Title: Dynamical behaviours of an impulsive food-chain system with Hassell-Varley functional response and mutual interference

Authors: Si Zhou; Yuanfu Shao; Qin Liu; Zhen Wang

Addresses: School of Science, Guilin University of Technology, Guilin, Guangxi 541004, China ' School of Science, Guilin University of Technology, Guilin, Guangxi 541004, China ' School of Science, Guilin University of Technology, Guilin, Guangxi 541004, China ' School of Science, Guilin University of Technology, Guilin, Guangxi 541004, China

Abstract: An impulsively controlled food-chain system with Hassell-Varley functional response and mutual interference is established in this paper. By applying theories and methods of ecology and ordinary differential equation, the dynamical complexity of this system is investigated. We give conditions of the extinction of prey and top predator and show that this system is uniformly bounded. By use of Floquet theory of impulsive equation and small amplitude perturbation skills, we consider the local stability and global stability of the prey-free and top predator-free periodic solution. Moreover, we obtain sufficient conditions for the system to be permanent via impulsive comparison theorem. Finally, numerical simulations are given to substantiate our theoretical results and to illustrate various dynamical behaviours of this system.

Keywords: stability; permanence; impulsive; Hassell-Varley functional response; mutual interference.

DOI: 10.1504/IJDSDE.2018.096206

International Journal of Dynamical Systems and Differential Equations, 2018 Vol.8 No.4, pp.243 - 269

Received: 01 Apr 2017
Accepted: 15 Sep 2017
Published online: 19 Nov 2018 *

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