A reaction–diffusion system modeling predator–prey with prey-taxis

By B. Ainseba, Mostafa Bendahmane, A. Noussair. 2008

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Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis ✩ (2016, background): “It has been recognized that in the spatial predator–prey interaction, in addition to the random diffusion of predator and prey, the spatiotemporal variations of the predator velocity are affected by the prey gradient [1,27,32].”
Global bifurcation of solutions for a predator–prey model with prey‐taxis (2015, methodology): “For system (1), the existence of weak solutions was studied in [1] by using the Schauder fixed-point theorem, and the uniqueness was analyzed via duality technique.”
Global stability of prey-taxis systems (2017, unknown): “In the existing works as recalled above, either the technical truncation assumption (see [1, 12,34]) or smallness assumption (see [46]) was imposed for the prey-taxis coefficient to ensure the global boundedness of solutions.”
Depleting the signal: Analysis of chemotaxis‐consumption models—A survey (2023, unknown): “Another class of systems which can be viewed as extensions of (CC1) is formed by the prey-taxis models ([8])    ut = ∆u− χ∇ · (u∇v) + γuh(v) + f(u) x ∈ Ω, t > 0, vt = ∆v − uh(v) + g(v) x ∈ Ω, t > 0, ∂u ∂ν = ∂v ∂ν = 0, x ∈ ∂Ω, t > 0, u(x, 0) = u0(x), v(x, 0) = v0(x), x ∈ Ω, (CC7)”