Almost periodic dynamics for impulsive delay neural networks of a general type on almost periodic time scales

2016 ◽  
Vol 36 ◽  
pp. 238-251 ◽  
Author(s):  
Chao Wang ◽  
Ravi P. Agarwal
Keyword(s):  
Neural Networks ◽  
Time Scales ◽  
General Type ◽  
Almost Periodic ◽  
Impulsive Delay ◽  
Periodic Dynamics ◽  
Almost Periodic Time Scales

scholarly journals A Further Study of Almost Periodic Time Scales with Some Notes and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Chao Wang ◽  
Ravi P. Agarwal
Keyword(s):  
Neural Networks ◽  
Time Scales ◽  
Dynamic Equations ◽  
Almost Periodicity ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Cauchy Matrix ◽  
Nonlinear Dynamic Equations ◽  
Almost Periodic Time Scales

We introduce three equivalent concepts of almost periodic time scales as a further study of the corresponding concept proposed in Li and Wang (2011) and several examples of almost periodic time scales which are not periodic are provided. Furthermore, the concepts of almost periodic functions are redefined under the sense of this new timescale concept. Finally, almost periodicity of Cauchy matrix for dynamic equations is proved under these new definitions. Based on these results, the existence of almost periodic solutions to a class of nonlinear dynamic equations is investigated by the almost periodicity of Cauchy matrix on almost periodic time scales. Besides, as an application, we apply our results to a class of high-order Hopfield neural networks.

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.

scholarly journals Almost Periodic Dynamics for Memristor-Based Shunting Inhibitory Cellular Neural Networks with Leakage Delays

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Lin Lu ◽  
Chaoling Li
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Cellular Neural Networks ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Leakage Delays ◽  
The Neural Network ◽  
Existence And Stability ◽  
Exponentially Stable ◽  
Periodic Dynamics

We investigate a class of memristor-based shunting inhibitory cellular neural networks with leakage delays. By applying a new Lyapunov function method, we prove that the neural network which has a unique almost periodic solution is globally exponentially stable. Moreover, the theoretical findings of this paper on the almost periodic solution are applied to prove the existence and stability of periodic solution for memristor-based shunting inhibitory cellular neural networks with leakage delays and periodic coefficients. 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 of Wu (2011) and Chen and Cao (2002).

Almost periodic dynamics of memristive inertial neural networks with mixed delays

2020 ◽  
Vol 536 ◽  
pp. 332-350
Author(s):  
Rakkiyappan Rajan ◽  
Velmurugan Gandhi ◽  
Premalatha Soundharajan ◽  
Young Hoon Joo
Keyword(s):  
Neural Networks ◽  
Mixed Delays ◽  
Almost Periodic ◽  
Inertial Neural Networks ◽  
Periodic Dynamics

scholarly journals Almost Periodic Solutions for Neutral-Type BAM Neural Networks with Delays on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yongkun Li ◽  
Li Yang
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Time Scales ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Bam Neural Networks ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Linear Dynamic ◽  
Dynamical Behaviors

Using the existence of the exponential dichotomy of linear dynamic equations on time scales, a fixed point theorem and the theory of calculus on time scales, we obtain some sufficient conditions for the existence and exponential stability of almost periodic solutions for a class of neutral-type BAM neural networks with delays on time scales. Finally, a numerical example illustrates the feasibility of our results and also shows that the continuous-time neural network and its discrete-time analogue have the same dynamical behaviors. The results of this paper are completely new even if the time scale𝕋=ℝorℤand complementary to the previously known results.

scholarly journals Almost Periodic Time Scales and Almost Periodic Functions on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Yongkun Li ◽  
Bing Li
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Basic Properties ◽  
New Concepts ◽  
Almost Periodic Time Scales

We propose some new concepts of almost periodic time scales and almost periodic functions on time scales and give some basic properties of these new types of almost periodic time scales and almost periodic functions on time scales. We also give some comments on a recent paper by Wang and Agarwal (2014) concerning a new almost periodic time scale.

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