MATLAB: Phase plane of a differential system

phase plane

Hi, i'm trying to plot a phase plane but it doesn't work 🙁

This is the matlab code:

clear all
clc
[X,Y] = meshgrid(0:0.2:5,0:0.2:5);
u = -((3*X)/(2+X))*(Y-X);
v = zeros(26);
figure
quiver(X,Y,u,v);

And matlab answer me: Warning: Matrix is singular to working precision.

Thank you very much for your help !!!

Best Answer

You need to do element-wise (array) operations.

Change the ‘u’ assignment to:

u = -((3*X)./(2+X)).*(Y-X);

and it works.

See the documentation on Array vs. Matrix Operations for details on the differences.

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MATLAB: No Arrows showing in plot When using quiver

As the grid starts from 0 and you have used this zero in the reciprocal to get (u,v) you will get inf in the u,v.; quiver uses maximum value of u and v to scale the arrows and plot. Try to repalce inf with some other value or avoid zero.

[x,y] = meshgrid(1:0.2:5,1:0.2:5);
u = 2./x;
v = 2.*y./(x.^2);
figure
quiver(x,y,u,v,1,'r')

MATLAB: Plotting trajectories of a system of equations.

First, use the matlabFunction (link) function to create anonymous functions (or function files) from your symbolic expressions. Second, use the ‘X’ and ‘Y’ matrices to calculate ‘U’ and ‘V’.

Other than that, you did everything correctly.

Try this:

syms x(t) y(t);
a=1;
A = [a 0; 0 1];
Z = [x;y];
odes = diff(Z) == A*Z
[xSol(t), ySol(t)] = dsolve(odes);
xSol(t) = simplify(xSol(t))
ySol(t) = simplify(ySol(t))
xfcn = matlabFunction(xSol)                             % Create Anonymous Function From Symbolic Function

yfcn = matlabFunction(ySol)                             % Create Anonymous Function From Symbolic Function
xdom = linspace(-10,10,100);
ydom = linspace(-10,10,100);
[X,Y] = meshgrid(xdom,ydom);
U = a.*X;                                               % Use ‘X’ To Calculate Derivatives
V = -1*Y;                                               % Use ‘Y’ To Calculate Derivatives
quiver(X,Y,U,V,5)                                       % Scale Arrows At 5
axis([-1  1    -1  1])                                  % Zoom In To View Details

Best Answer

Related Solutions

MATLAB: No Arrows showing in plot When using quiver

MATLAB: Plotting trajectories of a system of equations.

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