Existence and Global Asymptotical Stability of Periodic Solution for the T-Periodic Logistic System with Time-Varying Generating Operators and T0-Periodic Impulsive Perturbations on Banach Spaces
This paper studies the existence and global asymptotical stability of periodic PC-mild solution for the T-periodic Logistic system with time-varying generating operators and T0-periodic impulsive perturbations on Banach spaces. Two sufficient conditions that guarantee the exponential stability of th...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2008-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2008/524945 |
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| _version_ | 1849403824648749056 |
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| author | JinRong Wang X. Xiang W. Wei Qian Chen |
| author_facet | JinRong Wang X. Xiang W. Wei Qian Chen |
| author_sort | JinRong Wang |
| collection | DOAJ |
| description | This paper studies the existence and global asymptotical stability of periodic PC-mild solution for the T-periodic Logistic system with time-varying generating operators and T0-periodic impulsive perturbations on Banach spaces. Two sufficient conditions that guarantee the exponential stability of the impulsive evolution operator corresponding to homogenous well-posed T-periodic system with time-varying generating operators and T0-periodic impulsive perturbations are given. It is shown that the system have a unique periodic PC-mild solution which is globally asymptotically stable when T and T0 are rational dependent and its period must be nT0 for some n∈N. At last, an example is given for demonstration. |
| format | Article |
| id | doaj-art-96fc646c73f14b3eae34fcfa856b5681 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-96fc646c73f14b3eae34fcfa856b56812025-08-20T03:37:09ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2008-01-01200810.1155/2008/524945524945Existence and Global Asymptotical Stability of Periodic Solution for the T-Periodic Logistic System with Time-Varying Generating Operators and T0-Periodic Impulsive Perturbations on Banach SpacesJinRong Wang0X. Xiang1W. Wei2Qian Chen3Department of Computer, College of Computer Science and Technology, Guizhou University, Guiyang, Guizhou 550025, ChinaDepartment of Mathematics, College of Science, Guizhou University, Guiyang, Guizhou 550025, ChinaDepartment of Mathematics, College of Science, Guizhou University, Guiyang, Guizhou 550025, ChinaDepartment of Electronic Science, College of Electronic Science and Information Technology, Guizhou University, Guiyang, 550025, ChinaThis paper studies the existence and global asymptotical stability of periodic PC-mild solution for the T-periodic Logistic system with time-varying generating operators and T0-periodic impulsive perturbations on Banach spaces. Two sufficient conditions that guarantee the exponential stability of the impulsive evolution operator corresponding to homogenous well-posed T-periodic system with time-varying generating operators and T0-periodic impulsive perturbations are given. It is shown that the system have a unique periodic PC-mild solution which is globally asymptotically stable when T and T0 are rational dependent and its period must be nT0 for some n∈N. At last, an example is given for demonstration.http://dx.doi.org/10.1155/2008/524945 |
| spellingShingle | JinRong Wang X. Xiang W. Wei Qian Chen Existence and Global Asymptotical Stability of Periodic Solution for the T-Periodic Logistic System with Time-Varying Generating Operators and T0-Periodic Impulsive Perturbations on Banach Spaces Discrete Dynamics in Nature and Society |
| title | Existence and Global Asymptotical Stability of Periodic Solution for the T-Periodic Logistic System with Time-Varying Generating Operators and T0-Periodic Impulsive Perturbations on Banach Spaces |
| title_full | Existence and Global Asymptotical Stability of Periodic Solution for the T-Periodic Logistic System with Time-Varying Generating Operators and T0-Periodic Impulsive Perturbations on Banach Spaces |
| title_fullStr | Existence and Global Asymptotical Stability of Periodic Solution for the T-Periodic Logistic System with Time-Varying Generating Operators and T0-Periodic Impulsive Perturbations on Banach Spaces |
| title_full_unstemmed | Existence and Global Asymptotical Stability of Periodic Solution for the T-Periodic Logistic System with Time-Varying Generating Operators and T0-Periodic Impulsive Perturbations on Banach Spaces |
| title_short | Existence and Global Asymptotical Stability of Periodic Solution for the T-Periodic Logistic System with Time-Varying Generating Operators and T0-Periodic Impulsive Perturbations on Banach Spaces |
| title_sort | existence and global asymptotical stability of periodic solution for the t periodic logistic system with time varying generating operators and t0 periodic impulsive perturbations on banach spaces |
| url | http://dx.doi.org/10.1155/2008/524945 |
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