Stability and Bifurcation Analysis of a Commensal Model with Allee Effect and Herd Behavior-Reference-Cited by-同舟云学术

Stability and Bifurcation Analysis of a Commensal Model with Allee Effect and Herd Behavior

Published:2022-11 Issue:14 Volume:32 Page:
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Cai Junning¹²³,Pinto Manuel⁴,Xia Yonghui¹

Affiliation:

1. Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China

2. Department of Applied Mathematics, Guangxi University of Finance and Economics, Nanning, Guangxi 530003, P. R. China

3. Guangxi Key Laboratory of Big Data in Finance and Economics, Nanning, Guangxi 530003, P. R. China

4. Departamento de Matemáticas, Universidad de Chile, Santiago, Chile

Abstract

In this paper, we study a commensal model with Allee effect and herd behavior. Firstly, the stability of all possible equilibria are investigated. Secondly, using the Sotomayor’s theorem, we prove the existence of saddle-node bifurcation and pitchfork bifurcation. Finally, all the theoretical predictions on the bifurcation are verified by numerical simulations.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127422502170

Reference23 articles.

1. Modeling herd behavior in population systems

2. Animal aggregations, a study in general sociology. / by W. C. Allee.

3. Spatiotemporal Patterns of a Predator–Prey System with an Allee Effect and Holling Type III Functional Response

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1. Theoretical and Numerical Bifurcation Analysis of a Discrete Predator–Prey System of Ricker Type with Weak Allee Effect;Qualitative Theory of Dynamical Systems;2024-08-19

2. Stability and bifurcation analysis of a population dynamic model with Allee effect via piecewise constant argument method;Journal of Applied Mathematics and Computing;2024-05-24