scholarly journals Existence and Exponential Stability of Periodic Solution for a Class of Generalized Neural Networks with Arbitrary Delays

2009 ◽  
Vol 2009 ◽  
pp. 1-15
Author(s):  
Yimin Zhang ◽  
Yongkun Li ◽  
Kuohui Ye
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Continuation Theorem ◽  
Generalized Neural Networks

By the continuation theorem of coincidence degree andM-matrix theory, we obtain some sufficient conditions for the existence and exponential stability of periodic solutions for a class of generalized neural networks with arbitrary delays, which are milder and less restrictive than those of previous known criteria. Moreover our results generalize and improve many existing ones.

Exponential stability of anti-periodic solutions for neural networks with multiple discrete and distributed delays

2008 ◽  
Vol 223 (3) ◽  
pp. 299-308 ◽  
Author(s):  
X Liu ◽  
J Cao
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Matrix Theory ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Generalized Neural Networks ◽  
Discrete Delays ◽  
Analysis Of Stability

In this paper, the anti-periodic solutions are considered for generalized neural networks with multiple discrete delays and distributed delays. Several new sufficient conditions are established for ensuring the existence and exponential stability of anti-periodic solutions based on the Lyapunov method and M-matrix theory. It is shown that, by means of the techniques developed, the analysis of stability for anti-periodic solutions is different from the familiar periodic ones. The obtained results generalize and improve the earlier works. Two numerical examples are given to illustrate the effectiveness of the proposed theories.

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 Periodic Solutions for a Numerical Discretization Neural Network

2010 ◽  
Vol 2010 ◽  
pp. 1-17
Author(s):  
Chun Lu
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Global Exponential Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Numerical Discretization

The existence and global exponential stability of periodic solutions for a class of numerical discretization neural networks are considered. Using coincidence degree theory and Lyapunov method, sufficient conditions for the existence and global exponential stability of periodic solutions are obtained. Numerical simulations are given to illustrate the results.

scholarly journals Existence and Global Exponential Stability of Periodic Solutions for General Neural Networks with Time-Varying Delays

2008 ◽  
Vol 2008 ◽  
pp. 1-14 ◽  
Author(s):  
Xinsong Yang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Time Varying ◽  
Inequality Techniques ◽  
Coincidence Degree Theorem

By using the coincidence degree theorem and differential inequality techniques, sufficient conditions are obtained for the existence and global exponential stability of periodic solutions for general neural networks with time-varying (including bounded and unbounded) delays. Some known results are improved and some new results are obtained. An example is employed to illustrate our feasible results.

Existence and stability of anti-periodic solutions for impulsive fuzzy Cohen-Grossberge neural networks on time scales

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Qianhong Zhang ◽  
Lihui Yang ◽  
Jingzhong Liu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Time Scales ◽  
Lyapunov Functional ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Existence And Stability

AbstractBy applying the method of coincidence degree and constructing suitable Lyapunov functional, some sufficient conditions are established for the existence and global exponential stability of anti-periodic solutions for a kind of impulsive fuzzy Cohen-Grossberg neural networks on time scales. Moreover an example is given to illustrate our results.

scholarly journals Existence and global exponential stability of periodic solution of high-order Cohen-Grossberg neural network with impulses

2009 ◽  
Vol 42 (2) ◽  
Author(s):  
Jing Liu
Keyword(s):  
Neural Network ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
High Order ◽  
Continuation Theorem ◽  
Mawhin’S Continuation Theorem

AbstractSufficient conditions are obtained for the existence and global exponential stability of periodic solution of high-order Cohen-Grossberg neural network with impulses by using Mawhin’s continuation theorem of coincidence degree and by means of a method based differential inequality.

scholarly journals Existence and Stability of Periodic Solutions for Impulsive Fuzzy Cohen-Grossberg Neural Networks on Time Scales

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Qianhong Zhang ◽  
Jingzhong Liu ◽  
Yuanfu Shao
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Time Scales ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Globally Exponential Stability ◽  
Existence And Stability

Abstract By applying the method of coincidence degree and constructing a suitable Lyapunov functional, some sufficient conditions are established for the existence and globally exponential stability of periodic solutions for a kind of impulsive fuzzy Cohen- Grossberg neural networks on time scales. Moreover an example is given to illustrate our results.

scholarly journals Existence, Uniqueness and Exponential Stability of Periodic Solution for Discrete-Time Delayed BAM Neural Networks Based on Coincidence Degree Theory and Graph Theoretic Method

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1055 ◽  
Author(s):  
Manickam Iswarya ◽  
Ramachandran Raja ◽  
Grienggrai Rajchakit ◽  
Jinde Cao ◽  
Jehad Alzabut ◽  
...  
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Coincidence Degree Theory ◽  
Bam Neural Networks ◽  
Graph Theoretic

In this work, a general class of discrete time bidirectional associative memory (BAM) neural networks (NNs) is investigated. In this model, discrete and continuously distributed time delays are taken into account. By utilizing this novel method, which incorporates the approach of Kirchhoff’s matrix tree theorem in graph theory, Continuation theorem in coincidence degree theory and Lyapunov function, we derive a few sufficient conditions to ensure the existence, uniqueness and exponential stability of the periodic solution of the considered model. At the end of this work, we give a numerical simulation that shows the effectiveness of this work.

scholarly journals Antiperiodic Solutions for Quaternion-Valued Shunting Inhibitory Cellular Neural Networks with Distributed Delays and Impulses

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Nina Huo ◽  
Yongkun Li
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Cellular Neural Networks ◽  
Continuation Theorem ◽  
Distributed Delays

This paper is concerned with quaternion-valued shunting inhibitory cellular neural networks (QVSICNNs) with distributed delays and impulses. By using a new continuation theorem of the coincidence degree theory, the existence of antiperiodic solutions for QVSICNNs is obtained. By constructing a suitable Lyapunov function, some sufficient conditions are derived to guarantee the global exponential stability of antiperiodic solutions for QVSICNNs. Finally, an example is given to show the feasibility of obtained results.

Periodic solutions for stochastic Cohen–Grossberg neural networks with time-varying delays

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Wanqin Wu ◽  
Li Yang ◽  
Yaping Ren
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Deterministic Systems ◽  
Theoretical Results

AbstractThis paper is concerned with the periodic solutions for a class of stochastic Cohen–Grossberg neural networks with time-varying delays. Since there is a non-linearity in the leakage terms of stochastic Cohen–Grossberg neural networks, some techniques are needed to overcome the difficulty in dealing with the nonlinearity. By applying fixed points principle and Gronwall–Bellman inequality, some sufficient conditions on the existence and exponential stability of periodic solution for the stochastic neural networks are established. Moreover, a numerical example is presented to validate the theoretical results. Our results are also applicable to the existence and exponential stability of periodic solution for the corresponding deterministic systems.

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