scholarly journals Periodic Solutions for Impulsive Stochastic BAM Neural Networks with Time-Varying Delays in Leakage Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Li Yang ◽  
Yongkun Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Integral Inequality ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Bam Neural Networks

By using an integral inequality, we establish some sufficient conditions for the existence andp-exponential stability of periodic solutions for a class of impulsive stochastic BAM neural networks with time-varying delays in leakage terms. Moreover, we present an example to illustrate the feasibility of our results.

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 Periodic Solutions of a Cohen-Grossberg-Type BAM Neural Networks with Distributed Delays and Impulses

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Qiming Liu ◽  
Rui Xu
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Bam Neural Networks ◽  
Mathematical Transformation

A class of Cohen-Grossberg-type BAM neural networks with distributed delays and impulses are investigated in this paper. Sufficient conditions to guarantee the uniqueness and global exponential stability of the periodic solutions of such networks are established by using suitable Lyapunov function, the properties ofM-matrix, and some suitable mathematical transformation. The results in this paper improve the earlier publications.

Global exponential stability analysis of anti-periodic solutions of discontinuous bidirectional associative memory (BAM) neural networks with time-varying delays

2020 ◽  
Vol 21 (7-8) ◽  
pp. 807-820
Author(s):  
Xiangying Fu ◽  
Fanchao Kong
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Associative Memory ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Bidirectional Associative Memory ◽  
Globally Exponential Stability ◽  
Discontinuous Activations ◽  
Neural Network System

AbstractThis paper is concerned with a class of bidirectional associative memory (BAM) neural networks with discontinuous activations and time-varying delays. Under the basic framework of differential inclusions theory, the existence result of solutions in sense of Filippov solution is firstly established by using the fundamental solution matrix of coefficients and inequality analysis technique. Also, the boundness of the solutions can be estimated. Secondly, based on the non-smooth Lyapunov-like approach and by construsting suitable Lyapunov–Krasovskii functionals, some new sufficient criteria are given to ascertain the globally exponential stability of the anti-periodic solutions for the proposed neural network system. Furthermore, we have collated our effort with some previous existing ones in the literatures and showed that it can take more advantages. Finally, two examples with numerical simulations are exploited to illustrate the correctness.

scholarly journals Exponential Stability for Discrete-Time Stochastic BAM Neural Networks with Discrete and Distributed Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-23
Author(s):  
R. Raja ◽  
R. Sakthivel ◽  
S. Marshal Anthoni
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Global Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Analysis Problem ◽  
The Stability

This paper deals with the stability analysis problem for a class of discrete-time stochastic BAM neural networks with discrete and distributed time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional and employing M-matrix theory, we find some sufficient conditions ensuring the global exponential stability of the equilibrium point for stochastic BAM neural networks with time-varying delays. The conditions obtained here are expressed in terms of LMIs whose feasibility can be easily checked by MATLAB LMI Control toolbox. A numerical example is presented to show the effectiveness of the derived LMI-based stability conditions.

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.

scholarly journals Exponential Stability of Antiperiodic Solution for BAM Neural Networks with Time-Varying Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaofei Li ◽  
Chuan Qin ◽  
Quanxin Zhu
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Exponential Stability ◽  
Negative Feedback ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Activation Functions ◽  
Leakage Delays ◽  
Inequality Techniques

In this paper, a kind of BAM neural networks with leakage delays in the negative feedback terms and time-varying delays in activation functions was considered. By constructing a suitable Lyapunov function and using inequality techniques, some sufficient conditions to ensure the existence and exponential stability of antiperiodic solutions of these neural networks were derived. These conditions extend some results recently appearing in recent papers. Lastly, an example is given to show the feasibility of these conditions.

scholarly journals Periodic Solutions and Exponential Stability of a Class of Neural Networks with Time-Varying Delays

2009 ◽  
Vol 2009 ◽  
pp. 1-14
Author(s):  
Yingxin Guo ◽  
Mingzhi Xue
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Globally Stable

Employing fixed point theorem, we make a further investigation of a class of neural networks with delays in this paper. A family of sufficient conditions is given for checking global exponential stability. These results have important leading significance in the design and applications of globally stable neural networks with delays. Our results extend and improve some earlier publications.

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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