Qualitative analysis of a ratio-dependent Holling–Tanner model

Abstract

In this paper, we consider a Holling–Tanner system with ratio-dependence. First, we establish the sufficient conditions for the global stability of positive equilibrium by constructing Lyapunov function. Second, through a simple change of variables, we transform the ratio-dependent Holling–Tanner model into a better studied Liénard equation. As a result, the uniqueness of limit cycle can be solved.