Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 22, Issue -, Pages 54-65Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2014.07.013
Keywords
Spatiotemporal patterns; Turing bifurcation; Spatiotemporal delay; Multiple scale method; Amplitude equations
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Funding
- National Natural Science Foundation of China [11032009, 11272236]
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Employing the theories of Turing bifurcation in the partial differential equations, we investigate the dynamical behavior of a single species reaction-diffusion model with spatiotemporal delay. The linear stability and the conditions for the occurrence of Turing bifurcation in this model are obtained. Moreover, the amplitude equations which represent different spatiotemporal patterns are also obtained near the Turing bifurcation point by using multiple scale method. In Turing space, it is found that the spatiotemporal distributions of the density of this researched species have spots pattern and stripes pattern. Finally, some numerical simulations corresponding to the different spatiotemporal patterns are given to verify our theoretical analysis. (C) 2014 Elsevier Ltd. All rights reserved.
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