Global boundedness of solutions in a reaction–diffusion system of Beddington–DeAngelis-type predator–prey model with nonlinear prey-taxis and random diffusion

Abstract

In this paper, a reaction-diffusion system of a predator-prey model with Beddington-DeAngelis functional response is considered. This model describes a prey-taxis mechanism that is an immediate movement of the predator u in response to a change of the prey v (which leads to the collection of u). We use some approaches to prove the global existence-boundedness of classical solutions and overcome the substantial difficulty of the existence of a nonlinear prey-taxis term. MSC: Primary 35A01; secondary 35K57

Global bifurcation in a diffusive Beddington-DeAngelis predator–prey model with population flux by attractive transition

“…Although the study of predator-prey dynamics under the influence of the DeAngelis response has been quite popular, the inclusion of cross-diffusion in the system has gained recent traction. Luo in [6] showed that the solutions of a spatial DeAngelis predator-prey system with diffusion and prey-taxis are globally bounded. The global bifurcation structure of a predator-prey interaction with double Beddington DeAngelis response was studied in [7].…”

Periodic solution and its stability of a delayed Beddington‐DeAngelis type predator‐prey system with discontinuous control strategy

“…Lee and Baek studied a predator‐prey system with BD functional response and constant rate harvesting and investigated various dynamical behaviors of the system including saddle‐node points and a cusp of codimension 2 . Luo analyzed a reaction diffusion system of a predator‐prey model with BD functional response . Liu et al studied a robust stage structured predator‐prey model with BD functional response …”

“…Although the dynamical behaviors of a BD type predator‐prey system has been extensively investigated,() to the best of our knowledge, the delayed Beddington‐DeAngelis (BD) type predator‐prey system, especially under discontinuous control strategy, has been seldom considered. Moreover, owing to the characteristic of discontinuous control strategy, the results obtained for the system with optimal continuous harvesting policy, threshold policy, or weighted escapement policy cannot be directly applied to delayed BD type predator‐prey system with discontinuous control strategy.…”

Spatiotemporal dynamics of a predator–prey system with prey-taxis and intraguild predation

“…where (x, t) ∈ (0, L) × (0, +∞), time delay τ > 0 is the mature time of the predator. Though some significant results on prey-taxis models have been obtained (see [24][25][26][27][28][29] for example), there is no result about the predator-prey model with both time delay and prey-taxis such as (4). Therefore, the main purpose of this paper is to explore the effects of prey-taxis and time delay on stability.…”