GUARANTEED ATTRACTIVITY OF EQUILIBRIUM POINTS IN A CLASS OF DELAYED NEURAL NETWORKS

2006 ◽  
Vol 16 (09) ◽  
pp. 2737-2743 ◽  
Author(s):  
XIAOFAN YANG ◽  
XIAOFENG LIAO ◽  
YUANYAN TANG ◽  
DAVID J. EVANS
Keyword(s):  
Neural Networks ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Practical Importance ◽  
Activation Functions ◽  
Qualitative Properties ◽  
Domains Of Attraction ◽  
Delayed Neural Networks ◽  
Exponentially Stable ◽  
First Time

This paper addresses qualitative properties of equilibrium points in a class of delayed neural networks. We derive a sufficient condition for the local exponential stability of equilibrium points, and give an estimate on the domains of attraction of locally exponentially stable equilibrium points. Our condition and estimate are formulated in terms of the network parameters, the neurons' activation functions and the associated equilibrium point; hence, they are easily checkable. Another advantage of our results is that they neither depend on monotonicity of the activation functions nor on symmetry of the interconnection matrix. Our work has practical importance in evaluating the performance of the related associative memory. To our knowledge, this is the first time to present an estimate on the domains of attraction of equilibrium points for delayed neural networks.

Multistability of Delayed Recurrent Neural Networks with Mexican Hat Activation Functions

2017 ◽  
Vol 29 (2) ◽  
pp. 423-457 ◽  
Author(s):  
Peng Liu ◽  
Zhigang Zeng ◽  
Jun Wang
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Activation Function ◽  
Mexican Hat ◽  
Exponentially Stable ◽  
Attraction Basins ◽  
Stability Results

This letter studies the multistability analysis of delayed recurrent neural networks with Mexican hat activation function. Some sufficient conditions are obtained to ensure that an [Formula: see text]-dimensional recurrent neural network can have [Formula: see text] equilibrium points with [Formula: see text], and [Formula: see text] of them are locally exponentially stable. Furthermore, the attraction basins of these stable equilibrium points are estimated. We show that the attraction basins of these stable equilibrium points can be larger than their originally partitioned subsets. The results of this letter improve and extend the existing stability results in the literature. Finally, a numerical example containing different cases is given to illustrate the theoretical results.

On exponential stability of delayed neural networks with a general class of activation functions

2002 ◽  
Vol 298 (2-3) ◽  
pp. 122-132 ◽  
Author(s):  
Changyin Sun ◽  
Kanjian Zhang ◽  
Shumin Fei ◽  
Chun-Bo Feng
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
General Class ◽  
Activation Functions ◽  
Delayed Neural Networks

scholarly journals Matrix Measure Approach for Stability and Synchronization of Complex-Valued Neural Networks with Deviating Argument

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Wenbo Zhou ◽  
Biwen Li ◽  
Jin-E Zhang
Keyword(s):  
Neural Networks ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Activation Functions ◽  
Matrix Measure ◽  
Numerical Examples ◽  
Coupled Neural Networks ◽  
Deviating Argument ◽  
Exponentially Stable ◽  
Complex Valued

This paper concentrates on global exponential stability and synchronization for complex-valued neural networks (CVNNs) with deviating argument by matrix measure approach. The Lyapunov function is no longer required, and some sufficient conditions are firstly obtained to ascertain the addressed system to be exponentially stable under different activation functions. Moreover, after designing a suitable controller, the synchronization of two complex-valued coupled neural networks is realized, and the derived condition is easy to be confirmed. Finally, some numerical examples are given to demonstrate the superiority and feasibility of the presented theoretical analysis and results.

A New Approach for Estimating the Attraction Domain for Hopfield-Type Neural Networks

2009 ◽  
Vol 21 (1) ◽  
pp. 101-120 ◽  
Author(s):  
Dequan Jin ◽  
Jigen Peng
Keyword(s):  
Neural Networks ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Numerical Results ◽  
New Method ◽  
Attraction Domain ◽  
Network System ◽  
Asymptotically Stable ◽  
New Approach

In this letter, using methods proposed by E. Kaslik, St. Balint, and their colleagues, we develop a new method, expansion approach, for estimating the attraction domain of asymptotically stable equilibrium points of Hopfield-type neural networks. We prove theoretically and demonstrate numerically that the proposed approach is feasible and efficient. The numerical results that obtained in the application examples, including the network system considered by E. Kaslik, L. Brăescu, and St. Balint, indicate that the proposed approach is able to achieve better attraction domain estimation.

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 Multistability and Multiperiodicity for a General Class of Delayed Cohen-Grossberg Neural Networks with Discontinuous Activation Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yanke Du ◽  
Yanlu Li ◽  
Rui Xu
Keyword(s):  
Neural Networks ◽  
Periodic Orbits ◽  
General Class ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Multiple Equilibrium ◽  
Activation Functions ◽  
Discontinuous Activation ◽  
Discontinuous Activation Functions ◽  
Multiple Equilibrium Points

A general class of Cohen-Grossberg neural networks with time-varying delays, distributed delays, and discontinuous activation functions is investigated. By partitioning the state space, employing analysis approach and Cauchy convergence principle, sufficient conditions are established for the existence and locally exponential stability of multiple equilibrium points and periodic orbits, which ensure thatn-dimensional Cohen-Grossberg neural networks withk-level discontinuous activation functions can haveknequilibrium points orknperiodic orbits. Finally, several examples are given to illustrate the feasibility of the obtained results.

On the Synthesis of Brain-State-in-a-Box Neural Models with Application to Associative Memory

2000 ◽  
Vol 12 (2) ◽  
pp. 451-472 ◽  
Author(s):  
Fation Sevrani ◽  
Kennichi Abe
Keyword(s):  
Neural Networks ◽  
Associative Memory ◽  
Equilibrium Points ◽  
Domain Of Attraction ◽  
Neural Model ◽  
Brain State ◽  
Qualitative Properties ◽  
The Stability ◽  
The Brain ◽  
Insight Into

In this article we present techniques for designing associative memories to be implemented by a class of synchronous discrete-time neural networks based on a generalization of the brain-state-in-a-box neural model. First, we address the local qualitative properties and global qualitative aspects of the class of neural networks considered. Our approach to the stability analysis of the equilibrium points of the network gives insight into the extent of the domain of attraction for the patterns to be stored as asymptotically stable equilibrium points and is useful in the analysis of the retrieval performance of the network and also for design purposes. By making use of the analysis results as constraints, the design for associative memory is performed by solving a constraint optimization problem whereby each of the stored patterns is guaranteed a substantial domain of attraction. The performance of the designed network is illustrated by means of three specific examples.

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