The instability of periodic solutions for a population model with cross-diffusion

This paper is concerned with a population model with prey refuge and a Holling type Ⅲ functional response in the presence of self-diffusion and cross-diffusion, and its Turing pattern formation problem of Hopf bifurcating periodic solutions was studied. First, we discussed the stability of periodic...

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Published inAIMS mathematics Vol. 8; no. 12; pp. 29910 - 29924
Main Authors Li, Weiyu, Wang, Hongyan
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
cross-diffusion
periodic solutions
population model
refuge
turing pattern
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Abstract This paper is concerned with a population model with prey refuge and a Holling type Ⅲ functional response in the presence of self-diffusion and cross-diffusion, and its Turing pattern formation problem of Hopf bifurcating periodic solutions was studied. First, we discussed the stability of periodic solutions for the ordinary differential equation model, and derived the first derivative formula of periodic functions for the perturbed model. Second, applying the Floquet theory, we gave the conditions of Turing patterns occurring at Hopf bifurcating periodic solutions. Additionally, we determined the range of cross-diffusion coefficients for the diffusive population model to form Turing patterns at the stable periodic solutions. Finally, our research was summarized and the relevant conclusions were simulated numerically.
AbstractList This paper is concerned with a population model with prey refuge and a Holling type Ⅲ functional response in the presence of self-diffusion and cross-diffusion, and its Turing pattern formation problem of Hopf bifurcating periodic solutions was studied. First, we discussed the stability of periodic solutions for the ordinary differential equation model, and derived the first derivative formula of periodic functions for the perturbed model. Second, applying the Floquet theory, we gave the conditions of Turing patterns occurring at Hopf bifurcating periodic solutions. Additionally, we determined the range of cross-diffusion coefficients for the diffusive population model to form Turing patterns at the stable periodic solutions. Finally, our research was summarized and the relevant conclusions were simulated numerically.
Author Li, Weiyu
Wang, Hongyan
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Snippet This paper is concerned with a population model with prey refuge and a Holling type Ⅲ functional response in the presence of self-diffusion and...
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StartPage 29910
SubjectTerms cross-diffusion
periodic solutions
population model
refuge
turing pattern
Title The instability of periodic solutions for a population model with cross-diffusion
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