Uniform boundedness for a predator-prey system with chemotaxis and dormancy of predators

Dáger, René; Navarro, Víctor; Negreanu, Mihaela

doi:10.1090/qam/1583

Authors: René Dáger, Víctor Navarro and Mihaela Negreanu
Journal: Quart. Appl. Math. 79 (2021), 367-382
MSC (2010): Primary 35K57, 35K59, 35B45, 35B50, 92D25, 92D40
DOI: https://doi.org/10.1090/qam/1583
Published electronically: October 14, 2020
MathSciNet review: 4246497
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Abstract: This paper deals with a nonlinear system of reaction-diffusion partial differential equations modelling the evolution of a prey-predator biological system with chemotaxis. The system is constituted by three coupled equations: a fully parabolic chemotaxis system describing the behavior of the active predators and preys and an ordinary equation, describing the dynamics of the dormant predators, coupled to it. Chemotaxis in this context affects the active predators so that they move towards the regions where the density of resting eggs (dormant predators) is higher. Under suitable assumptions on the initial data and the coefficients of the system, the global-in-time existence of classical solutions is proved in any space dimension. Besides, numerical simulations are performed to illustrate the behavior of the solutions of the system. The theoretical and numerical findings show that the model considered here can provide very interesting and complex dynamics.

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