Analytical detection of stationary turing pattern in a predator-prey system with generalist predator

Subrata Dey¹ ; Malay Banerjee¹ ; Saktipada Ghorai¹

¹ Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur 208016, Uttar Pradesh, India

Mathematical modelling of natural phenomena, Tome 17 (2022), article no. 33

Résumé

A prey-predator model with Holling type-II functional response and a generalist predator exhibits complex dynamics in response to parameter variation. Generalist predators implicitly exploiting multiple food resources reduce predation pressure on their focal prey species that causes it to become more stable compared to a prey-predator system with specialist predator. In the temporal system, bistability and tristability are observed along with various global and local bifurcations. Existence of homogeneous and heterogeneous positive steady state solutions are shown to exist for suitable ranges of parameter values in the corresponding spatio-temporal diffusive system. Weakly nonlinear analysis, using multi-scale perturbation technique, is employed to derive amplitude equation for the stationary patterns near the Turing bifurcation threshold. The analytical results of the amplitude equations are validated using exhaustive numerical simulations. We also identify bifurcation of multiple stable stationary patch solutions as well as dynamic pattern solution for parameter values in the Turing and Turing-Hopf regions.

Détail

DOI : 10.1051/mmnp/2022032

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