Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 67, Issue 10, Pages 1978-1997Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2014.04.015
Keywords
Pattern formation; Normal form; Dynamical classification; Steady state; Periodic solution
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Funding
- State Key Program of National Natural Science Foundation of China [11032009]
- Scientific Research Foundation for the Returned Overseas Chinese Scholars
- Program for New Century Excellent Talents in University [NCET-11-0385]
- Natural Science and Engineering Council of Canada [227048-2010]
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Spatiotemporal dynamics in a ratio-dependent predator-prey model with diffusion is studied by analytical methods. Normal forms associated with codimension-two Hopf-Turing bifurcation are derived, which can be used to understand and classify the spatiotemporal dynamics of the model for values of parameters close to the Hopf-Turing bifurcation point. In the vicinity of this degenerate point, a wealth of complex spatiotemporal dynamics are observed. Our theoretical results are confirmed by numerical simulations. (C) 2014 Elsevier Ltd. All rights reserved.
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