It is just the Lotka Voltera  system

https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations

The above link contains materials about this system.

I remember I learned  about these material from a talk by Zeeman at 2001. I think Zeeman also  devoted some researchs on this topic. So searching Lotka Voltera system +Zeeman gives you some other materials.