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.