scholarly journals Global asymptotic stability in an almost-periodic Lotka-Volterra system

1986 ◽  
Vol 27 (3) ◽  
pp. 346-360 ◽  
Author(s):  
K. Gopalsamy
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Volterra System ◽  
Periodic Coefficients ◽  
Globally Asymptotically Stable

AbstractSufficient conditions are obtained for the existence of a globally asymptotically stable strictly positive (componentwise) almost-periodic solution of a Lotka-Volterra system with almost periodic coefficients.

scholarly journals Global asymptotic stability in a periodic Lotka-Volterra system

1985 ◽  
Vol 27 (1) ◽  
pp. 66-72 ◽  
Author(s):  
K. Gopalsamy
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Stable Periodic Solution ◽  
Volterra System ◽  
Periodic Coefficients ◽  
Globally Asymptotically Stable ◽  
Stable Periodic

AbstractA set of easily verifiable sufficient conditions are obtained for the existence of a globally asymptotically stable periodic solution in a Lotka-Volterra system with periodic coefficients.

THE STABILITY AND ALMOST PERIODIC SOLUTION FOR GENERALIZED LOGISTIC ALMOST PERIODIC SYSTEM WITH DELAYS

2011 ◽  
Vol 04 (03) ◽  
pp. 313-328 ◽  
Author(s):  
XIANGLAI ZHUO
Keyword(s):  
Periodic Solution ◽  
Periodic System ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Computational Techniques ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Globally Asymptotically Stable ◽  
Discrete Delays ◽  
The Stability

The stability and almost periodic solution for generalized logistic almost periodic system with infinite and discrete delays is considered. Some sufficient conditions for the boundedness of the system are obtained to guarantee that the system is globally asymptotically stable. We also show that the almost periodic system has a unique globally asymptotically stable strictly positive almost periodic solution by using the almost periodic functional Hull theory and new computational techniques. Furthermore, some recent results are improved, and an open question is answered.

scholarly journals Stability Analysis of Three-Species Almost Periodic Competition Models with Grazing Rates and Diffusions

2011 ◽  
Vol 2011 ◽  
pp. 1-14
Author(s):  
Chang-you Wang ◽  
Rui-fang Wang ◽  
Ming Yi ◽  
Rui Li
Keyword(s):  
Periodic Solution ◽  
Upper And Lower Solutions ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Almost Periodic Solution ◽  
Species Competition ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Globally Asymptotically Stable ◽  
Positive Space

Almost periodic solution of a three-species competition system with grazing rates and diffusions is investigated. By using the method of upper and lower solutions and Schauder fixed point theorem as well as Lyapunov stability theory, we give sufficient conditions to ensure the existence and globally asymptotically stable for the strictly positive space homogenous almost periodic solution, which extend and include corresponding results obtained by Q. C. Lin (1999), F. D. Chen and X. X. Chen (2003), and Y. Q. Liu, S. L, Xie, and Z. D. Xie (1996).

scholarly journals ANALYSIS OF GLOBAL ASYMPTOTIC STABILITY AND PSEUDO ALMOST PERIODIC SOLUTION OF A CLASS OF CHAOTIC NEURAL NETWORKS

2013 ◽  
Vol 18 (4) ◽  
pp. 489-504 ◽  
Author(s):  
Farouk Cherif
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Pseudo Almost Periodic Solution ◽  
Chaotic Neural Networks ◽  
Pseudo Almost Periodic

In this paper we give sufficient conditions ensuring the existence and uniqueness of pseudo almost periodic solution of a class of delayed chaotic neural networks. Further, we study the global asymptotic stability (GAS) of the considered model and give a set of criteria on (GAS) by constructing new Lyapunov functional.

Stability analysis of n-species Lotka–Volterra almost periodic competition models with grazing rates and diffusions

2014 ◽  
Vol 07 (02) ◽  
pp. 1450011
Author(s):  
Yi-Jin Zhang ◽  
Chang-You Wang
Keyword(s):  
Periodic Solution ◽  
Upper And Lower Solutions ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Globally Asymptotically Stable ◽  
Competition Models ◽  
Positive Space

In this paper, almost periodic solution of a n-species Lotka–Volterra competition system with grazing rates and diffusions is investigated. By using the method of upper and lower solutions and Schauder fixed point theorem as well as Lyapunov stability theory, we give sufficient conditions under which the strictly positive space homogeneous almost periodic solution of the system is globally asymptotically stable. Moreover, some numerical simulations are given to validate our theoretical analysis.

scholarly journals Permanence and Almost Periodic Solution for an Enterprise Cluster Model Based on Ecology Theory with Feedback Controls on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Yuanhong Zhi ◽  
Zunling Ding ◽  
Yongkun Li
Keyword(s):  
Periodic Solution ◽  
Time Scales ◽  
Cluster Model ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Feedback Controls ◽  
Competition And Cooperation ◽  
Enterprise Cluster

We present a model with feedback controls based on ecology theory, which effectively describes the competition and cooperation of enterprise cluster in real economic environments. Applying the comparison theorem of dynamic equations on time scales and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and the existence of uniformly asymptotically stable almost periodic solution of the system are obtained.

scholarly journals Almost Periodic Solution of a Multispecies Discrete Mutualism System with Feedback Controls

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Hui Zhang ◽  
Feng Feng ◽  
Bin Jing ◽  
Yingqi Li
Keyword(s):  
Numerical Simulation ◽  
Periodic Solution ◽  
Lyapunov Function ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Feedback Controls ◽  
Positive Almost Periodic Solution ◽  
Mutualism System

We consider an almost periodic multispecies discrete Lotka-Volterra mutualism system with feedback controls. We firstly obtain the permanence of the system by utilizing the theory of difference equation. By means of constructing a suitable Lyapunov function, sufficient conditions are obtained for the existence of a unique positive almost periodic solution which is uniformly asymptotically stable. An example together with numerical simulation indicates the feasibility of the main result.

scholarly journals Global Analysis of Almost Periodic Solution of a Discrete Multispecies Mutualism System

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Hui Zhang ◽  
Bin Jing ◽  
Yingqi Li ◽  
Xiaofeng Fang
Keyword(s):  
Periodic Solution ◽  
Global Analysis ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Periodic Sequences ◽  
Almost Periodic Sequences ◽  
Globally Attractive ◽  
Mutualism System

This paper discusses a discrete multispecies Lotka-Volterra mutualism system. We first obtain the permanence of the system. Assuming that the coefficients in the system are almost periodic sequences, we obtain the sufficient conditions for the existence of a unique almost periodic solution which is globally attractive. In particular, for the discrete two-species Lotka-Volterra mutualism system, the sufficient conditions for the existence of a unique uniformly asymptotically stable almost periodic solution are obtained. An example together with numerical simulation indicates the feasibility of the main result.

scholarly journals Almost periodic solution of a discrete competitive system with delays and feedback controls

2019 ◽  
Vol 17 (1) ◽  
pp. 120-130 ◽  
Author(s):  
Yalong Xue ◽  
Xiangdong Xie ◽  
Qifa Lin
Keyword(s):  
Numerical Simulation ◽  
Periodic Solution ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Competitive System ◽  
Feedback Controls ◽  
Uniformly Asymptotic Stability ◽  
Positive Almost Periodic Solution

Abstract A discrete nonlinear almost periodic multispecies competitive system with delays and feedback controls is proposed and investigated. We obtain sufficient conditions to ensure the permanence of the system. Also, we establish a criterion for the existence and uniformly asymptotic stability of unique positive almost periodic solution of the system. In additional, an example together with its numerical simulation are presented to illustrate the feasibility of the main result.

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