Stability, Hopf bifurcations and spatial patterns in a delayed diffusive predator–prey model with herd behavior

Xiaosong Tang and Yongli Song

Applied Mathematics and Computation, 2015, vol. 254, issue C, 375-391

Abstract: In this paper, we consider a delayed diffusive predator–prey model with herd behavior. Firstly, by choosing the appropriate bifurcation parameter, the stability of the positive equilibria and the existence of Hopf bifurcations, induced by diffusion and delay respectively, are investigated by analyzing the corresponding characteristic equation. Then, applying the normal form theory and the center manifold argument for partial functional differential equations, the formula determining the properties of the Hopf bifurcation are obtained. Furthermore, the instability of the Hopf bifurcation leads to the emergence of spatial patterns. Finally, some numerical simulations are also carried out to illustrate and expand the theoretical results.

Keywords: Predator–prey model; Herd behavior; Delay; Diffusion; Hopf bifurcation; Pattern formation (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300314018049
Full text for ScienceDirect subscribers only

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:apmaco:v:254:y:2015:i:c:p:375-391

DOI: 10.1016/j.amc.2014.12.143

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().