Global Stability Analysis of Coexistence Steady State in a General Predator–Prey System with Double Prey-Taxis
Year: 2026
Type: article
Abstract: In this paper, we consider a general two-prey one-predator reaction–diffusion system with prey competition and double prey-taxis. We first present some preliminary results, including global-in-time existence and a priori estimates of classical solutions to this system with ratio-dependent and non-ratio-dependent predator functional responses. Our main concern is the global stability of spatially homogeneous coexistence steady states. For generalized prey-dependent models, we show that the global asymptotic stability of the coexistence steady state relates to two prey-taxis coefficients provided that the predator functional response, the conversion, and diffusion rates are given. Since there is little prospect of establishing a unified Lyapunov functional for the systems with a predator-dependent functional response, we propose an explicit predator-dependent model and construct the corresponding Lyapunov functional. The theoretical results can cover most three-species chemotaxis systems.
Source: Mathematics
DOI: 10.3390/math14030499
Authors: Guoting Chen, Huan Dai, Mengfeng Sun
Institutions: Harbin Institute of Technology, Shanghai University
Language: English
Field: Medicine
Domain: Health Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7126196299
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