Work

Dynamical Regimes in a Delayed Predator–Prey Model with Predator Hunting Cooperation: Bifurcations, Stability, and Complex Dynamics

Year: 2025

Type: article

Abstract: In this paper, a predator–prey model with hunting cooperation and maturation delay is studied. Through theoretical analysis, we investigate the existence of multiple stability switches of the positive equilibrium. By applying Hopf bifurcation theory, the conditions for Hopf bifurcation are derived, indicating the emergence of periodic solutions as the maturation delay passes through critical values. Utilizing center manifold theory and normal form analysis, we determine the stability and direction of the bifurcating orbits. Numerical simulations are performed to validate the theoretical results. Furthermore, the simulations vividly demonstrate the appearance of period-doubling bifurcations, which is the onset of chaotic behavior. Bifurcation diagrams and phase portraits are employed to precisely characterize the transition processes from a stable equilibrium to periodic, period-doubling solutions and chaotic states under different maturation delay values. The study reveals the significant influence of maturation delay on the stability and complex dynamics of predator–prey systems with hunting cooperation.

Source: Modelling—International Open Access Journal of Modelling in Engineering Science

DOI: 10.3390/modelling6030084

Authors: Chao Peng, Jiao Jiang

Institution: Shanghai Maritime University

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

Open Access status: gold

Estimated APC paid: $1,207

Funder: National Natural Science Foundation of China