I have a system of 5 ODEs. A phase plane was drawn for two of the variables, to see how they interact together. This is the phase plane that I got.
How can I interpret this phase plane? If I have a system of 2 ODEs then I can say that this equilibrium point is asymptomatically stable. But here as there are 5 ODEs and I am only considering two of the variables can I still say that this is asymptomatically stable .
What else can be said about this system by looking at the phase plane?
How to analyse systems with more than 2 ODEs?
In this can I say this spirals in, as I know it start with (1000,0) and when I use
ode45 in Matlab and solve the system the equilibrium point found was in point
Code for direction fields
%trajectory code [tsol,usol]=ode15s(@rhs,[0 time],[1000,0,0, 10^8,0]); A=usol(:,1)+usol(:,2); B=usol(:,5); figure plot(A,B); hold on; %direction fields Ngrid=100; y1=linspace(1000,10^7,Ngrid); y2=linspace(0,10^8,Ngrid); [x,y]=meshgrid(y1,y2); t=0; for i=1:Ngrid for j=1:Ngrid Yprime=rhs(t,[x(i),0,0,10^8,y(j)]); Yprime=Yprime/norm(Yprime); u(i,j)=Yprime(2)+Yprime(1); v(i,j)=Yprime(5); sfactor=0.6; end end quiver(x,y,u,v,sfactor,'r')
When I try to draw the direction fields it changes my trajectory plot as well. I used the code as in Plotting phase plane in Matlab for SIR model . I think the problem is the two variables I draw the phase plane of reaches large values such as $10^6$ and $10^7$. How can I adjust the code to draw the direction fields correctly? In the above code, why is t=0 chosen specifically? Is it because we should know the initial conditions? In the line
I should give
x,y coordnates to the variables I draw the phase plane and for the other variables the initial conditions right?
rhs is the function with my 5 ODEs