Impulsive Control on Seasonally Perturbed General Holling Type Two-Prey One-Predator Model
We investigate the dynamical behaviors of two-prey one-predator model with general Holling type functional responses. The effect of seasonal perturbation on the model has been discussed analytically as well as numerically. The periodic fluctuation is considered in prey growth rate and the predator m...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/9268257 |
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| author | Chandrima Banerjee Pritha Das |
| author_facet | Chandrima Banerjee Pritha Das |
| author_sort | Chandrima Banerjee |
| collection | DOAJ |
| description | We investigate the dynamical behaviors of two-prey one-predator model with general Holling type functional responses. The effect of seasonal perturbation on the model has been discussed analytically as well as numerically. The periodic fluctuation is considered in prey growth rate and the predator mortality rate of the model. The impulsive effects involving biological and chemical control strategy, periodic releasing of natural enemies, and spraying pesticide at different fixed times are introduced in the model with seasonal perturbation. We derive the conditions of stability for impulsive system using Floquet theory, small amplitude perturbation skills. A local asymptotically stable prey (pest) eradicated periodic solution is obtained when the impulsive period is less than some critical value. Numerical simulations of the model with and without seasonal disturbances exhibit different dynamics. Also we simulate numerically the model involving seasonal perturbations without impulse and with impulse. Finally, concluding remarks are given. |
| format | Article |
| id | doaj-art-2afef639300548cb8b5f64911bcbf53d |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-2afef639300548cb8b5f64911bcbf53d2025-02-03T06:07:08ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/92682579268257Impulsive Control on Seasonally Perturbed General Holling Type Two-Prey One-Predator ModelChandrima Banerjee0Pritha Das1Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal 711103, IndiaDepartment of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal 711103, IndiaWe investigate the dynamical behaviors of two-prey one-predator model with general Holling type functional responses. The effect of seasonal perturbation on the model has been discussed analytically as well as numerically. The periodic fluctuation is considered in prey growth rate and the predator mortality rate of the model. The impulsive effects involving biological and chemical control strategy, periodic releasing of natural enemies, and spraying pesticide at different fixed times are introduced in the model with seasonal perturbation. We derive the conditions of stability for impulsive system using Floquet theory, small amplitude perturbation skills. A local asymptotically stable prey (pest) eradicated periodic solution is obtained when the impulsive period is less than some critical value. Numerical simulations of the model with and without seasonal disturbances exhibit different dynamics. Also we simulate numerically the model involving seasonal perturbations without impulse and with impulse. Finally, concluding remarks are given.http://dx.doi.org/10.1155/2016/9268257 |
| spellingShingle | Chandrima Banerjee Pritha Das Impulsive Control on Seasonally Perturbed General Holling Type Two-Prey One-Predator Model Discrete Dynamics in Nature and Society |
| title | Impulsive Control on Seasonally Perturbed General Holling Type Two-Prey One-Predator Model |
| title_full | Impulsive Control on Seasonally Perturbed General Holling Type Two-Prey One-Predator Model |
| title_fullStr | Impulsive Control on Seasonally Perturbed General Holling Type Two-Prey One-Predator Model |
| title_full_unstemmed | Impulsive Control on Seasonally Perturbed General Holling Type Two-Prey One-Predator Model |
| title_short | Impulsive Control on Seasonally Perturbed General Holling Type Two-Prey One-Predator Model |
| title_sort | impulsive control on seasonally perturbed general holling type two prey one predator model |
| url | http://dx.doi.org/10.1155/2016/9268257 |
| work_keys_str_mv | AT chandrimabanerjee impulsivecontrolonseasonallyperturbedgeneralhollingtypetwopreyonepredatormodel AT prithadas impulsivecontrolonseasonallyperturbedgeneralhollingtypetwopreyonepredatormodel |