How can i draw the phase portrait in my code for 3 non-linear coupled ODEs in 3D plane

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Akhtar Jan 2021-12-5

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1603565-how-can-i-draw-the-phase-portrait-in-my-code-for-3-non-linear-coupled-odes-in-3d-plane

评论： William Rose 2021-12-6

采纳的回答： William Rose

function SC1C2

clear

clc

clf

close all

%==== parameters =====

k1 = 1.5;

k_1 = 0.5;

k2 = 1;

k3 = 2;

k_3 = 1;

k4 = 3;

%======Initial conditions =====

initialx = 4;

initialy = 0;

initialz = 0;

runtime = 10; % Simulation run time

iterations = 1; % Sets iteration no. to 1

pausetime = 0.01; % Pause time between animation

az=-37.5; % Sets azemouth angle

el= 30; % Sets elevation angle.

deq1=@(t,x) [k_1*x(2)-k1*x(1)-k3*x(1)*x(2)-k_3*x(3);

k1*x(1)-(k_1+k2)*x(2)-k3*x(1)*x(2)+(k4+k_3)*x(3);

k3*x(1)*x(2)-(k4+k_3)*x(3)];

[t,sol] = ode45(deq1,[0 runtime],[initialx initialy initialz]);

arraysize = size(t);

for i = 1 : max(arraysize)

plot3(sol(iterations,1),sol(iterations,2),sol(iterations,3),'-o','markersize',6,'MarkerFaceColor','m')

hold on

grid on

xlabel('S','fontsize',12)

ylabel('C1','fontsize',12)

zlabel('C2','fontsize',12)

iterations = iterations + 1;

pause(pausetime)

axis([min(sol(:,1)) max(sol(:,1)) min(sol(:,2)) max(sol(:,2)) min(sol(:,3)) max(sol(:,3))])

view(az,el)

az = az+1;

end

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采纳的回答

William Rose 2021-12-5

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1603565-how-can-i-draw-the-phase-portrait-in-my-code-for-3-non-linear-coupled-odes-in-3d-plane#answer_848035

编辑：William Rose 2021-12-5

@Akhtar Jan,

Matlabs quiver3() is very nice for this.

"quiver3(X,Y,Z,U,V,W) plots arrows with directional components U, V, and W at the Cartesian coordinates specified by X, Y, and Z. For example, the first arrow originates from the point X(1), Y(1), and Z(1), extends in the direction of the x-axis according to U(1), extends in the direction of the y-axis according to V(1), and extends in the direction of the z-axis according to W(1). By default, the quiver3 function scales the arrow lengths so that they do not overlap."