Dynamic and pattern formation of a diffusive predator–prey model with indirect prey-taxis and indirect predator-taxis

• Published in: Nonlinear analysis: real world applications Vol. 84; p. 104299
• Main Authors: Wu, Sainan, Wang, Yiran, Geng, Dongxu
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2025
• Subjects: Global stability; Indirect predator-taxis; Indirect prey-taxis; Nonconstant steady state solution; Periodic solution; Predator–prey model; Spatiotemporal pattern; 92D25; 35B35; Global stability; Indirect predator-taxis; Nonconstant steady state solution; Indirect prey-taxis; Periodic solution; Predator–prey model; Spatiotemporal pattern; 35K55; 35Q92
• ISSN: 1468-1218
• DOI: 10.1016/j.nonrwa.2024.104299

This paper is concerned with a diffusive predator–prey model with indirect prey-taxis and indirect predator-taxis, which describes the interaction between the predator and the prey. It means that the predator is attracted to the chemical excreted by prey, meanwhile, the prey is repelled to the chemical excreted by predator. The linear stability of constant steady states to the system is obtained. We prove the existence of Hopf bifurcations by choosing the indirect predator-taxis coefficient as the bifurcation parameter and find that both the indirect prey-taxis and indirect predator-taxis promote the system to produce more complex spatiotemporal patterns. Through the bifurcation theory, the existence of steady state bifurcations is established. Moreover, we show the global stability of the semi-trivial steady state and positive constant steady state. Finally, we use numerical examples to check the theoretical results and gain the spatiotemporal patterns.