Turing–Hopf bifurcations in a predator–prey model with herd behavior, quadratic mortality and prey-taxis

Xia Liu, Tonghua Zhang, Xinzhu Meng and Tongqian Zhang

Physica A: Statistical Mechanics and its Applications, 2018, vol. 496, issue C, 446-460

Abstract: In this paper, we propose a predator–prey model with herd behavior and prey-taxis. Then, we analyze the stability and bifurcation of the positive equilibrium of the model subject to the homogeneous Neumann boundary condition. By using an abstract bifurcation theory and taking prey-tactic sensitivity coefficient as the bifurcation parameter, we obtain a branch of stable nonconstant solutions bifurcating from the positive equilibrium. Our results show that prey-taxis can yield the occurrence of spatial patterns.

Keywords: Turing pattern; Turing–Hopf bifurcation; Reaction–diffusion equations; Herd behavior; Diffusion (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437118300062
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:496:y:2018:i:c:p:446-460

DOI: 10.1016/j.physa.2018.01.006

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().