PERIODICITY AND STABILITY IN RECURRENT CELLULAR NEURAL NETWORKS WITH IMPULSIVE EFFECTS

2011 ◽  
Vol 04 (04) ◽  
pp. 399-422 ◽  
Author(s):  
HAIBO GU ◽  
HAIJUN JIANG ◽  
ZHIDONG TENG
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Activation Functions ◽  
Analysis Problem ◽  
Mawhin’S Continuation Theorem

In this paper, the exponential stability analysis problem is considered for a class of impulsive recurrent cellular neural networks (IRCNNs) with time-varying delays. Without assuming the boundedness on the activation functions, some sufficient conditions are derived for checking the existence and exponential stability of periodic solution for this system by using Mawhin's continuation theorem of coincidence degree theory and constructing suitable Lyapunov functional. It is believed that these results are significant and useful for the design and applications of IRCNNs. Finally, an example with numerical simulation is given to show the effectiveness of the proposed method and results.

scholarly journals Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

2011 ◽  
Vol 21 (4) ◽  
pp. 649-658 ◽  
Author(s):  
Qianhong Zhang ◽  
Lihui Yang ◽  
Daixi Liao
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
Inequality Technique

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.

scholarly journals Antiperiodic Solutions for Quaternion-Valued Shunting Inhibitory Cellular Neural Networks with Distributed Delays and Impulses

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Nina Huo ◽  
Yongkun Li
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Cellular Neural Networks ◽  
Continuation Theorem ◽  
Distributed Delays

This paper is concerned with quaternion-valued shunting inhibitory cellular neural networks (QVSICNNs) with distributed delays and impulses. By using a new continuation theorem of the coincidence degree theory, the existence of antiperiodic solutions for QVSICNNs is obtained. By constructing a suitable Lyapunov function, some sufficient conditions are derived to guarantee the global exponential stability of antiperiodic solutions for QVSICNNs. Finally, an example is given to show the feasibility of obtained results.

scholarly journals Exponential Stability and Periodicity of Fuzzy Delayed Reaction-Diffusion Cellular Neural Networks with Impulsive Effect

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Guowei Yang ◽  
Yonggui Kao ◽  
Changhong Wang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Cellular Neural Networks ◽  
Impulsive Effect ◽  
Time Varying ◽  
Delayed Reaction

This paper considers dynamical behaviors of a class of fuzzy impulsive reaction-diffusion delayed cellular neural networks (FIRDDCNNs) with time-varying periodic self-inhibitions, interconnection weights, and inputs. By using delay differential inequality,M-matrix theory, and analytic methods, some new sufficient conditions ensuring global exponential stability of the periodic FIRDDCNN model with Neumann boundary conditions are established, and the exponential convergence rate index is estimated. The differentiability of the time-varying delays is not needed. An example is presented to demonstrate the efficiency and effectiveness of the obtained results.

EXISTENCE AND GLOBAL EXPONENTIAL STABILITY OF PERIODIC SOLUTION OF A CLASS OF IMPULSIVE NETWORKS WITH INFINITE DELAYS

2007 ◽  
Vol 17 (01) ◽  
pp. 35-42 ◽  
Author(s):  
YONGHUI XIA ◽  
JINDE CAO ◽  
MUREN LIN
Keyword(s):  
Periodic Solution ◽  
Exponential Stability ◽  
Lyapunov Functions ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Mawhin’S Continuation Theorem ◽  
Neuron Networks ◽  
Infinite Delays

Sufficient conditions are obtained for the existence and global exponential stability of a unique periodic solution of a class of impulsive tow-neuron networks with variable and unbounded delays. The approaches are based on Mawhin's continuation theorem of coincidence degree theory and Lyapunov functions.

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.

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 Periodic Solutions for a Numerical Discretization Neural Network

2010 ◽  
Vol 2010 ◽  
pp. 1-17
Author(s):  
Chun Lu
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Global Exponential Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Numerical Discretization

The existence and global exponential stability of periodic solutions for a class of numerical discretization neural networks are considered. Using coincidence degree theory and Lyapunov method, sufficient conditions for the existence and global exponential stability of periodic solutions are obtained. Numerical simulations are given to illustrate the results.

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 Stability Analysis for Memristor-Based Complex-Valued Neural Networks with Time Delays

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 120
Author(s):  
Ping Hou ◽  
Jun Hu ◽  
Jie Gao ◽  
Peican Zhu
Keyword(s):  
Numerical Simulation ◽  
Neural Networks ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Activation Functions ◽  
Complex Valued ◽  
Theoretical Results

In this paper, the problem of stability analysis for memristor-based complex-valued neural networks (MCVNNs) with time-varying delays is investigated extensively. This paper focuses on the exponential stability of the MCVNNs with time-varying delays. By means of the Brouwer’s fixed-point theorem and M-matrix, the existence, uniqueness, and exponential stability of the equilibrium point for MCVNNs are studied, and several sufficient conditions are obtained. In particular, these results can be applied to general MCVNNs whether the activation functions could be explicitly described by dividing into two parts of the real parts and imaginary parts or not. Two numerical simulation examples are provided to illustrate the effectiveness of the theoretical 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.

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