Faeze

Now I think yes they are autonomous equations Thank you. The problem is f(p) is not an explicit function of p. And I do not want to solve this ODE. My question is if I can say something about the equilibriun of a system with these two ODEs when I have information that I mentioned?

Not sure. I am not familiar with this area that much. If we can write them as you said, what would we get?

I have an ordinary differential equation in the form of dp/dt=p-f(p). Since p and f(p) are bounded, any equilibrium of this ODE should satisfy p*=f(p*). I have another ODE in the form of dw/dt=g(w). I know this ODE diverges and because w is bounded between zero and one, at the equilibrium w* is zero or one. Now I consider a system that has p and w and both of them are changing which gives me two ODEs, dp/dt=p-f(p,w) and dw/dt=g(w,p). I know for any fixed w, we have p*=f(p*,w) at the equilibrium and for any fixed p, w* equals zero or one. Does anyone know if I can claim there is any equlibrium for general case and at the equilibrium p*=f(p*,w*) and w* equals zero or one?