Matlab tool to plot 3d phase portrait
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I have the following system of differential equations
x' = -alpha0 * x + beta0 * x * y;
y' = alpha1 * y - beta1 * x * y;
z' = -alpha2 * (z - 5.5)^3 - beta2 * x * y;
I wanted to take a look at the phase portrait of this system for various values of the coefficients. Is there an inbuilt matlab tool that can do that?
采纳的回答
If you want to use multiple slider widgets for alpha and beta to visualize the interactive 3D phase portrait, then you need to use the Graphical User Interface Design Environment or the App designer to create your desired graphical user interface (GUI).
help GUIDE
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Steven Lord
2024-5-12
0 个投票
Use odeset to set the OutputFcn option to @odephas3. See the ballode or orbitode example files for a demonstration of how to use the OutputFcn option, though I believe those use @odeplot and @odephas2 instead of @odephas3.
3 个评论
I am sorry but I don't understand, can you provide links to the tools that you are mentioning? I wanted to know if there is an interactive tool for it. I followed this example and wrote the code manually this way:
%% Phase plane
clc;clear all;
[x1,y1,z1] = meshgrid(0:0.2:2,0:0.2:2,0:0.2:2);
u = zeros(size(x1));
v = zeros(size(y1));
w = zeros(size(z1));
t=0;
for i = 1:numel(x1)
Yprime = rhs(t,[x1(i); y1(i); z1(i)]);
u(i) = Yprime(1);
v(i) = Yprime(2);
w(i) = Yprime(3);
end
quiver3(x1,y1,z1,u,v,w); figure(gcf)
function f = rhs(t,y)
alpha0 = 1;
beta0 = 1;
alpha1 = 1;
beta1 = 1;
alpha2 = 1;
beta2 = 1;
f = zeros(size(y));
f(1) = -alpha0*y(1) + beta0*y(1)*y(2);
f(2) = alpha1*y(2) - beta1*y(1)*y(2);
f(3) = -alpha2*(y(3) - 5.5)^3 - beta2*y(1)*y(2);
end
@Steven Lord suggested calling '@odephas3' to generate the 3D phase plot. Is this what you were looking for? The 'quiver3' function is used for plotting a 3D vector field, which can be challenging for humans to visualize when projected on a static 2D plane. However, on your MATLAB machine, you can manually rotate the view using your mouse.
initX = [0 0 0
0 0 1
1 0 0
1 0 1
1 1 0
1 1 1];
tspan = [0 10];
X0 = initX(3,:); % test different initial values
opts = odeset('OutputFcn', @odephas3); % <-- insert this
[t, X] = ode45(@ode, tspan, X0, opts);
%% Differential Equations
function dX = ode(t, X)
dX = zeros(3, 1);
x = X(1);
y = X(2);
z = X(3);
alpha0 = 1;
beta0 = 1;
alpha1 = 1;
beta1 = 1;
alpha2 = 1;
beta2 = 1;
dX(1) = -alpha0 * x + beta0 * x * y;
dX(2) = alpha1 * y - beta1 * x * y;
dX(3) = -alpha2 * (z - 5.5)^3 - beta2 * x * y;
end
Shreshtha Chaturvedi
2024-5-12
编辑：Shreshtha Chaturvedi
2024-5-12
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