scholarly journals Existence and Global Asymptotical Stability of Periodic Solution for theT-Periodic Logistic System with Time-Varying Generating Operators andT0-Periodic Impulsive Perturbations on Banach Spaces

2008 ◽  
Vol 2008 ◽  
pp. 1-16 ◽  
Author(s):  
JinRong Wang ◽  
X. Xiang ◽  
W. Wei ◽  
Qian Chen
Keyword(s):  
Banach Spaces ◽  
Mild Solution ◽  
Sufficient Conditions ◽  
Asymptotical Stability ◽  
Time Varying ◽  
Global Asymptotical Stability ◽  
Globally Asymptotically Stable ◽  
Impulsive Perturbations ◽  
Generating Operators ◽  
Well Posed

This paper studies the existence and global asymptotical stability of periodic PC-mild solution for theT-periodic Logistic system with time-varying generating operators andT0-periodic impulsive perturbations on Banach spaces. Two sufficient conditions that guarantee the exponential stability of the impulsive evolution operator corresponding to homogenous well-posedT-periodic system with time-varying generating operators andT0-periodic impulsive perturbations are given. It is shown that the system have a unique periodic PC-mild solution which is globally asymptotically stable whenTandT0are rational dependent and its period must benT0for somen∈N. At last, an example is given for demonstration.

scholarly journals Persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations

2020 ◽  
Vol 25 (4) ◽  
Author(s):  
Dan Yang ◽  
Xiaodi Li ◽  
Zhongmin Liu ◽  
Jinde Cao
Keyword(s):  
Control Theory ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Impulsive Perturbations

In this paper, we develop the impulsive control theory to nonautonomous logistic system with time-varying delays. Some sufficient conditions ensuring the persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations are derived. It is shown that the persistence of the considered system is heavily dependent on the impulsive perturbations. The proposed method of this paper is completely new. Two examples and the simulations are given to illustrate the proposed method and results.

scholarly journals Global Asymptotical Stability Analysis for Fractional Neural Networks with Time-Varying Delays

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 138
Author(s):  
Zhixin Zhang ◽  
Yufeng Zhang ◽  
Jia-Bao Liu ◽  
Jiang Wei
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Asymptotical Stability ◽  
Time Varying ◽  
Global Asymptotical Stability ◽  
Stability Criteria ◽  
Lmi Approach ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay

In this paper, the global asymptotical stability of Riemann-Liouville fractional-order neural networks with time-varying delays is studied. By combining the Lyapunov functional function and LMI approach, some sufficient criteria that guarantee the global asymptotical stability of such fractional-order neural networks with both discrete time-varying delay and distributed time-varying delay are derived. The stability criteria is suitable for application and easy to be verified by software. Lastly, some numerical examples are presented to check the validity of the obtained results.

Dynamics of an N-Species Gilpin–Ayala Impulsive Competition System

2019 ◽  
Vol 20 (7-8) ◽  
pp. 737-746
Author(s):  
Libo Wang ◽  
Guigui Xu
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Almost Periodic Solution ◽  
Asymptotical Stability ◽  
Global Asymptotical Stability ◽  
Almost Periodic ◽  
Competition System

AbstractIn this paper, we consider an N-species Gilpin–Ayala impulsive competition system. By using comparison theorem, Lyapunov functional, and almost periodic functional hull theory of the impulsive differential equations, this paper gives some new sufficient conditions for the permanence, global asymptotical stability, and almost periodic solution of the model. Our results extend some previously known results. The method used in this paper provides a possible method to study the permanence, global asymptotical stability, and almost periodic solution of the models with impulsive perturbations in biological populations.

scholarly journals Global Asymptotical Stability of Neutral-Type Neural Networks with D-Operator and Mixed Delays

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Qing Yang ◽  
Bo Du ◽  
Xiwang Cheng
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Asymptotical Stability ◽  
Mixed Delays ◽  
Global Asymptotical Stability ◽  
Numerical Example ◽  
The Stability ◽  
Theoretical Results

In this manuscript, we investigate the stability problems of neutral-type neural networks with D-operator and mixed delays. Some sufficient conditions are obtained for guaranteeing the existence, uniqueness, and global asymptotical stability of periodic solutions to the considered neural networks. Finally, a numerical example is performed to illustrate the theoretical results.

scholarly journals Second method of Lyapunov for stability of linear impulsive differential-difference equations with variable impulsive perturbations

1998 ◽  
Vol 11 (2) ◽  
pp. 209-216 ◽  
Author(s):  
D. D. Bainov ◽  
I. M. Stamova ◽  
A. S. Vatsala
Keyword(s):  
Difference Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Asymptotical Stability ◽  
Uniform Stability ◽  
Auxiliary Functions ◽  
Piecewise Continuous ◽  
Impulsive Perturbations ◽  
Second Method Of Lyapunov

The present work is devoted to the study of stability of the zero solution to linear impulsive differential-difference equations with variable impulsive perturbations. With the aid of piecewise continuous auxiliary functions, which are generalizations of the classical Lyapunov's functions, sufficient conditions are found for the uniform stability and uniform asymptotical stability of the zero solution to equations under consideration.

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