Turing–Hopf Bifurcation and Its Normal Form in a Diffusive Three-Species Food Chain System with Strong Allee Effect-Reference-Cited by-同舟云学术

Turing–Hopf Bifurcation and Its Normal Form in a Diffusive Three-Species Food Chain System with Strong Allee Effect

Published:2022-06-10 Issue:07 Volume:32 Page:
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Sun Guangxun¹^ORCID,Dai Binxiang¹,Wang Lin²

Affiliation:

1. School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, P. R. China

2. Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB E3B 5A3, Canada

Abstract

In this paper, we consider a diffusive three-species food chain system with strong Allee effect subject to the Neumann boundary condition. The dynamics of the local system including stability of interior equilibria and Hopf bifurcation are discussed. For the diffusive system, we study the existence of non-negative solutions, stability of a positive homogeneous steady state, diffusion-driven Turing instability and the occurrence of Turing–Hopf bifurcation. Employing the multiple scale analysis, we derive the normal form of Turing–Hopf bifurcation, which helps us classify the dynamical behaviors of the diffusive system near the Turing–Hopf bifurcation point.

Funder

National Natural Science Foundation of China

Fundamental Research Funds for Central Universities of the Central South University

Natural Sciences and Engineering Research Council of Canada

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021812742250105X

Reference43 articles.

1. An application of the invariance principle to reaction-diffusion equations

2. Turing–Hopf Bifurcation and Spatio-Temporal Patterns of a Ratio-Dependent Holling–Tanner Model with Diffusion

3. Dynamics of an intraguild predation food web model with strong Allee effect in the basal prey

4. Turing–Hopf bifurcation and multi-stable spatio-temporal patterns in the Lengyel–Epstein system

5. Spatiotemporal dynamics in a ratio-dependent predator-prey model with time delay near the Turing–Hopf bifurcation point

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