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: JinRong Wang, X. Xiang, W. Wei, Qian Chen
Format: Article
Language:English
Published: Wiley 2008-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2008/524945
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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.
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institution Kabale University
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publisher Wiley
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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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AT xxiang existenceandglobalasymptoticalstabilityofperiodicsolutionforthetperiodiclogisticsystemwithtimevaryinggeneratingoperatorsandt0periodicimpulsiveperturbationsonbanachspaces
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