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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832567541337161728 |
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| author | Lei Zhang Zhibin Li |
| author_facet | Lei Zhang Zhibin Li |
| author_sort | Lei Zhang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b34100facf45455b86f872671efd2af9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b34100facf45455b86f872671efd2af92025-02-03T01:01:14ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/675378675378Spatial Complexity of a Predator-Prey Model with Holling-Type ResponseLei Zhang0Zhibin Li1Computer Science and Technology Department, East China Normal University, Shanghai 200241, ChinaComputer Science and Technology Department, East China Normal University, Shanghai 200241, ChinaWe 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.http://dx.doi.org/10.1155/2014/675378 |
| spellingShingle | Lei Zhang Zhibin Li Spatial Complexity of a Predator-Prey Model with Holling-Type Response Abstract and Applied Analysis |
| title | Spatial Complexity of a Predator-Prey Model with Holling-Type Response |
| title_full | Spatial Complexity of a Predator-Prey Model with Holling-Type Response |
| title_fullStr | Spatial Complexity of a Predator-Prey Model with Holling-Type Response |
| title_full_unstemmed | Spatial Complexity of a Predator-Prey Model with Holling-Type Response |
| title_short | Spatial Complexity of a Predator-Prey Model with Holling-Type Response |
| title_sort | spatial complexity of a predator prey model with holling type response |
| url | http://dx.doi.org/10.1155/2014/675378 |
| work_keys_str_mv | AT leizhang spatialcomplexityofapredatorpreymodelwithhollingtyperesponse AT zhibinli spatialcomplexityofapredatorpreymodelwithhollingtyperesponse |