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 Solution in a Lotka–Volterra Recurrent Neural Networks with Time-Varying Delays

2017 ◽  
Vol 18 (1) ◽  
pp. 19-27 ◽  
Author(s):  
Li Yang ◽  
Zhouhong Li ◽  
Liyan Pang ◽  
Tianwei Zhang
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Mawhin’S Continuation Theorem ◽  
Existence And Stability

Abstract:By means of Mawhin’s continuation theorem of coincidence degree theory and Lyapunov function, some simple sufficient conditions are obtained for the existence and stability of a unique positive almost periodic solution of a delayed Lotka–Volterra recurrent neural networks. To a certain extent, the work in this paper corrects the defect of a recent paper. Finally, an example and simulations are given to illustrate the feasibility and effectiveness of the main result.

scholarly journals Pseudo Almost-Periodic Solution of Shunting Inhibitory Cellular Neural Networks with Delay

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Haihui Wu
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Cellular Neural Networks ◽  
Contraction Mapping Principle ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Pseudo Almost Periodic Solution ◽  
Globally Exponential Stability ◽  
Banach Contraction ◽  
Pseudo Almost Periodic

Shunting inhibitory cellular neural networks are studied. Some sufficient criteria are obtained for the existence and uniqueness of pseudo almost-periodic solution of this system. Our results improve and generalize those of the previous studies. This is the first paper considering the pseudo almost-periodic SICNNs. Furthermore, several methods are applied to establish sufficient criteria for the globally exponential stability of this system. The approaches are based on constructing suitable Lyapunov functionals and the well-known Banach contraction mapping principle.

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