https://doi.org/10.1140/epjp/s13360-023-04243-3
Regular Article
Turing instability and Hopf bifurcation induced by prey refuge in a diffusive predator–prey system with stage structure and anti-predation
1
School of Mathematics and Statistics, Ludong University, 264025, Yantai, People’s Republic of China
2
College of Mathematics and Systems Science, Shandong University of Science and Technology, 266590, Qingdao, People’s Republic of China
3
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, 21589, Jeddah, Saudi Arabia
Received:
20
May
2023
Accepted:
28
June
2023
Published online:
17
July
2023
This paper studies a class of reaction-diffusion predator–prey system with stage-structured and anti-predation behavior. Based on the original deterministic system, we consider the prey refuge and study how it affects the stability of the populations. We first give the boundedness of solutions and then investigate the stability of equilibrium points with biological significance in the temporal system and spatial system. Further, the prey refuge is regarded as a bifurcation parameter for discussing the relevant Hopf bifurcation properties. Moreover, theoretical results show that the diffusion can cause Turing instability, interestingly, we find that a large diffusion rate of the prey can cause Turing instability, while large diffusion rates of predators would inhibit the appearance of Turing instability. Biologically, moderate anti-predation behavior among populations can promote system stability.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
