Seasonally Perturbed Prey-Predator Ecological System with the Beddington-DeAngelis Functional Response
On the basis of the theories and methods of ecology and ordinary differential equation, a seasonally perturbed prey-predator system with the Beddington-DeAngelis functional response is studied analytically and numerically. Mathematical theoretical works have been pursuing the investigation of unifor...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/150359 |
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| _version_ | 1849398995105873920 |
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| author | Hengguo Yu Min Zhao |
| author_facet | Hengguo Yu Min Zhao |
| author_sort | Hengguo Yu |
| collection | DOAJ |
| description | On the basis of the theories and methods of ecology and ordinary differential equation, a seasonally perturbed prey-predator system with the Beddington-DeAngelis functional response is studied analytically and numerically. Mathematical theoretical works have been pursuing the investigation of uniformly persistent, which depicts the threshold expression of some critical parameters. Numerical analysis indicates that the seasonality has a strong effect on the dynamical complexity and species biomass using bifurcation diagrams and Poincaré sections. The results show that the seasonality in three different parameters can give rise to rich and complex dynamical behaviors. In addition, the largest Lyapunov exponents are computed. This computation further confirms the existence of chaotic behavior and the accuracy of numerical simulation. All these results are expected to be of use in the study of the dynamic complexity of ecosystems. |
| format | Article |
| id | doaj-art-a44df961cf9141fa8fc2dfe35ce146b0 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-a44df961cf9141fa8fc2dfe35ce146b02025-08-20T03:38:26ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/150359150359Seasonally Perturbed Prey-Predator Ecological System with the Beddington-DeAngelis Functional ResponseHengguo Yu0Min Zhao1School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaSchool of Life and Environmental Science, Wenzhou University, Wenzhou, Zhejiang 325027, ChinaOn the basis of the theories and methods of ecology and ordinary differential equation, a seasonally perturbed prey-predator system with the Beddington-DeAngelis functional response is studied analytically and numerically. Mathematical theoretical works have been pursuing the investigation of uniformly persistent, which depicts the threshold expression of some critical parameters. Numerical analysis indicates that the seasonality has a strong effect on the dynamical complexity and species biomass using bifurcation diagrams and Poincaré sections. The results show that the seasonality in three different parameters can give rise to rich and complex dynamical behaviors. In addition, the largest Lyapunov exponents are computed. This computation further confirms the existence of chaotic behavior and the accuracy of numerical simulation. All these results are expected to be of use in the study of the dynamic complexity of ecosystems.http://dx.doi.org/10.1155/2012/150359 |
| spellingShingle | Hengguo Yu Min Zhao Seasonally Perturbed Prey-Predator Ecological System with the Beddington-DeAngelis Functional Response Discrete Dynamics in Nature and Society |
| title | Seasonally Perturbed Prey-Predator Ecological System with the Beddington-DeAngelis Functional Response |
| title_full | Seasonally Perturbed Prey-Predator Ecological System with the Beddington-DeAngelis Functional Response |
| title_fullStr | Seasonally Perturbed Prey-Predator Ecological System with the Beddington-DeAngelis Functional Response |
| title_full_unstemmed | Seasonally Perturbed Prey-Predator Ecological System with the Beddington-DeAngelis Functional Response |
| title_short | Seasonally Perturbed Prey-Predator Ecological System with the Beddington-DeAngelis Functional Response |
| title_sort | seasonally perturbed prey predator ecological system with the beddington deangelis functional response |
| url | http://dx.doi.org/10.1155/2012/150359 |
| work_keys_str_mv | AT hengguoyu seasonallyperturbedpreypredatorecologicalsystemwiththebeddingtondeangelisfunctionalresponse AT minzhao seasonallyperturbedpreypredatorecologicalsystemwiththebeddingtondeangelisfunctionalresponse |