Global existence and boundedness in a reaction–diffusion–taxis system with three species

Xue, Xiangxin; Wang, Yong

doi:10.1186/s13662-018-1550-x

Cited by 3 publications

(1 citation statement)

References 16 publications

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Zhuang

Yuan

2019

Adv Differ Equ

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This paper is concerned with a reaction-diffusion predator-prey model with prey-taxis and intraguild predation. We first discuss the basic properties of solutions with the aid of differential equation theory. Then, we investigate the local and global stability of constant equilibrium solution by linear stability analysis and Lyapunov function method, respectively. Moreover, we establish the existences of nonconstant positive steady states and time-periodic solutions through detailed bifurcation analyses. Finally, we give some numerical simulations and conclusions to illustrate the theoretical findings.

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Section: Introductionmentioning

confidence: 99%

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

Zhuang

Yuan

2019

Adv Differ Equ

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Stochastic reaction–diffusion system modeling predator–prey interactions with prey-taxis and noises

Bendahmane

Herbert

Tagoudjeu

et al. 2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper, we are concerned with a new stochastic system of nonlinear partial differential equations modeling the Lotka–Volterra interactions of predators and preys in the presence of prey-taxis, spatial diffusion, and noises. The spatial and temporal variations of the predator’s velocity are determined by the prey gradient. In the first part, we derive a macroscopic model from stochastic kinetic equations by using the micro–macro decomposition method. In the second part, we sketch the proof of the existence of weak martingale solutions by using a Faedo–Galerkin method. In the last part, we develop a one- and two-dimensional finite volume approximation for the stochastic kinetic and macroscopic models, respectively. Our one-dimensional space numerical scheme is uniformly stable along the transition from kinetic to macroscopic regimes. We close with various numerical tests illustrating the convergence of our numerical method and some features of our stochastic macro-scale system.

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Dynamic bifurcation for a three-species cooperating model

2021

J. Phys.: Conf. Ser.

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Global existence and boundedness in a reaction–diffusion–taxis system with three species

Abstract: The global existence and boundedness of a reaction-diffusion-taxis system with three interacting species, among which two species consist of predators competing for one species of prey, are investigated. MSC: 35K57; 35K59; 35B45; 92D25

Cited by 3 publications

References 16 publications

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

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

Stochastic reaction–diffusion system modeling predator–prey interactions with prey-taxis and noises

Dynamic bifurcation for a three-species cooperating model

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