Dynamical Analysis for the Hybrid Network Model of Delayed Predator-Prey Gompertz Systems with Impulsive Diffusion between Two Patches
In this paper, we consider a hybrid network model of delayed predator-prey Gompertz systems with impulsive diffusion between two patches, in which the patches represent nodes of the network such that the prey population interacts locally in each patch and diffusion occurs along the edges connecting...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2020-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/5041761 |
| id |
doaj-54ce637d141c42db86fc3ce859dd43c6 |
|---|---|
| record_format |
Article |
| spelling |
doaj-54ce637d141c42db86fc3ce859dd43c62020-11-25T03:54:05ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/50417615041761Dynamical Analysis for the Hybrid Network Model of Delayed Predator-Prey Gompertz Systems with Impulsive Diffusion between Two PatchesLi Xiang0Yurong Zhang1Dan Zhang2Zhichun Yang3Lingzhi Huang4Computer College, Civil Aviation Flight University of China, Guanghan 618307, ChinaKey Laboratory for Optimization and Control of Ministry of Education, Mathematical College, Chongqing Normal University, Chongqing 401331, ChinaKey Laboratory for Optimization and Control of Ministry of Education, Mathematical College, Chongqing Normal University, Chongqing 401331, ChinaKey Laboratory for Optimization and Control of Ministry of Education, Mathematical College, Chongqing Normal University, Chongqing 401331, ChinaKey Laboratory for Optimization and Control of Ministry of Education, Mathematical College, Chongqing Normal University, Chongqing 401331, ChinaIn this paper, we consider a hybrid network model of delayed predator-prey Gompertz systems with impulsive diffusion between two patches, in which the patches represent nodes of the network such that the prey population interacts locally in each patch and diffusion occurs along the edges connecting the nodes. Using the discrete dynamical system determined by the stroboscopic map which has a globally stable positive fixed point, we obtain the global attractive condition of predator-extinction periodic solution for the network system. Furthermore, by employing the theory of delay functional and impulsive differential equation, we obtain sufficient condition with time delay for the permanence of the network.http://dx.doi.org/10.1155/2020/5041761 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Li Xiang Yurong Zhang Dan Zhang Zhichun Yang Lingzhi Huang |
| spellingShingle |
Li Xiang Yurong Zhang Dan Zhang Zhichun Yang Lingzhi Huang Dynamical Analysis for the Hybrid Network Model of Delayed Predator-Prey Gompertz Systems with Impulsive Diffusion between Two Patches Discrete Dynamics in Nature and Society |
| author_facet |
Li Xiang Yurong Zhang Dan Zhang Zhichun Yang Lingzhi Huang |
| author_sort |
Li Xiang |
| title |
Dynamical Analysis for the Hybrid Network Model of Delayed Predator-Prey Gompertz Systems with Impulsive Diffusion between Two Patches |
| title_short |
Dynamical Analysis for the Hybrid Network Model of Delayed Predator-Prey Gompertz Systems with Impulsive Diffusion between Two Patches |
| title_full |
Dynamical Analysis for the Hybrid Network Model of Delayed Predator-Prey Gompertz Systems with Impulsive Diffusion between Two Patches |
| title_fullStr |
Dynamical Analysis for the Hybrid Network Model of Delayed Predator-Prey Gompertz Systems with Impulsive Diffusion between Two Patches |
| title_full_unstemmed |
Dynamical Analysis for the Hybrid Network Model of Delayed Predator-Prey Gompertz Systems with Impulsive Diffusion between Two Patches |
| title_sort |
dynamical analysis for the hybrid network model of delayed predator-prey gompertz systems with impulsive diffusion between two patches |
| publisher |
Hindawi Limited |
| series |
Discrete Dynamics in Nature and Society |
| issn |
1026-0226 1607-887X |
| publishDate |
2020-01-01 |
| description |
In this paper, we consider a hybrid network model of delayed predator-prey Gompertz systems with impulsive diffusion between two patches, in which the patches represent nodes of the network such that the prey population interacts locally in each patch and diffusion occurs along the edges connecting the nodes. Using the discrete dynamical system determined by the stroboscopic map which has a globally stable positive fixed point, we obtain the global attractive condition of predator-extinction periodic solution for the network system. Furthermore, by employing the theory of delay functional and impulsive differential equation, we obtain sufficient condition with time delay for the permanence of the network. |
| url |
http://dx.doi.org/10.1155/2020/5041761 |
| work_keys_str_mv |
AT lixiang dynamicalanalysisforthehybridnetworkmodelofdelayedpredatorpreygompertzsystemswithimpulsivediffusionbetweentwopatches AT yurongzhang dynamicalanalysisforthehybridnetworkmodelofdelayedpredatorpreygompertzsystemswithimpulsivediffusionbetweentwopatches AT danzhang dynamicalanalysisforthehybridnetworkmodelofdelayedpredatorpreygompertzsystemswithimpulsivediffusionbetweentwopatches AT zhichunyang dynamicalanalysisforthehybridnetworkmodelofdelayedpredatorpreygompertzsystemswithimpulsivediffusionbetweentwopatches AT lingzhihuang dynamicalanalysisforthehybridnetworkmodelofdelayedpredatorpreygompertzsystemswithimpulsivediffusionbetweentwopatches |
| _version_ |
1715091211516116992 |