Eur. Phys. J. Special Topics 227, 971–981 (2018)
https://doi.org/10.1140/epjst/e2018-800022-0

Regular Article

Bifurcations, chaos and synchronization of a predator–prey system with Allee effect and seasonally forcing in prey’s growth rate

National Institute of Applied Sciences and Technology, INSAT, Centre Urbain Nord, BP 676-1080 Tunis Cedex, Tunisia

^a e-mail: afef.ben.saad88@gmail.com

Received: 16 February 2018
Received in final form: 27 April 2018
Published online: 19 October 2018

Abstract

In this paper, a predator–prey model with Allee effect and seasonally forcing in the prey’s growth rate is introduced and analysed. Nonlinear analysis, using equilibrium points computed via Symbolic Math software tools, bifurcation diagrams, phase diagrams, Lyapunov exponents and Kaplan–Yorke dimension, proves that such effects lead to undesirable biological dynamics including chaos behaviours. In order to establish a certain balance in the ecosystem and avoid chaotic dynamics, the biological system is controlled in order to follow an unforced reference model via a synchronization approach. Simulation results prove the efficiency of the proposed approach to allow the predator–prey system regaining natural dynamics.