Spiral wave generation in a diffusive predator-prey model with two time delays
Bull. Korean Math. Soc. 2015 Vol. 52, No. 4, 1113-1122
https://doi.org/10.4134/BKMS.2015.52.4.1113
Published online July 31, 2015
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
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