Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2015; 52(4): 1113-1122

Printed July 31, 2015

https://doi.org/10.4134/BKMS.2015.52.4.1113

Copyright © The Korean Mathematical Society.

Spiral wave generation in a diffusive predator-prey model with two time delays

Wenzhen Gan and Peng Zhu

Jiangsu University of Technology, Jiangsu University of Technology

Abstract

This paper is concerned with the pattern formation of a diffusive predator-prey model with two time delays. Based upon an analysis of Hopf bifurcation, we demonstrate that time delays can induce spatial patterns under some conditions. Moreover, by use of a series of numerical simulations, we show that the type of spatial patterns is the spiral wave. Finally, we demonstrate that the spiral wave is asymptotically stable.

Keywords: time delay, spiral wave, spatial pattern, Hopf bifurcation

MSC numbers: 35B35, 35B40, 92D40