Analysis and design of associative memories based on recurrent neural network with discontinuous activation functions

This paper considers a recurrent neural network (RNN) with a special class of discontinuous activation function which is piecewise constants in the state space. One sufficient condition is established to ensure that the novel recurrent neural networks can have (4k−1)ⁿ locally exponential stable equilibrium points. Such RNN is suitable for synthesizing high-capacity associative memories. The design procedure is presented with the method of singular value decomposition. Finally, the validity and performance of the results are illustrated by use of two numerical examples.     

Multivalued associative memories based on recurrent networks

A multivalued neural associative memory model based on a recurrent network structure is proposed. This model adopts the same principle proposed in the authors' previous work, the exponential correlation associative memories (ECAM). The model also has a very high storage capacity and strong error-correction capability. The major components of the new model include a weighted average process and some similarity-measure computation. As in ECAM, in order to enhance the differences among the weights and make the largest weights more overwhelming, the new model incorporates a nonlinear function in the calculation of weights. Several possible similarity measures suitable for this model are suggested. Simulation results of the performance of the new model with different measures show that, loaded with 500 64-component patterns, the model can sustain noise with power about one fifth to three fifths of the average signal power.     

On neural networks that design neural associative memories

The design problem of generalized brain-state-in-a-box (GBSB) type associative memories is formulated as a constrained optimization program, and "designer" neural networks for solving the program in real time are proposed. The stability of the designer networks is analyzed using Barbalat's lemma. The analyzed and synthesized neural associative memories do not require symmetric weight matrices. Two types of the GBSB-based associative memories are analyzed, one when the network trajectories are constrained to reside in the hypercube [-1, 1](n) and the other type when the network trajectories are confined to stay in the hypercube [0, 1](n). Numerical examples and simulations are presented to illustrate the results obtained.     

Analysis of associative memories based on cellular neural networks with value-varying templates

ABSTRACT

In many research literatures, the dynamical behaviour of cellular neural networks (CNNs) is simplified by using cloning template. However, the flaws of cloning template are obvious, because the correlation between weights of cells in CNNs is enhanced. In order to overcome the shortcomings of cloning template, value-varying templates can be used in CNNs. In this paper, associative memories based on CNNs with value-varying templates are investigated. A criterion about stability of CNNs is presented. Then, the problem about obtaining parameters of CNNs can be translated into a problem of solving linear equations for each cell. A design procedure of associative memories is given by our theories and methods. From the procedure, the parameters of CNNs can be obtained. Finally, three examples are used to demonstrate the effectiveness of our theories and methods. And the results show that success rate of associative memories is higher than previous methods.     

Stability analysis of stochastic recurrent neural networks with unbounded time-varying delays

In this paper, the stability analysis issue of stochastic recurrent neural networks with unbounded time-varying delays is investigated. By the idea of Lyapunov function and the semi-martingale convergence theorem, both pth moment exponential stability and almost sure exponential stability are obtained. Moreover, the M-matrix technique is borrowed to make the results more applicable. Our criteria can be used not only in the case of bounded delay but also in the case of unbounded delay. Some earlier results are improved and generalized. An example is also given to demonstrate our results.     

Multistability of discrete-time recurrent neural networks with unsaturating piecewise linear activation functions

This paper studies the multistability of a class of discrete-time recurrent neural networks with unsaturating piecewise linear activation functions. It addresses the nondivergence, global attractivity, and complete stability of the networks. Using the local inhibition, conditions for nondivergence are derived, which not only guarantee nondivergence, but also allow for the existence of multiequilibrium points. Under these nondivergence conditions, global attractive compact sets are obtained. Complete stability is studied via constructing novel energy functions and using the well-known Cauchy Convergence Principle. Examples and simulation results are used to illustrate the theory.     

Analysis of associative memories based on stability of cellular neural networks with time delay

In the paper, associative memories based on cellular neural networks with time delay are presented. In some previous papers, the relationship between cloning templates is closer and stronger. Therefore, some methods are used to make the relationship loose. First, some theories on stability of cellular neural networks are given. Then, associative memories based on cellular neural networks are given on the basis of these theories. In addition, a design procedure of associative memories is introduced. Finally, some examples are given to verify the theoretical results and design procedures.     

Global asymptotic stability of recurrent neural networks with multiple time-varying delays.

In this paper, several sufficient conditions are established for the global asymptotic stability of recurrent neural networks with multiple time-varying delays. The Lyapunov-Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) approach are employed in our investigation. The results are shown to be generalizations of some previously published results and are less conservative than existing results. The present results are also applied to recurrent neural networks with constant time delays.     

Stability analysis of stochastic memristor-based recurrent neural networks with mixed time-varying delays

In this paper, the stability problem of stochastic memristor-based recurrent neural networks with mixed time-varying delays is investigated. Sufficient conditions are established in terms of linear matrix inequalities which can guarantee that the stochastic memristor-based recurrent neural networks are asymptotically stable and exponentially stable in the mean square, respectively. Two examples are given to demonstrate the effectiveness of the obtained results.

     

Some multistability properties of bidirectional associative memory recurrent neural networks with unsaturating piecewise linear transfer functions

Multistability is an important dynamical property in neural networks in order to enable certain applications where monostable networks could be computationally restrictive. This paper studies some multistability properties for a class of bidirectional associative memory recurrent neural networks with unsaturating piecewise linear transfer functions. Based on local inhibition, conditions for globally exponential attractivity are established. These conditions allow coexistence of stable and unstable equilibrium points. By constructing some energy-like functions, complete convergence is studied.     

Parameters estimation and synchronization of uncertain coupling recurrent dynamical neural networks with time-varying delays based on adaptive control

Neural Computing and Applications - This paper mainly studies the parameters estimation and synchronization of coupling recurrent dynamical neural networks (CRDNNs). Here, the weights and coupling...     

Two algebraic criteria for input-to-state stability of recurrent neural networks with time-varying delays

This paper presents two algebraic criteria for the input-to-state stability of recurrent neural networks with time-varying delays. The criteria which also ensure global exponential stability when the input u(t) is equal to 0 and is easy to be verified only with the connection weights of the recurrent neural networks. Two numerical examples are given to demonstrate the effectiveness of the proposed criteria.     

Improved conditions for global exponential stability of recurrent neural networks with time-varying delays

This paper presents new theoretical results on global exponential stability of recurrent neural networks with bounded activation functions and time-varying delays. The stability conditions depend on external inputs, connection weights, and time delays of recurrent neural networks. Using these results, the global exponential stability of recurrent neural networks can be derived, and the estimated location of the equilibrium point can be obtained. As typical representatives, the Hopfield neural network (HNN) and the cellular neural network (CNN) are examined in detail.     

New results on robust exponential stability for discrete recurrent neural networks with time-varying delays

This paper is concerned with the problem of robust exponential stability analysis for uncertain discrete recurrent neural networks with time-varying delays. In terms of linear matrix inequality (LMI) approach, some novel stability conditions are proposed via a new Lyapunov function. Neither any model transformation nor free-weighting matrices are employed in our theoretical derivation. The established stability criteria significantly improve and simplify some existing stability conditions. Numerical examples are given to demonstrate the effectiveness of the proposed methods.     

Dissipativity analysis of neural networks with time-varying delays

A new definition of dissipativity for neural networks is presented in this paper. By constructing proper Lyapunov functionals and using some analytic techniques, sufficient conditions are given to ensure the dissipativity of neural networks with or without time-varying parametric uncertainties and the integro-differential neural networks in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the obtained results.     

Stability of switched neural networks with time-varying delays

This paper investigates the globally exponential stability of switched neural networks with time-varying delays. By virtue of mode-dependent average dwell time, some significant criteria of exponential stability are obtained for delayed switched neural networks with only stable subsystems or with both stable subsystems and unstable subsystems. The proposed theoretical results could be utilized not only to verify the globally exponential stability of switched neural networks, but also to design appropriate switching signal to guarantee the globally exponential stabilization. They can explicitly reflect the effect of mode-dependent average dwell time on the stability of switched neural networks. In contrast to the previous results, the proposed criteria are more straightforward and effective in the real-world application. Three numerical examples are introduced to illustrate the effectiveness of the proposed results.

     

Improved exponential stability criteria for recurrent neural networks with time-varying discrete and distributed delays

In this paper, the problem of the global exponential stability analysis is investigated for a class of recurrent neural networks (RNNs) with time-varying discrete and distributed delays. Due to a novel technique when estimating the upper bound of the derivative of Lyapunov functional, we establish new exponential stability criteria in terms of LMIs. It is shown that the obtained criteria can provide less conservative results than some existing ones. Numerical examples are given to show the effectiveness of the proposed results.     

Stability results for stochastic bidirectional associative memory neural networks with multiple discrete and distributed time-varying delays

This paper is concerned with the global asymptotic stability of a class of stochastic bidirectional associative memory neural networks with both multiple discrete and distributed time-varying delays. A new criterion of asymptotic stability is derived in terms of linear matrix inequality, which can be efficiently solved by a standard numerical software. An illustrative numerical example is also given to show the applicability and effectiveness of the proposed results.     

An estimation of the domain of attraction for recurrent neural networks with time-varying delays

Based on Lyapunov–Krasovskii functional or Lyapunov–Razumikhin functional method and invariant set principle, we presented a new method to estimate the domain of attraction for general recurrent neural networks with time-varying delays. Convex optimization method is proposed to enlarge and estimate the domain of attraction. Local exponential stability conditions are derived, which can be expressed as linear matrix inequalities (LMIs) in terms of all the varying parameters and hence can be easily checked in both analysis and design.