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http://dx.doi.org/10.4134/BKMS.2015.52.4.1113

SPIRAL WAVE GENERATION IN A DIFFUSIVE PREDATOR-PREY MODEL WITH TWO TIME DELAYS  

GAN, WENZHEN (SCHOOL OF MATHEMATICS AND PHYSICS JIANGSU UNIVERSITY OF TECHNOLOGY)
ZHU, PENG (SCHOOL OF MATHEMATICS AND PHYSICS JIANGSU UNIVERSITY OF TECHNOLOGY)
Publication Information
Bulletin of the Korean Mathematical Society / v.52, no.4, 2015 , pp. 1113-1122 More about this Journal
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;
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