Global dynamics and pattern formation for predator-prey system with density-dependent motion-Reference-Cited by-同舟云学术

Global dynamics and pattern formation for predator-prey system with density-dependent motion

Published:2022 Issue:2 Volume:20 Page:2296-2320
ISSN:1551-0018
Container-title:Mathematical Biosciences and Engineering
language:
Short-container-title:MBE

Author:

Feng Tingfu¹,Wu Leyun²

Affiliation:

1. Department of Mathematics, Kunming University, Kunming, Yunnan, China

2. Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Hong Kong, China

Abstract

<abstract><p>In this paper, we concern with the predator-prey system with generalist predator and density-dependent prey-taxis in two-dimensional bounded domains. We derive the existence of classical solutions with uniform-in-time bound and global stability for steady states under suitable conditions through the Lyapunov functionals. In addition, by linear instability analysis and numerical simulations, we conclude that the prey density-dependent motility function can trigger the periodic pattern formation when it is monotone increasing.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Computational Mathematics,General Agricultural and Biological Sciences,Modeling and Simulation,General Medicine

Reference40 articles.

1. H. I. Freedman, Deterministic mathematical models in population ecology, volume 57. Marcel Dekker Incorporated, 1980.

2. A. J. Lotka, Elements of mathematical biology, Dover Publications, 1956.

3. A. D Bazykin, Nonlinear dynamics of interacting populations, World Scientific, 1998. https://doi.org/10.1142/2284

4. H. I. Freedman, R. M. Mathsen, Persistence in predator-prey systems with ratio-dependent predator influence, Bull. Math. Biol., 55 (1993), 817–827. https://doi.org/10.1016/S0092-8240(05)80190-9

5. G. F. Gause, N. P. Smaragdova, A. A. Witt, Further studies of interaction between predators and prey, J. Anim. Ecol., 5 (1936), 1–18. https://doi.org/10.2307/1087

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Global solutions near homogeneous steady states in a fully cross-diffusive predator–prey system with density-dependent motion;Zeitschrift für angewandte Mathematik und Physik;2023-11-06