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

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kadir can erbas 2021-8-26

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https://ww2.mathworks.cn/matlabcentral/answers/1441354-i-want-to-draw-dual-phase-portraits-in-a-4x4-linear-differential-equation-system-my-codes-contain-4

编辑： kadir can erbas 2021-9-12

采纳的回答： Wan Ji

在 MATLAB Online 中打开

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{:});

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Answer 1

Wan Ji 2021-8-26

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1441354-i-want-to-draw-dual-phase-portraits-in-a-4x4-linear-differential-equation-system-my-codes-contain-4#answer_775069

在 MATLAB Online 中打开

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 ')

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kadir can erbas 2021-8-29

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.

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