This paper studies the synchronization characteristics of a locally connected, planar network of (leaky) integrateand-fire (I/F) neurons after Hopfield & Hertz (1995). Hopfield & Herz showed that, with the assumption of instantaneous ignal transmission, locally connected networks converge to periodic, synchronized oscillations. We verify these results as well as study their robustness when sign...

The original Hopfield neural networks model is adapted so that the weights of the resulting network are time varying. In this paper, the Discrete Hopfield neural networks with weight function matrix DHNNWFM the weight changes with time, are considered, and the stability of DHNNWFM is analyzed. Combined with the Lyapunov function, we obtain some important results that if weight function matrix W...

In this paper, a new genetic approach based on arithmetic crossover for solving the economic dispatch problem is proposed. Elitism, arithmetic crossover and mutation are used in the genetic algorithm to generate successive sets of possible operating policies. The proposed technique improves the quality of the solution. The new genetic approach is compared with an improved Hopfield NN approach (...

In this paper, the model of stochastic fuzzy Hopfield neural networks with time-varying delays and impulses (ISFVDHNNs) is established as a modified Takagi-Sugeno (TS) fuzzy model in which the consequent parts are composed of a set of stochastic Hopfield neural networks with time-varying delays and impulses. Then, the global exponential stability in the mean square for ISFVDHNNs is studied by e...

This paper presents a novel approach to the emulation of locomotor central pattern generators (CPGs) of legged animals. Based on Scheduling by Multiple Edge Reversal (SMER), a simple but powerful distributed algorithm, it is shown how oscillatory building blocks (OBBs) can be created and how OBB-based networks can be implemented as asymmetric Hopfield-like neural networks for the generation of ...

Many popular probabilistic models for temporal sequences assume simple hidden dynamics or low dimensionality of discrete variables. For higher dimensional discrete hidden variables, recourse is often made to approximate mean field theories, which to date have been applied to models with only simple hidden unit dynamics. We consider a class of models in which the discrete hidden space is defined...

For a given 0 < δ < 2 if [Nδ] neurons deviating from the memorized patterns are allowed, we constructively show that if and only if α(δ) := p(N)/N = (1 − 2δ)2/(1 − δ)2 all stored patterns are fixed points of the Hopfield model. If [NδN ] neurons are allowed with δN → 0 then αN = (1−2δN )2/(8−1(1−δN ))2 → 0 where 8 is the distribution function of the normal distribution. The result obtained by A...

The Hopfield model in a transverse field is investigated in order to clarify how quantum fluctuations affect the macroscopic behavior of neural networks. Using the Trotter decomposition and the replica method, we find that the α (the ratio of the number of stored patterns to the system size)-∆ (the strength of the transverse field) phase diagram of this model in the ground state resembles the α...