The limit cycles of a general Kolmogorov system

In this paper, the general Kolmogorov system {dxdt=ϕ(x)f(x,y),dydt=ρ(y)g(x,y) is studied. By using the theory of generalized rotated vector fields and the Poincare–Bendixson annular region theorem, we prove the sufficient conditions for the existence and uniqueness of limit cycles in this system. And our results extend almost all the related existing studies on the Kolmogorov and predator–prey systems.