Global bifurcation and structure of stationary patterns of a diffusive system of plant-herbivore interactions with toxin-determined functional responses

Cunbin An; Cunbin An

doi:10.3934/era.2023107

Electronic Research Archive

2023, Volume 31, Issue 4: 2095-2107. doi: 10.3934/era.2023107

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Global bifurcation and structure of stationary patterns of a diffusive system of plant-herbivore interactions with toxin-determined functional responses

Cunbin An ^,

School of Mathematics and Statistics, Shanxi Datong University, Datong, Shanxi 037009, China

Academic Editor: Fengqi Yi

Received: 08 September 2022 Revised: 09 February 2023 Accepted: 12 February 2023 Published: 17 February 2023

In this paper, a homogeneous diffusive system of plant-herbivore interactions with toxin-determined functional responses is considered. We are mainly interested in studying the existence of global steady state bifurcations of the diffusive system. In particular, we also consider the case when the bifurcation parameter, one of the diffusion rates, tends to infinity. The corresponding system is called shadow system. By using time-mapping methods, we can show the existence of the positive non-constant steady state solutions. The results tend to describe the mechanism of the spatial pattern formations for this particular system of plant-herbivore interactions.
- plant-herbivore interactions,
- toxin-determined functional responses,
- steady state bifurcations,
- non-constant positive solutions,
- shadow system
Citation: Cunbin An. Global bifurcation and structure of stationary patterns of a diffusive system of plant-herbivore interactions with toxin-determined functional responses[J]. Electronic Research Archive, 2023, 31(4): 2095-2107. doi: 10.3934/era.2023107

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Abstract

In this paper, a homogeneous diffusive system of plant-herbivore interactions with toxin-determined functional responses is considered. We are mainly interested in studying the existence of global steady state bifurcations of the diffusive system. In particular, we also consider the case when the bifurcation parameter, one of the diffusion rates, tends to infinity. The corresponding system is called shadow system. By using time-mapping methods, we can show the existence of the positive non-constant steady state solutions. The results tend to describe the mechanism of the spatial pattern formations for this particular system of plant-herbivore interactions.

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