Mathematical and numerical analysis of a three-species predator-prey model with herd behavior and time fractional-order derivative |
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| Authors: | Behzad Ghanbari Salih Djilali |
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| Institution: | 1. Department of Engineering Science, Kermanshah University of Technology, Kermanshah, Iran;2. Faculty of Exact and Computer Sciences, Mathematics Department, Hassiba Benbouali University, Chlef, Algeria |
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| Abstract: | In this paper, we investigate with a time fractional-order derivative in a three-species predator-prey model with the presence of prey social behavior. A new approximation for predator-prey interaction in the presence of prey social behavior has been considered. For the model analysis, the study has been divided into two principal parts. First of all, we study the local stability of the equilibria and the existence of Hopf bifurcation. Then, for the numerical analysis, the Caputo fractional derivative operator is utilized to approximate the numerical solution of the model. An excellent agreement is seen between the numerical results and the theoretical predictions. |
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| Keywords: | fractional derivative herd behavior Hopf bifurcation numerical schema predator-prey model |
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