Taxis-Driven Pattern Formation in Tri-Trophic Food Chain Model with Omnivory

Evgeniya Giricheva ()
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Evgeniya Giricheva: Institute of Automation and Control Processes, Far Eastern Branch of the Russian Academy of Science, 5 Radio Street, Vladivostok 690014, Russia

Mathematics, 2024, vol. 12, issue 2, 1-18

Abstract: The spatiotemporal dynamics of a three-component model of a food web are considered. The model describes the interactions between populations of resources, prey, and predators that consume both species. It assumes that the predator responds to the spatial change in the resource and prey densities by occupying areas where species density is higher (prey-taxis) and that the prey population avoids areas with a high predator density (predator-taxis). This work studies the conditions for the taxis-driven instability leading to the emergence of stationary patterns resulting from Turing instability and autowaves caused by wave instability. The existence of nonconstant positive steady states for the system is assessed through a rigorous bifurcation analysis. Meanwhile, the conditions for the existence of both types of instabilities are obtained by linear stability analysis. It is shown that the presence of cross-diffusion in the system supports the formation of spatially heterogeneous patterns. For low values of the resource-tactic and predator-tactic coefficients, Turing and wave instabilities coexist. The system undergoes only Turing instability for high levels of these parameters.

Keywords: food web model; prey- and predator-taxis; nonconstant positive steady states; Turing and wave instability; pattern formation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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