Pattern formation with jump discontinuity in a predator–prey model with Holling-II functional response

This paper is focused on the existence and uniqueness of nonconstant steady states in a reaction–diffusion–ODE system, which models the predator–prey interaction with Holling-II functional response. Firstly, we aim to study the occurrence of regular stationary solutions through the application of bi...

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Bibliographic Details
Main Authors: Gaihui Guo, Xiaoyi Yang, Conghui Zhang, Shanbing Li
Format: Article
Language:English
Published: Cambridge University Press
Series:European Journal of Applied Mathematics
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Online Access:https://www.cambridge.org/core/product/identifier/S0956792525000063/type/journal_article
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Summary:This paper is focused on the existence and uniqueness of nonconstant steady states in a reaction–diffusion–ODE system, which models the predator–prey interaction with Holling-II functional response. Firstly, we aim to study the occurrence of regular stationary solutions through the application of bifurcation theory. Subsequently, by a generalized mountain pass lemma, we successfully demonstrate the existence of steady states with jump discontinuity. Furthermore, the structure of stationary solutions within a one-dimensional domain is investigated and a variety of steady-state solutions are built, which may exhibit monotonicity or symmetry. In the end, we create heterogeneous equilibrium states close to a constant equilibrium state using bifurcation theory and examine their stability.
ISSN:0956-7925
1469-4425