Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 43, Issue 4, Pages 1736-1752Publisher
WILEY
DOI: 10.1002/mma.5999
Keywords
fractional derivative; herd behavior; Hopf bifurcation; numerical schema; predator-prey model
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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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