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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Double Allee Effect-Induced Extinction and Bifurcation in a Discrete-Time Predator-Prey Model

Journal of Applied Nonlinear Dynamics 15(3) (2026) 589--614 | DOI:10.5890/JAND.2026.09.006

Rajesh Ranjan Patra$^1$, Sarit Maitra$^2$, Susmita Sarkar$^2$

$^1$ Department of Applied Mathematics, Alliance School of Sciences, Alliance University, Bangalore-562106, India

$^2$ Department of Mathematics, National Institute of Technology Durgapur, Durgapur-713209, India

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Abstract

The importance of the Allee effect in studying extinction vulnerability is widely recognized by researchers, and neglecting it could adversely impact the management of threatened or exploited populations [1]. In this article, we examine a discrete predator-prey model where the prey population is associated with two component Allee effects. We derive sufficient conditions for the existence and local stability nature of the fixed points of the system. The occurrence of Neimark-Sacker bifurcation is established, and sufficient conditions are obtained along with the normal form. Numerically, we demonstrate that the system exhibits Neimark-Sacker bifurcation for various system parameters. Additionally, the numerical simulations indicate that certain system parameters have threshold values, above or below which the populations are driven to extinction due to the impact of the double Allee effect.

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