Work

Global well-posedness and Turing–Hopf bifurcation of prey-taxis systems with hunting cooperation

Year: 2025

Type: article

Abstract: This paper is concerned with a predator–prey system with hunting cooperation and prey-taxis under homogeneous Neumann boundary conditions. We establish the existence of globally bounded solutions in two dimensions. In three or higher dimensions, the global boundedness of solutions is obtained for the small prey-tactic coefficient. By using hunting cooperation and prey species diffusion as bifurcation parameters, we conduct linear stability analysis and find that both hunting cooperation and prey species diffusion can drive the instability to induce Hopf, Turing and Turing–Hopf bifurcations in appropriate parameter regimes. It is also found that prey-taxis is a factor stabilizing the positive constant steady state. We use numerical simulations to illustrate various spatiotemporal patterns arising from the abovementioned bifurcations including spatially homogeneous and inhomogeneous time-periodic patterns, stationary spatial patterns and chaotic fluctuations.

Source: European Journal of Applied Mathematics

DOI: 10.1017/s0956792525000026

Authors: Weirun Tao, Zhi-An Wang

Institutions: Southeast University, Hong Kong Polytechnic 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: $3,550

Funders: National Natural Science Foundation of China, Hong Kong Polytechnic University, Southeast University