Dynamical Behavior for a Food-Chain Model with Impulsive Harvest and Digest Delay
We investigate the dynamics of a food-chain system with digest delay and periodic harvesting for the prey. By using the comparison theorem, small amplitude skills in the impulsive differential equation, and a special qualitative analysis method in the delay differential equation, we prove that there...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/168571 |
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| _version_ | 1849397146895253504 |
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| author | Baodan Tian Shouming Zhong Ning Chen Yanhong Qiu |
| author_facet | Baodan Tian Shouming Zhong Ning Chen Yanhong Qiu |
| author_sort | Baodan Tian |
| collection | DOAJ |
| description | We investigate the dynamics of a food-chain system with digest delay and periodic harvesting for the prey. By using the comparison theorem, small amplitude skills in the impulsive differential equation, and a special qualitative analysis method in the delay differential equation, we prove that there exists a predators-eradication periodic solution which is globally attractive and show that the pest population can be controlled under the economic threshold level and the system can be uniformly permanent when the harvest period T is long enough or the harvesting rate δ is not too large. Furthermore, we perform a series of numerical simulations to display the effects of the digest delay and periodic harvesting on the dynamic behavior of the food-chain system. |
| format | Article |
| id | doaj-art-af6d856ea8c84d99a893043b87ec7554 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-af6d856ea8c84d99a893043b87ec75542025-08-20T03:39:06ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/168571168571Dynamical Behavior for a Food-Chain Model with Impulsive Harvest and Digest DelayBaodan Tian0Shouming Zhong1Ning Chen2Yanhong Qiu3School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, ChinaSchool of Science, Southwest University of Science and Technology, Mianyang 621010, ChinaSchool of Science, Southwest University of Science and Technology, Mianyang 621010, ChinaWe investigate the dynamics of a food-chain system with digest delay and periodic harvesting for the prey. By using the comparison theorem, small amplitude skills in the impulsive differential equation, and a special qualitative analysis method in the delay differential equation, we prove that there exists a predators-eradication periodic solution which is globally attractive and show that the pest population can be controlled under the economic threshold level and the system can be uniformly permanent when the harvest period T is long enough or the harvesting rate δ is not too large. Furthermore, we perform a series of numerical simulations to display the effects of the digest delay and periodic harvesting on the dynamic behavior of the food-chain system.http://dx.doi.org/10.1155/2014/168571 |
| spellingShingle | Baodan Tian Shouming Zhong Ning Chen Yanhong Qiu Dynamical Behavior for a Food-Chain Model with Impulsive Harvest and Digest Delay Journal of Applied Mathematics |
| title | Dynamical Behavior for a Food-Chain Model with Impulsive Harvest and Digest Delay |
| title_full | Dynamical Behavior for a Food-Chain Model with Impulsive Harvest and Digest Delay |
| title_fullStr | Dynamical Behavior for a Food-Chain Model with Impulsive Harvest and Digest Delay |
| title_full_unstemmed | Dynamical Behavior for a Food-Chain Model with Impulsive Harvest and Digest Delay |
| title_short | Dynamical Behavior for a Food-Chain Model with Impulsive Harvest and Digest Delay |
| title_sort | dynamical behavior for a food chain model with impulsive harvest and digest delay |
| url | http://dx.doi.org/10.1155/2014/168571 |
| work_keys_str_mv | AT baodantian dynamicalbehaviorforafoodchainmodelwithimpulsiveharvestanddigestdelay AT shoumingzhong dynamicalbehaviorforafoodchainmodelwithimpulsiveharvestanddigestdelay AT ningchen dynamicalbehaviorforafoodchainmodelwithimpulsiveharvestanddigestdelay AT yanhongqiu dynamicalbehaviorforafoodchainmodelwithimpulsiveharvestanddigestdelay |