Spatial Complexity of a Predator-Prey Model with Holling-Type Response
We focus on a spatially extended Holling-type IV predator-prey model that contains some important factors, such as noise (random fluctuations), external periodic forcing, and diffusion processes. By a brief stability and bifurcation analysis, we arrive at the Hopf and Turing bifurcation surface and...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/675378 |
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| Summary: | We focus on a spatially extended Holling-type IV
predator-prey model that contains some important factors, such as noise
(random fluctuations), external periodic forcing, and diffusion
processes. By a brief stability and bifurcation analysis, we arrive
at the Hopf and Turing bifurcation surface and derive the symbolic
conditions for Hopf and Turing bifurcation on the spatial domain.
Based on the stability and bifurcation analysis, we obtain spiral
pattern formation via numerical simulation. Additionally, we study the
model with a color noise and external periodic forcing. From the
numerical results, we know that noise or external periodic forcing
can induce instability and enhance the oscillation of the species
density, and the cooperation between noise and external periodic
forces inherent to the deterministic dynamics of periodically driven
models gives rise to the appearance of a rich transport
phenomenology. Our results show that modeling by reaction-diffusion
equations is an appropriate tool for investigating fundamental
mechanisms of complex spatiotemporal dynamics. |
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| ISSN: | 1085-3375 1687-0409 |