Journal
APPLIED MATHEMATICAL MODELLING
Volume 40, Issue 7-8, Pages 4765-4777Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2015.12.003
Keywords
Herbivore-plant system; Hopf bifurcation; Periodic outbreak
Funding
- National Natural Science Foundation of China [11501338, 11331009, 11171314, 11301490]
- China Postdoctoral Science Foundation [2014M561210]
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Empirical studies indicate that many populations of herbivorous insects exhibit periodic outbreaks, but the intrinsic causes of this behavior are not well understood. Thus, in this study, we investigated a herbivore-plant system with time delay based on reaction diffusion equations. Using normal formal theory and the center manifold theorem for partial functional differential equations, we show that this model exhibits the property of Hopf bifurcation. Therefore, interactions between the time delay and spatial diffusion will induce periodic outbreaks in herbivore populations. These results may suggest a new mechanism for herbivore outbreaks. (C) 2015 Elsevier Inc. All rights reserved.
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