Stability for a Holling Type IV Food Chain System With Impulsive Perturbations

Abstract

Abstract. We investigate a three species food chain system with a Holling type IVfunctional response and impulsive perturbations. We find conditions for local and globalstabilities of prey(or predator) free periodic solutions by applying the Floquet theory andthe comparison theorems. 1. IntroductionIt is currently very much in vogue to study population models with impulsiveperturbations containing biological and chemical controls. Especially, simple multi-species systems consisting of a three species food chain with impulsive perturbationshave been discussed by a number of researchers [13], [17], [18], [19], [20] and thereare also many literatures on impulsive prey-predator population models [10], [11],[12].A well-known model of such systems is a food chain system with Holling typeIV functional response [7], [14], [20], which can be described the following equation:(1.1)x 0 (t) = x(t)(a−bx(t))−c 1 x(t)y(t)1+e 1 x 2 (t),y 0 (t) = −d 1 y(t)+c 2 x(t)y(t)1+e 1 x 2 (t)−c 3 y(t)z(t)1+e