Dynamical Behaviors of a Large Class of General Delayed Neural Networks

2005 ◽  
Vol 17 (4) ◽  
pp. 949-968 ◽  
Author(s):  
Tianping Chen ◽  
Wenlian Lu ◽  
Guanrong Chen
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Dynamical Systems ◽  
Large Class ◽  
Delayed Systems ◽  
Delayed Neural Networks ◽  
Dynamical Behaviors ◽  
Special Cases ◽  
Exponentially Stable ◽  
Delayed System

Research of delayed neural networks with varying self-inhibitions, interconnection weights, and inputs is an important issue. In the real world, self-inhibitions, interconnection weights, and inputs should vary as time varies. In this letter, we discuss a large class of delayed neural networks with periodic inhibitions, interconnection weights, and inputs. We prove that if the activation functions are of Lipschitz type and some set of inequalities, for example, the set of inequalities 3.1 in theorem 1, is satisfied, the delayed system has a unique periodic solution, and any solution will converge to this periodic solution. We also prove that if either set of inequalities 3.20 in theorem 2 or 3.23 in theorem 3 is satisfied, then the system is exponentially stable globally. This class of delayed dynamical systems provides a general framework for many delayed dynamical systems. As special cases, it includes delayed Hopfield neural networks and cellular neural networks as well as distributed delayed neural networks with periodic self-inhibitions, interconnection weights, and inputs. Moreover, the entire discussion applies to delayed systems with constant self-inhibitions, interconnection weights, and inputs.

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).

scholarly journals Sliding Intermittent Control for BAM Neural Networks with Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Jianqiang Hu ◽  
Jinling Liang ◽  
Hamid Reza Karimi ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Control Method ◽  
Impulsive Control ◽  
Intermittent Control ◽  
Bam Neural Networks ◽  
Periodically Intermittent Control ◽  
Control Scheme ◽  
Special Cases ◽  
Exponentially Stable ◽  
Continuous Feedback

This paper addresses the exponential stability problem for a class of delayed bidirectional associative memory (BAM) neural networks with delays. A sliding intermittent controller which takes the advantages of the periodically intermittent control idea and the impulsive control scheme is proposed and employed to the delayed BAM system. With the adjustable parameter taking different particular values, such a sliding intermittent control method can comprise several kinds of control schemes as special cases, such as the continuous feedback control, the impulsive control, the periodically intermittent control, and the semi-impulsive control. By using analysis techniques and the Lyapunov function methods, some sufficient criteria are derived for the closed-loop delayed BAM neural networks to be globally exponentially stable. Finally, two illustrative examples are given to show the effectiveness of the proposed control scheme and the obtained theoretical results.

Multiple Almost Periodic Solutions in Nonautonomous Delayed Neural Networks

2007 ◽  
Vol 19 (12) ◽  
pp. 3392-3420 ◽  
Author(s):  
Kuang-Hui Lin ◽  
Chih-Wen Shih
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Contraction Mapping Principle ◽  
Time Lags ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Neuron Network ◽  
Delayed Neural Networks ◽  
External Bias ◽  
Exponentially Stable

A general methodology that involves geometric configuration of the network structure for studying multistability and multiperiodicity is developed. We consider a general class of nonautonomous neural networks with delays and various activation functions. A geometrical formulation that leads to a decomposition of the phase space into invariant regions is employed. We further derive criteria under which the n-neuron network admits 2n exponentially stable sets. In addition, we establish the existence of 2n exponentially stable almost periodic solutions for the system, when the connection strengths, time lags, and external bias are almost periodic functions of time, through applying the contraction mapping principle. Finally, three numerical simulations are presented to illustrate our theory.

scholarly journals Quantized passive filtering for switched delayed neural networks

2021 ◽  
Vol 26 (1) ◽  
pp. 93-112
Author(s):  
Youmei Zhou ◽  
Yajuan Liu ◽  
Jianping Zhou ◽  
Zhen Wang
Keyword(s):  
Neural Networks ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Passive Filter ◽  
Delayed Neural Networks ◽  
Noise Interference ◽  
Exponentially Stable ◽  
Error System ◽  
Inequality Techniques

The issue of quantized passive filtering for switched delayed neural networks with noise interference is studied in this paper. Both arbitrary and semi-Markov switching rules are taken into account. By choosing Lyapunov functionals and applying several inequality techniques, sufficient conditions are proposed to ensure the filter error system to be not only exponentially stable, but also exponentially passive from the noise interference to the output error. The gain matrix for the proposed quantized passive filter is able to be determined through the feasible solution of linear matrix inequalities, which are computationally tractable with the help of some popular convex optimization tools. Finally, two numerical examples are given to illustrate the usefulness of the quantized passive filter design methods.

Pth moment input-to-state stability of stochastic impulsive switched delayed systems

2019 ◽  
Vol 41 (12) ◽  
pp. 3468-3476
Author(s):  
Lijun Gao ◽  
Shengyan Wang
Keyword(s):  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Delayed Systems ◽  
Stable Function ◽  
Exponentially Stable ◽  
Delayed System ◽  
The Relationship ◽  
Delayed Impulses ◽  
Moment Integral

This paper investigates the pth moment input-to-state stability (ISS) and the pth moment integral input-to-state stability (iISS) of stochastic impulsive switched delayed system with delayed impulses. By employing the method of multiple Lyapunov-Krasovskii functionals and the uniformly exponentially stable function, some relaxed Krasovskii-type sufficient conditions ensuring the pISS/piISS of the addressed systems are developed. These conditions imply the relationship among the impulsive frequency, the time delay existing in impulses, and the coefficients of the estimated upper bound for the derivative of a Lyapunov function. It is shown that if the continuous stochastic delayed dynamics is ISS, and the impulsive effects are destabilizing, then the stochastic impulsive switched delayed system is ISS with respect to the relationship. Compared with the existing results, the conditions obtained results have three relaxations, that is, the derivative of Lyapunov functions of subsystems are allowed to be sign-changing time-varying function rather than a negative definite constant, all subsystems are allowed to be unstable, and the effect of delayed impulses are considered. Finally, an example is provided to illustrate the effectiveness of the results.

Sign in / Sign up

Export Citation Format

Share Document