Complex Behavior Analysis of a Fractional-Order Land Dynamical Model with Holling-II Type Land Reclamation Rate on Time Delay
In this paper, a fractional-order land model with Holling-II type transformation rate and time delay is investigated. First of all, the variable-order fractional derivative is defined in the Caputo type. Second, by applying time delay as the bifurcation parameter, some criteria to determine the stab...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/1053283 |
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| author | Li Wu Zhouhong Li Yuan Zhang Binggeng Xie |
| author_facet | Li Wu Zhouhong Li Yuan Zhang Binggeng Xie |
| author_sort | Li Wu |
| collection | DOAJ |
| description | In this paper, a fractional-order land model with Holling-II type transformation rate and time delay is investigated. First of all, the variable-order fractional derivative is defined in the Caputo type. Second, by applying time delay as the bifurcation parameter, some criteria to determine the stability and Hopf bifurcation of the model are presented. It turns out that the time delay can drive the model to be oscillatory, even when its steady state is stable. Finally, one numerical example is proposed to justify the validity of theoretical analysis. These results may provide insights to the development of a reasonable strategy to control land-use change. |
| format | Article |
| id | doaj-art-849045c2d83540ed95e59cf083e3e4ee |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-849045c2d83540ed95e59cf083e3e4ee2025-02-03T06:46:54ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/10532831053283Complex Behavior Analysis of a Fractional-Order Land Dynamical Model with Holling-II Type Land Reclamation Rate on Time DelayLi Wu0Zhouhong Li1Yuan Zhang2Binggeng Xie3College of Resources and Environmental Sciences, Hunan Normal University, Changsha, Hunan 410028, ChinaDepartment of Mathematics, Yuxi Normal University, Yuxi, Yunnan 653100, ChinaDepartment of Mathematics, Yuxi Normal University, Yuxi, Yunnan 653100, ChinaCollege of Resources and Environmental Sciences, Hunan Normal University, Changsha, Hunan 410028, ChinaIn this paper, a fractional-order land model with Holling-II type transformation rate and time delay is investigated. First of all, the variable-order fractional derivative is defined in the Caputo type. Second, by applying time delay as the bifurcation parameter, some criteria to determine the stability and Hopf bifurcation of the model are presented. It turns out that the time delay can drive the model to be oscillatory, even when its steady state is stable. Finally, one numerical example is proposed to justify the validity of theoretical analysis. These results may provide insights to the development of a reasonable strategy to control land-use change.http://dx.doi.org/10.1155/2020/1053283 |
| spellingShingle | Li Wu Zhouhong Li Yuan Zhang Binggeng Xie Complex Behavior Analysis of a Fractional-Order Land Dynamical Model with Holling-II Type Land Reclamation Rate on Time Delay Discrete Dynamics in Nature and Society |
| title | Complex Behavior Analysis of a Fractional-Order Land Dynamical Model with Holling-II Type Land Reclamation Rate on Time Delay |
| title_full | Complex Behavior Analysis of a Fractional-Order Land Dynamical Model with Holling-II Type Land Reclamation Rate on Time Delay |
| title_fullStr | Complex Behavior Analysis of a Fractional-Order Land Dynamical Model with Holling-II Type Land Reclamation Rate on Time Delay |
| title_full_unstemmed | Complex Behavior Analysis of a Fractional-Order Land Dynamical Model with Holling-II Type Land Reclamation Rate on Time Delay |
| title_short | Complex Behavior Analysis of a Fractional-Order Land Dynamical Model with Holling-II Type Land Reclamation Rate on Time Delay |
| title_sort | complex behavior analysis of a fractional order land dynamical model with holling ii type land reclamation rate on time delay |
| url | http://dx.doi.org/10.1155/2020/1053283 |
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