0.01AL
How would I do it?
thank you for helping!
采纳的回答
Hi @Tuân Nguyen
You can basically plot the direction field like this:
[A, L] = meshgrid(0.1:10/14:10.1, -5:10/14:5);
M = (- 0.5*L + 0.0001*A.*L)./(2*A.*(1 - 0.0001*A) - 0.01*A.*L);
N = sqrt(1 + M.^2);
U = 1./N;
V = M./N;
quiver(A, L, U, V, 0.5)
axis square
hold on
% differential equation
f = @(A, L) (- 0.5*L + 0.0001*A*L)/(2*A*(1 - 0.0001*A) - 0.01*A*L);
tspan = 0.1:0.01:10.1; % simulation time
init = 4; % initial condition L(0.1) = 4
[A, L] = ode45(f, tspan, init);
plot(A, L, 'r', 'linewidth', 1.5)
hold off
Result:
For more info, please visit the documentation:
4 个评论
Tuân Nguyen
2022-4-25
编辑：Tuân Nguyen
2022-4-25
Sam Chak
2022-4-25
Alright, I've fixed the the ODE as requested.
Note that the simulation cannot be run from A = 0, else it will cause singularity issue (division-by-zero).
In this example, I run A from 0.1 to 10.1, and select the initial condition, L(0.1) = 4.
Tuân Nguyen
2022-4-25
Sam Chak
2022-4-25
Cảm ơn for your acceptance!
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