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• W3209557046 abstract "The role of predator evasion mediated by chemical signaling is studied in a diffusive prey–predator model when prey-taxis is taken into account (model A) or not (model B) with taxis strength coefficients [Formula: see text] and [Formula: see text], respectively. In the kinetic part of the models, it is assumed that the rate of prey consumption includes functional responses of Holling, Beddington–DeAngelis or Crowley–Martin. Existence of global-in-time classical solutions to model A is proved in space dimension [Formula: see text] while to model B for any [Formula: see text]. The Crowley–Martin response combined with bounded rate of signal production precludes blow-up of solution in model A for [Formula: see text]. Local and global stability of a constant coexistence steady state which is stable for the corresponding ordinary differential equation (ODE) and purely diffusive model are studied along with mechanism of Hopf bifurcation for model B when [Formula: see text] exceeds some critical value. In model A, it is shown that prey-taxis may destabilize the coexistence steady state provided [Formula: see text] and [Formula: see text] are big enough. Numerical simulation depicts emergence of complex space-time patterns for both models and indicates existence of solutions to model A which blow-up in finite time for [Formula: see text]." @default.
• W3209557046 created "2021-11-08" @default.
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• W3209557046 date "2021-12-30" @default.
• W3209557046 modified "2023-10-14" @default.
• W3209557046 title "Repulsive chemotaxis and predator evasion in predator–prey models with diffusion and prey-taxis" @default.
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• W3209557046 doi "https://doi.org/10.1142/s0218202522500014" @default.
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