scholarly journals Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yaping Ren ◽  
Yongkun Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Time Scales ◽  
Time Scale ◽  
Cellular Neural Networks ◽  
Activation Functions ◽  
State Dependent ◽  
Existence Of Periodic Solutions

We study delayed cellular neural networks on time scales. Without assuming the boundedness of the activation functions, we establish the exponential stability and existence of periodic solutions. The results in this paper are completely new even in case of the time scale𝕋=ℝorℤand improve some of the previously known 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 Antiperiodic Solutions to Impulsive Cohen-Grossberg Neural Networks with Delays on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yanqin Wang ◽  
Maoan Han
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Time Scales ◽  
Time Scale ◽  
Lyapunov Functional ◽  
Global Exponential Stability ◽  
Coincidence Degree

We use the method of coincidence degree and construct suitable Lyapunov functional to investigate the existence and global exponential stability of antiperiodic solutions of impulsive Cohen-Grossberg neural networks with delays on time scales. Our results are new even if the time scaleT=RorZ. An example is given to illustrate our feasible results.

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