Uniform global asymptotic stability of time-varying Lotka-Volterra predator-prey systems

The model to be dealt in this paper is N′=(a+ch(t)−dh(t)N−bP)N,P′=(−c+dN)P.Here, h is a nonnegative and locally integrable function. This model is a predator-prey system of Lotka-Volterra type with variable coefficients and it has a single interior equilibrium (c∕d,a∕b). Sufficient conditions are given for the interior equilibrium to be uniformly globally asymptotically stable. One of them is described by using a certain uniform divergence condition on h. Our result is proved by examining in detail the behaviour of all solutions of a planar system equivalent to this model.