Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters

In this paper, the problem of stochastic stability for a class of time-delay Hopfield neural networks with Markovian jump parameters is investigated. The jumping parameters are modeled as a continuous-time, discrete-state Markov process. Without assuming the boundedness, monotonicity and differentiability of the activation functions, some results for delay-dependent stochastic stability criteria for the Markovian jumping Hopfield neural networks (MJDHNNs) with time-delay are developed. We establish that the sufficient conditions can be essentially solved in terms of linear matrix inequalities.     

A novel approach based on recurrent neural networks applied to nonlinear systems optimization

This paper presents an efficient approach based on recurrent neural network for solving nonlinear optimization. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid subspace technique. These parameters guarantee the convergence of the network to the equilibrium points that represent an optimal feasible solution. The main advantage of the developed network is that it treats optimization and constraint terms in different stages with no interference with each other. Moreover, the proposed approach does not require specification of penalty and weighting parameters for its initialization. A study of the modified Hopfield model is also developed to analyze its stability and convergence. Simulation results are provided to demonstrate the performance of the proposed neural network.     

Pattern-specific neural network design

We present evidence that the performance of the traditional fully connected Hopfield model can be dramatically improved by carefully selecting an information-specific connectivity structure, while the synaptic weights of the selected connections are the same as in the Hopfield model. Starting from a completely disconnected network we let genuine Hebbian synaptic connections grow, one by one, until a desired degree of stability is achieved. Neural pathways are thus fixed notbefore, butduring the learning phase.     

Gibbs states of the Hopfield model with extensively many patterns

We consider the Hopfield model withM(N)=N patterns, whereN is the number of neurons. We show that if is sufficiently small and the temperature sufficiently low, then there exist disjoint Gibbs states for each of the stored patterns, almost surely with respect to the distribution of the random patterns. This solves a provlem left open in previous work. The key new ingredient is a self-averaging result on the free energy functional. This result has considerable additional interest and some consequences are discussed. A similar result for the free energy of the Sherrington-Kirkpatrick model is also given.     

Rigorous results on the thermodynamics of the dilute Hopfield model

We study the Hopfield model of an autoassociative memory on a random graph onN vertices where the probability of two vertices being joined by a link isp(N). Assuming thatp(N) goes to zero more slowly thanO(1/N), we prove the following results: (1) If the number of stored patternsm(N) is small enough such thatm(N)/Np(N) 0, asN, then the free energy of this model converges, upon proper rescaling, to that of the standard Curie-Weiss model, for almost all choices of the random graph and the random patterns. (2) If in additionm(N) < ln N/ln 2, we prove that there exists, forT< 1, a Gibbs measure associated to each original pattern, whereas for higher temperatures the Gibbs measure is unique. The basic technical result in the proofs is a uniform bound on the difference between the Hamiltonian on a random graph and its mean value.     

Rigorous bounds on the storage capacity of the dilute Hopfield model

We study a neural network model consisting ofN neurons where a dendritic connection between each pair of neurons exists with probabilityp and is absent with probability 1-p. For the Hopfield Hamiltonian on such a network, we prove that ifp c[(lnN)/N]^1/2, the model can store at leastm= _cpN patterns, where _c 0.027 ifc 3 and decreases proportional to 1/(–lnc) forc small. This generalizes the results of Newman for the standard Hopfield model.     

ON THE ASYMPTOTIC BEHAVIOR OF HOPFIELD NEURAL NETWORK WITH PERIODIC INPUTS

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Dynamic behaviors of a class of memristor-based Hopfield networks

In this Letter, we analyze the dynamic behaviors for a class of memristor-based Hopfield networks. Some sufficient conditions are obtained which ensure the essential bound of solutions and global exponential stability of memristor-based Hopfield networks by using analysis approaches, and the criteria act as significant values for qualitative analysis of memristor-based Hopfield networks. Finally, a numerical example is given to show the effectiveness of our results.     

Neural Networks in Which Synaptic Patterns Fluctuate with Time

We study a stochastic neural-network model in which neurons and synapses change with a priori probability p and 1–p, respectively, in the limit p0. This implies neuron activity competing with fast fluctuations of the synaptic connections—in fact, random oscillations around values given by a learning (for example, Hebb's) rule. The consequences for the system performance of a dynamics constantly checking at random the set of memorized patterns is thus studied both analytically and numerically. We describe various nonequilibrium phase transitions whose nature depends on the properties of fluctuations. We find, in particular, that under rather general conditions locally stable mixture states do not occur, and pattern recognition and retrieval processes are substantially improved for some classes of synaptic fluctuations.