I want to draw dual phase portraits in a 4x4 linear differential equation system. My codes contain 4 variables as below (x1, x2, y1, y2). For a given coefficients matrix, when

p=0.1; q=15;
x1dom = linspace(-p,p,q);x2dom = linspace(-p,p,q);y1dom = linspace(-p,p,q);y2dom = linspace(-p,p,q);
[X1,X2,Y1,Y2] = ndgrid(x1dom,x2dom,y1dom,y2dom);

A=[1.1 0 0.8 0 ; 0 1.2 0 0 ; 0 0 -0.9 0 ; 0 0 0 -0.5];

X1dot= A(1,1)*X1 + A(1,2)*X2 + A(1,3)*Y1 + A(1,4)*Y2; 
X2dot= A(2,1)*X1 + A(2,2)*X2 + A(2,3)*Y1 + A(2,4)*Y2; 
Y1dot= A(3,1)*X1 + A(3,2)*X2 + A(3,3)*Y1 + A(3,4)*Y2; 
Y2dot= A(4,1)*X1 + A(4,2)*X2 + A(4,3)*Y1 + A(4,4)*Y2; 

quiver(X1,X2,X1dot,X2dot)

Error using matlab.graphics.chart.primitive.Quiver/set
Error setting property 'XData' of class 'Quiver':
Value must be an array of numeric type with 3 or fewer dimensions.

Error in quiver (line 81)
set(h,'Parent',parax,'Color_I',c,'LineStyle_I',ls,pvpairs{:});

Answer 1

[Wan Ji]

Looks like an ode function, so use matlab ode solver to solve it. Here I give an example of ode 45.

A = rand(4,4); 
tspan = [0:0.01:1];
x30 = 1;
x40 = 2;
x0 = [0;0;x30;x40];
[t,x] = ode45(@(t,x)A*x,tspan,x0);
plot(x(:,1),x(:,2))
xlabel('x_1')
ylabel('x_2')
title(' phase portrait ')

[kadir can erbas]

This script gives a phase portrait for a single initial condition (x1=x2=0). Is there a more advanced script that displays directional trajectories for a few initial x1 and x2 conditions?

Thank You.