The dynamic behavior of time-delayed Leslie-Gower predator-prey model

Khayyam Salehi and Javad Alidousti

Applied Mathematics and Computation, 2026, vol. 508, issue C

Abstract: In this paper, we examine a delayed Leslie-Gower (LG) predator-prey system with the representation of interactions using a type II response function. It is considered that a prey that is afflicted can transmit the infection to another prey that is susceptible. The infection does not spread instantaneously but with a time delay to account for the necessary incubation period. A delay has the potential to disrupt a stable internal equilibrium. Given that adding harvesting to the prey population capable of mitigating abrupt population fluctuations, when surpassing the threshold level, we can stabilize the system. In this study, we consider both delayed and delay-free LG models. It is shown that the possibility of delay may diminish the stability region and create more complex border structures. New dynamical phenomena such as Hopf and Bautin bifurcations in both delayed and delay-free systems are investigated. Moreover, double-Hopf and resonance bifurcations are explored in delayed systems. By employing the method of multiple scales, we calculate the normal form coefficients for each bifurcation. A comprehensive analysis of the system's dynamic behavior in relation to two parameters, encompassing co-dimension 1, co-dimension 2, and the basin of attraction, is conducted using Lyapunov exponents and Poincaré sections. Numerical simulations validate our analytical findings.

Keywords: Leslie-Gower model; Delay; Hopf bifurcation; Double-Hopf bifurcation; Bautin bifurcation; Resonance bifurcation; Co-dimensions 1 & 2 (search for similar items in EconPapers)
Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300325003480
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:508:y:2026:i:c:s0096300325003480

DOI: 10.1016/j.amc.2025.129622

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().