scholarly journals Representations of mild solutions of time-varying linear stochastic equations and the exponential stability of periodic systems

2004 ◽  
pp. 1-22 ◽  
Author(s):  
Viorica Mariela Ungureanu
Keyword(s):  
Exponential Stability ◽  
Mild Solutions ◽  
Stochastic Equations ◽  
Periodic Systems ◽  
Time Varying

scholarly journals Periodic Solutions of Semilinear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
JinRong Wang ◽  
X. Xiang ◽  
W. Wei
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Mixed Type ◽  
Evolution Operator ◽  
Mild Solutions ◽  
Integral Operators ◽  
Periodic Systems ◽  
Time Varying ◽  
Type Integral ◽  
Generating Operators

A class of semilinear impulsive periodic systems with time-varying generating operators on Banach space is considered. Using impulsive periodic evolution operator given by us, theT0-periodicPC-mild solution is introduced and suitablePoincaréoperator is constructed. Showing the compactness ofPoincaréoperator and using a new generalized Gronwall inequality with mixed type integral operators given by us, we utilize Leray-Schauder fixed point theorem to prove the existence ofT0-periodicPC-mild solutions. Our method is an innovation and it is much different from methods of other papers. At last, an example is given for demonstration.

scholarly journals Existence and exponential stability in the pth moment for impulsive neutral stochastic integro-differential equations driven by mixed fractional Brownian motion

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xia Zhou ◽  
Dongpeng Zhou ◽  
Shouming Zhong
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Exponential Stability ◽  
Fractional Brownian Motion ◽  
Mild Solutions ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Fractional Power ◽  
Banach Fixed Point Theorem ◽  
Mixed Fractional Brownian Motion

Abstract This paper consider the existence, uniqueness and exponential stability in the pth moment of mild solution for impulsive neutral stochastic integro-differential equations driven simultaneously by fractional Brownian motion and by standard Brownian motion. Based on semigroup theory, the sufficient conditions to ensure the existence and uniqueness of mild solutions are obtained in terms of fractional power of operators and Banach fixed point theorem. Moreover, the pth moment exponential stability conditions of the equation are obtained by means of an impulsive integral inequality. Finally, an example is presented to illustrate the effectiveness of the obtained results.

scholarly journals Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

2011 ◽  
Vol 21 (4) ◽  
pp. 649-658 ◽  
Author(s):  
Qianhong Zhang ◽  
Lihui Yang ◽  
Daixi Liao
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
Inequality Technique

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.

scholarly journals Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaohui Xu ◽  
Jiye Zhang ◽  
Quan Xu ◽  
Zilong Chen ◽  
Weifan Zheng
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Time Varying ◽  
Homeomorphism Mapping ◽  
Complex Valued

This paper studies the global exponential stability for a class of impulsive disturbance complex-valued Cohen-Grossberg neural networks with both time-varying delays and continuously distributed delays. Firstly, the existence and uniqueness of the equilibrium point of the system are analyzed by using the corresponding property of M-matrix and the theorem of homeomorphism mapping. Secondly, the global exponential stability of the equilibrium point of the system is studied by applying the vector Lyapunov function method and the mathematical induction method. The established sufficient conditions show the effects of both delays and impulsive strength on the exponential convergence rate. The obtained results in this paper are with a lower level of conservatism in comparison with some existing ones. Finally, three numerical examples with simulation results are given to illustrate the correctness of the proposed results.

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