Existence and global attractivity of positive periodic solutions for a Holling II two-prey one-predator system

Abstract

In this paper, a Holling II two-pery one-predator system is investigated. Based on the continuation theorem of coincidence degree theory and by constructing a suitable Lyapunov function, we derive a set of sufficient conditions that guarantee the existence of at least a positive periodic solution and global attractivity of periodic solutions. Mathematics Subject Classification 2000: 34K20; 34C25

Stability analysis of a food chain model consisting of two competitive preys and one predator

“…[17][18][19]). Xu and Shao [20] showed the existence and global attractivity of positive periodic solutions for a Holling type II two-prey one-predator system. Stability analysis of a two-prey and one-predator model with group help and Holling type I response for predation was studied in [21,22].…”

Existence and Uniqueness of Positive Periodic Solution of an Extended Rosenzweig-MacArthur Model via Brouwer's Topological Degree

“…The qualitative dynamical behaviors of these mathematical models are widely studied in populations of multiple interacting species in the ecosystem. [1] investigated the existence and global attractivity of positive periodic solutions for a Holling II two-prey and one-predator system. Periodic solutions for a three-species Lotka-Volterra food chain model with time delay were studied in [2].…”

Dynamics of a stochastic Holling II one-predator two-prey system with jumps

“…In Ref. [3], authors pointed out reality mining (the processing and 5 analysis of machine-sensed data on the social behavior of animals or humans) can make it possible to investigate the social 6 behavior of almost human populations in extraordinary detail. In Ref.…”

“…In particular, the predator-prey interaction have been studied extensively. In all predator-prey inter-2 action, the functional response, which refer to the number of prey eaten per predator per unit time as a function of prey 3 density, is a key element [6]. In Ref.…”

“…We 4 can also observe from these figures that positive jump noise is advantageous to the system while negative jump noise is 5 disadvantageous. 6 …”