Memory effect on Bazykin’s prey-predator model: Stability and bifurcation analysis

By U. Ghosh, Swadesh Pal, Malay Banerjee. 2021

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Abstract This paper deals with a system of two fractional order differential equations for prey-predator interaction with intra-specific competition among predators. The fractional order differential equation is considered in the sense of Caputo derivative and the derivation of the fractional order model is explained in terms of memory effect on population growth. Detailed mathematical results are provided to establish the positiveness, existence–uniqueness and boundedness of the solutions. The conditions required for local asymptotic stability of various equilibrium points and global stability of coexistence equilibrium are derived along with the Hopf-bifurcation condition for coexistence equilibrium. The effect of memory on the system dynamics through the shift of Hopf-bifurcation threshold is demonstrated with the help of exhaustive numerical simulations. This study also reveals the effect of memory based growth on global bifurcation threshold.

Subfields: Applied Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/decceb8e60e505d8509f6ac949ddeb6a6112ce33