Steady states of a predator–prey model with prey-taxis

Stability, Steady‐State Bifurcations, and Turing Patterns in a Predator–Prey Model with Herd Behavior and Prey‐taxis

“…The influence of the prey‐taxis on the spatiotemporal dynamics of the predator–prey model has been increasingly studied by many researchers. For instance, Hopf bifurcation, global existence of classical solution, traveling wave solution, Turing instability, and pattern formation have been recently studied; see .…”

“…The influence of the prey-taxis on the spatiotemporal dynamics of the predator-prey model has been increasingly studied by many researchers. For instance, Hopf bifurcation, global existence of classical solution, traveling wave solution, Turing instability, and pattern formation have been recently studied; see [30,[33][34][35][36][37][38][39][40][41][42][43][44]. However, to the best of our knowledge, there are no theoretical results on predator-prey model with herd behavior and prey-taxis such as (3).…”

Steady state for a predator–prey cross-diffusion system with the Beddington–DeAngelis and Tanner functional response

“…Now we offer a rigorous proof to guarantee that δ = 0. Here δ is described in Lemma 4.1 of [13]. For ρ > 0, we study the eigenvalue issue (CM (u * , v * ) -I)( , ) T = ρ( , ) T , ( , ) = (0, 0), which means that for some positive constant ρ, the model…”

Effect of prey‐taxis and diffusion on positive steady states for a predator‐prey system

“…In Chakraborty et al, pattern formation of predator‐prey model with different functional responses has been investigated numerically; Lee, Hillen, and Lewis studied the pattern formation induced by prey‐taxis in predator‐prey model with different nonlinear functional responses, linear and nonlinear predator death functions, and different prey growth terms; Lee, Hillen, and Lewis studied the continuous traveling wave solution for model with prey‐taxis. For the specific model of with , Li, Wang, and Shao considered the volume‐filling mechanism in prey‐tactic sensitivity model; Wang, Wang, and Zhang investigated the pattern formation using bifurcation theory.…”