On the Dynamical Behavior of Toxic-Phytoplankton-Zooplankton Model with Delay
A toxin producing phytoplankton-zooplankton model with inhibitory exponential substrate and time delay has been formulated and analyzed. Since the liberation of toxic substances by phytoplankton species is not an instantaneous process but is mediated by some time lag required for maturity of the spe...
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| Main Authors: | , , |
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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/10.1155/2015/756315 |
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| _version_ | 1832565268457455616 |
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| author | Mehbuba Rehim Weixin Wu Ahmadjan Muhammadhaji |
| author_facet | Mehbuba Rehim Weixin Wu Ahmadjan Muhammadhaji |
| author_sort | Mehbuba Rehim |
| collection | DOAJ |
| description | A toxin producing phytoplankton-zooplankton model with inhibitory exponential substrate and time delay has been formulated and analyzed. Since the liberation of toxic substances by phytoplankton species is not an instantaneous process but is mediated by some time lag required for maturity of the species and the zooplankton mortality due to the toxic phytoplankton bloom occurs after some time laps of the bloom of toxic phytoplankton, we induced a discrete time delay to both of the consume response function and distribution of toxic substance term. Furthermore, based on the fact that the predation rate decreases at large toxic-phytoplankton density, the system is modelled via a Tissiet type functional response. We study the dynamical behaviour and investigate the conditions to guarantee the coexistence of two species. Analytical methods and numerical simulations are used to obtain information about the qualitative behaviour of the models. |
| format | Article |
| id | doaj-art-e47ab02bc0a94ca78bba6ef184816be4 |
| 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-e47ab02bc0a94ca78bba6ef184816be42025-02-03T01:08:56ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/756315756315On the Dynamical Behavior of Toxic-Phytoplankton-Zooplankton Model with DelayMehbuba Rehim0Weixin Wu1Ahmadjan Muhammadhaji2College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, ChinaA toxin producing phytoplankton-zooplankton model with inhibitory exponential substrate and time delay has been formulated and analyzed. Since the liberation of toxic substances by phytoplankton species is not an instantaneous process but is mediated by some time lag required for maturity of the species and the zooplankton mortality due to the toxic phytoplankton bloom occurs after some time laps of the bloom of toxic phytoplankton, we induced a discrete time delay to both of the consume response function and distribution of toxic substance term. Furthermore, based on the fact that the predation rate decreases at large toxic-phytoplankton density, the system is modelled via a Tissiet type functional response. We study the dynamical behaviour and investigate the conditions to guarantee the coexistence of two species. Analytical methods and numerical simulations are used to obtain information about the qualitative behaviour of the models.http://dx.doi.org/10.1155/2015/756315 |
| spellingShingle | Mehbuba Rehim Weixin Wu Ahmadjan Muhammadhaji On the Dynamical Behavior of Toxic-Phytoplankton-Zooplankton Model with Delay Discrete Dynamics in Nature and Society |
| title | On the Dynamical Behavior of Toxic-Phytoplankton-Zooplankton Model with Delay |
| title_full | On the Dynamical Behavior of Toxic-Phytoplankton-Zooplankton Model with Delay |
| title_fullStr | On the Dynamical Behavior of Toxic-Phytoplankton-Zooplankton Model with Delay |
| title_full_unstemmed | On the Dynamical Behavior of Toxic-Phytoplankton-Zooplankton Model with Delay |
| title_short | On the Dynamical Behavior of Toxic-Phytoplankton-Zooplankton Model with Delay |
| title_sort | on the dynamical behavior of toxic phytoplankton zooplankton model with delay |
| url | http://dx.doi.org/10.1155/2015/756315 |
| work_keys_str_mv | AT mehbubarehim onthedynamicalbehavioroftoxicphytoplanktonzooplanktonmodelwithdelay AT weixinwu onthedynamicalbehavioroftoxicphytoplanktonzooplanktonmodelwithdelay AT ahmadjanmuhammadhaji onthedynamicalbehavioroftoxicphytoplanktonzooplanktonmodelwithdelay |