specific solution in a vector field of a equation system

I create a vector field of a equation system, also I want to represent the spefic solution of the system in that field but I think that I do it wrong.

this is the system:

dx/dt=P-ay

dy/dt=Q-bx

the code:

x1=-1;

x2=5;

y1=-1;

y2=5;

N = 20;

x = linspace(x1,x2,N);

y = linspace(y1,y2,N);

[X,Y]= meshgrid(x,y);

U1 = P - a.*Y;

V1 = Q - b.*X;

quiver (app.Axes2,X,Y,U1,V1);

xlim(app.Axes2,[0 5])

ylim(app.Axes2,[0 5])

hold (app.Axes2,'on')

yh = (P/a)./100;

xh1 = -10;

xh2 = 40;

plot (app.Axes2,[xh1,xh2],[yh,yh]);

hold (app.Axes2,'on')

yv1 = -10;

yv2 = 40;

xv = (Q/b)./100;

plot (app.Axes2,[xv,xv],[yv1,yv2])

hold (app.Axes2, 'on')

s = Q.*x-(b.*x.^2)/2-P.*y+(a.*y.^2)/2;

plot (app.Axes2,x,s,'r')

hold (app.Axes2,'off')

and the axes:

I think that the code is correct but it doesn't have any sense the axes for me, someone could help me?

Answer 1

[Nagasai Bharat]

Hi,

From my understanding you are manually trying to solve the equation. The following documentation should help you solve the system of differential equations in an efficient way.

Solve a System of Differential Equations - MATLAB & Simulink (mathworks.com)