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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 n-dimensional recurrent neural network can have 3k15k2 equilibrium points with 0 ≤ k1 + k2≤ n, and2k13k2 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. [ABSTRACT FROM AUTHOR]

Recent research in memristor-CMOS neuromorphic learning systems has led to the practical realization of neuro-inspired learning architectures. At present, the deep understanding of nonlinear dynamical mechanisms governing memristive neural systems is still an open issue. In this paper, the global exponential stability problem is investigated for a class of memristive neural systems with time-varying delays. By employing comparison principle, some novel global exponential stability results are derived. These stability conditions also improve upon some existing results. In addition, the obtained results are convenient to estimate the exponential convergence rate. These theoretical studies are very useful in analyzing the composite behavior of complex memristor circuits. [ABSTRACT FROM AUTHOR]

This paper presents a design method for synthesizing associative memories based on discrete-time recurrent neural networks. The proposed procedure enables both hetero- and auto- associative memories to be synthesized with high storage capacity and assured global asymptotic stability. The stored patterns are retrieved by feeding probes via external inputs rather than initial conditions. As typical representatives, discrete-time cellular neural networks (CNNs) designed with space-invariant cloning templates are examined in detail. In particular, it is shown that procedure herein can determine the input matrix of any CNN based on a space-invariant cloning template which involves only a few design parameters. Two specific examples and many experimental results are included to demonstrate the characteristics and performance of the designed associative memories. [ABSTRACT FROM AUTHOR]

In this letter, some sufficient conditions are obtained to guarantee recurrent neural networks with linear saturation activation functions, and time-varying delays have multiequilibria located in the saturation region and the boundaries of the saturation region. These results on pattern characterization are used to analyze and design autoassociative memories, which are directly based on the parameters of the neural networks. Moreover, a formula for the numbers of spurious equilibria is also derived. Four design procedures for recurrent neural networks with linear saturation activation functions and time-varying delays are developed based on stability results. Two of these procedures allow the neural network to be capable of learning and forgetting. Finally, simulation results demonstrate the validity and characteristics of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, the multiperiodicity of a general class of discrete-time delayed neural networks (DTDNNs) is formulated and studied. Several sufficient conditions are obtained to ensure n-neuron DTDNNs can have 2n periodic orbits and these periodic orbits are locally attractive. In addition, we give the conditions for a periodic orbit to be locally or globally attractive when the periodic orbit locates in a designated region. As two typical representatives, the Hopfield neural network and the cellular neural network are examined in detail. These conditions improve and extend the existing stability results in the literature. Simulations results are also discussed in three illustrative examples. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The Lagrangian formalism defined by Scherpen et al.for (switching) electrical circuits, is adapted to the Lagrangian formalism defined on Lie algebroids. This allows us to define regular Lagrangians and consequently, well-defined Hamiltonian descriptions of arbitrary LC networks. The relation with other Hamiltonian approaches is also analyzed and interpreted. [ABSTRACT FROM AUTHOR]