Complex Dynamics in a Singular Delayed Bioeconomic Model with and without Stochastic Fluctuation
A singular delayed biological economic predator-prey system with and without stochastic fluctuation is proposed. The conditions of singularity induced bifurcation are gained, and a state feedback controller is designed to eliminate such bifurcation. Furthermore, saddle-node bifurcation is also showe...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/302494 |
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| _version_ | 1832559022551597056 |
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| author | Xinyou Meng Qingling Zhang |
| author_facet | Xinyou Meng Qingling Zhang |
| author_sort | Xinyou Meng |
| collection | DOAJ |
| description | A singular delayed biological economic predator-prey system with and without stochastic fluctuation is proposed. The conditions of singularity induced bifurcation are gained, and a state feedback controller is designed to eliminate such bifurcation. Furthermore, saddle-node bifurcation is also showed. Next, the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analyzing the distribution of roots of the corresponding characteristic equation, and the hybrid control strategy is used to control the occurrence of Hopf bifurcation. In addition, some explicit formulas determining the spectral densities of the populations and harvest effort are given when the system is considered with stochastic fluctuation. Finally, numerical simulations are illustrated to verify the theoretical results. |
| format | Article |
| id | doaj-art-accfe6aba9ce4f52841d592d7d224a15 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-accfe6aba9ce4f52841d592d7d224a152025-02-03T01:31:02ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/302494302494Complex Dynamics in a Singular Delayed Bioeconomic Model with and without Stochastic FluctuationXinyou Meng0Qingling Zhang1Institute of Systems Science, Northeastern University, Shenyang 110819, ChinaInstitute of Systems Science, Northeastern University, Shenyang 110819, ChinaA singular delayed biological economic predator-prey system with and without stochastic fluctuation is proposed. The conditions of singularity induced bifurcation are gained, and a state feedback controller is designed to eliminate such bifurcation. Furthermore, saddle-node bifurcation is also showed. Next, the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analyzing the distribution of roots of the corresponding characteristic equation, and the hybrid control strategy is used to control the occurrence of Hopf bifurcation. In addition, some explicit formulas determining the spectral densities of the populations and harvest effort are given when the system is considered with stochastic fluctuation. Finally, numerical simulations are illustrated to verify the theoretical results.http://dx.doi.org/10.1155/2015/302494 |
| spellingShingle | Xinyou Meng Qingling Zhang Complex Dynamics in a Singular Delayed Bioeconomic Model with and without Stochastic Fluctuation Discrete Dynamics in Nature and Society |
| title | Complex Dynamics in a Singular Delayed Bioeconomic Model with and without Stochastic Fluctuation |
| title_full | Complex Dynamics in a Singular Delayed Bioeconomic Model with and without Stochastic Fluctuation |
| title_fullStr | Complex Dynamics in a Singular Delayed Bioeconomic Model with and without Stochastic Fluctuation |
| title_full_unstemmed | Complex Dynamics in a Singular Delayed Bioeconomic Model with and without Stochastic Fluctuation |
| title_short | Complex Dynamics in a Singular Delayed Bioeconomic Model with and without Stochastic Fluctuation |
| title_sort | complex dynamics in a singular delayed bioeconomic model with and without stochastic fluctuation |
| url | http://dx.doi.org/10.1155/2015/302494 |
| work_keys_str_mv | AT xinyoumeng complexdynamicsinasingulardelayedbioeconomicmodelwithandwithoutstochasticfluctuation AT qinglingzhang complexdynamicsinasingulardelayedbioeconomicmodelwithandwithoutstochasticfluctuation |