scholarly journals Existence and Global Uniform Asymptotic Stability of Almost Periodic Solutions for Cellular Neural Networks with Discrete and Distributed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Zongyi Hou ◽  
Hongying Zhu ◽  
Chunhua Feng
Keyword(s):  
Differential Equation ◽  
Neural Networks ◽  
Asymptotic Stability ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Lyapunov Functionals ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Uniform Asymptotic Stability

This paper discusses the existence and global uniform asymptotic stability of almost periodic solutions for cellular neural networks (CNNS). By utilizing the theory of the almost periodic differential equation and the Lyapunov functionals method, some sufficient conditions are obtained to ensure the existence and global uniform asymptotic stability. An example is given to illustrate the effectiveness of the main results.

scholarly journals Existence and Global Uniform Asymptotic Stability of Pseudo Almost Periodic Solutions for Cohen-Grossberg Neural Networks with Discrete and Distributed Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hongying Zhu ◽  
Chunhua Feng
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Periodic Solutions ◽  
Lyapunov Functional ◽  
Distributed Delays ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Uniform Asymptotic Stability ◽  
Pseudo Almost Periodic Solutions ◽  
Pseudo Almost Periodic

This paper studies the existence and uniform asymptotic stability of pseudo almost periodic solutions to Cohen-Grossberg neural networks (CGNNs) with discrete and distributed delays by applying Schauder fixed point theorem and constructing a suitable Lyapunov functional. An example is given to show the effectiveness of the main results.

Existence and Global Exponential Stability of Almost Periodic Solutions for Shunting Inhibitory Cellular Neural Networks with Distributed Leakage Delays on Time Scales

2016 ◽  
Vol 13 (10) ◽  
pp. 7054-7065
Author(s):  
Changjin Xu ◽  
Xiaofei Li ◽  
Songbo Hu ◽  
Haitao Wu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Leakage Delays ◽  
Linear Differential

In this paper, we deal with a class of shunting inhibitory cellular neural networks (SICNNs) with distributed leakage delays on time scales. Some sufficient conditions which ensure the existence and exponential stability of almost periodic solutions for such class of SICNNs are obtained by applying the exponential dichotomy of linear differential equations, Lapunov functional method and contraction mapping principle. An example is given to illustrate the effectiveness of the theoretical results. The results obtained in this paper are completely new and complement the previously known studies.

scholarly journals The Existence and Global Exponential Stability of Almost Periodic Solutions for Neutral-Type CNNs on Time Scales

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 321 ◽  
Author(s):  
Bing Li ◽  
Yongkun Li ◽  
Xiaofang Meng
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Time Scales ◽  
Global Exponential Stability ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Leakage Delays

In this paper, neutral-type competitive neural networks with mixed time-varying delays and leakage delays on time scales are proposed. Based on the contraction fixed-point theorem, some sufficient conditions that are independent of the backwards graininess function of the time scale are obtained for the existence and global exponential stability of almost periodic solutions of neural networks under consideration. The results obtained are brand new, indicating that the continuous time and discrete-time conditions of the network share the same dynamic behavior. Finally, two examples are given to illustrate the validity of the results obtained.

scholarly journals C1-Almost Periodic Solutions of BAM Neural Networks with Time-Varying Delays on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Yongkun Li ◽  
Lili Zhao ◽  
Li Yang
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
New Type ◽  
Inequality Techniques

On a new type of almost periodic time scales, a class of BAM neural networks is considered. By employing a fixed point theorem and differential inequality techniques, some sufficient conditions ensuring the existence and global exponential stability ofC1-almost periodic solutions for this class of networks with time-varying delays are established. Two examples are given to show the effectiveness of the proposed method and results.

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