Pattern Formation in a Diffusive Ratio-Dependent Holling-Tanner Predator-Prey Model with Smith Growth
The spatiotemporal dynamics of a diffusive ratio-dependent Holling-Tanner predator-prey model with Smith growth subject to zero-flux boundary condition are investigated analytically and numerically. The asymptotic stability of the positive equilibrium and the existence of Hopf bifurcation around the...
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| Format: | Article |
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Hindawi Limited
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/454209 |
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doaj-e9086393f30a42028724cc85c68eb1802020-11-24T21:55:37ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/454209454209Pattern Formation in a Diffusive Ratio-Dependent Holling-Tanner Predator-Prey Model with Smith GrowthBo Yang0School of Electronic and Information Engineering, Gansu Lianhe University, Lanzhou 730000, ChinaThe spatiotemporal dynamics of a diffusive ratio-dependent Holling-Tanner predator-prey model with Smith growth subject to zero-flux boundary condition are investigated analytically and numerically. The asymptotic stability of the positive equilibrium and the existence of Hopf bifurcation around the positive equilibrium are shown; the conditions of Turing instability are obtained. And with the help of numerical simulations, it is found that the model exhibits complex pattern replication: stripes, spots-stripes mixtures, and spots Turing patterns.http://dx.doi.org/10.1155/2013/454209 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Bo Yang |
| spellingShingle |
Bo Yang Pattern Formation in a Diffusive Ratio-Dependent Holling-Tanner Predator-Prey Model with Smith Growth Discrete Dynamics in Nature and Society |
| author_facet |
Bo Yang |
| author_sort |
Bo Yang |
| title |
Pattern Formation in a Diffusive Ratio-Dependent Holling-Tanner Predator-Prey Model with Smith Growth |
| title_short |
Pattern Formation in a Diffusive Ratio-Dependent Holling-Tanner Predator-Prey Model with Smith Growth |
| title_full |
Pattern Formation in a Diffusive Ratio-Dependent Holling-Tanner Predator-Prey Model with Smith Growth |
| title_fullStr |
Pattern Formation in a Diffusive Ratio-Dependent Holling-Tanner Predator-Prey Model with Smith Growth |
| title_full_unstemmed |
Pattern Formation in a Diffusive Ratio-Dependent Holling-Tanner Predator-Prey Model with Smith Growth |
| title_sort |
pattern formation in a diffusive ratio-dependent holling-tanner predator-prey model with smith growth |
| publisher |
Hindawi Limited |
| series |
Discrete Dynamics in Nature and Society |
| issn |
1026-0226 1607-887X |
| publishDate |
2013-01-01 |
| description |
The spatiotemporal dynamics of a diffusive ratio-dependent Holling-Tanner predator-prey model with Smith growth subject to zero-flux boundary condition are investigated analytically and numerically. The asymptotic stability of the positive equilibrium and the existence of Hopf bifurcation around the positive equilibrium are shown; the conditions of Turing instability are obtained. And with the help of numerical simulations, it is found that the model exhibits complex pattern replication: stripes, spots-stripes mixtures, and spots Turing patterns. |
| url |
http://dx.doi.org/10.1155/2013/454209 |
| work_keys_str_mv |
AT boyang patternformationinadiffusiveratiodependenthollingtannerpredatorpreymodelwithsmithgrowth |
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