In this letter, the absolute exponential stability result of neural networks with asymmetric connection matrices is obtained, which generalizes the existing one about absolute stability of neural networks, by a new proof approach. It is demonstrated that the network time constant is inversely proportional to the global exponential convergence rate of the network trajectories to the unique equilibrium. A numerical simulation example is also given to illustrate the obtained analysis results.

An adaptive stability-growth (ASG) learning algorithm is proposed for improving, as much as possible, the stability of a Hopfield-type associative memory. While the ASG algorithm can be used to determine the optimal stability instead of the well-known minimum-overlap (MO) learning algorithm with sufficiently large lower bound for MO value, it converges much more quickly than the MO algorithm in real implementation. Therefore, the proposed ASG algorithm is more suitable than the MO algorithm for real-world design of an optimal Hopfield-type associative memory.

Recurrent neural networks have the potential of performing parallel computation for associative memory and optimization, which is realized by the electronic implementation of neural networks in VLSI technology. Since the time delays in real electronic implementation of neural networks are unavoidably encountered and they can cause systems to oscillate, it is thus practically important to investigate the qualitative properties of neural networks with time delays. In this paper, a class of sufficient conditions is obtained, under which neural networks are globally asymptotically stable independent of time delays.

A main result in this paper is that for a Hopfield-type neural circuit with a symmetric connection matrix T, the negative semidenfiniteness of T is a necessary and sufficient condition for absolute exponential stability. While this result extends one of absolute stability in Forti, et al. [1], its proof given in this paper is simpler, which is completed by an approach different from one used in Forti et al. [1]. The most significant consequence is that the class of neural networks with negative semidefinite matrices T is the largest class of symmetric networks that can be employed for embedding and solving optimization problem with global exponential rate of convergence to the optimal solution and without the risk of spurious responses.

This paper proposes the overlapped block relaxation Newton method for greatly reducing the number of iterations needed for simulating large scale nonlinear circuits. The circuit is partitioned into subcircuits, i.e., overlapped blocks consisting of core nodes and overlapped nodes. The core nodes form the core circuit for each overlapped block and the overlapped nodes form the overlapped circuit. The Newton-Raphson method is applied to all overlapped blocks independently and the approximation vector for relaxation is determined by node voltages of core nodes. An overlapped circuit is considered to be the representative circuit of the outside circuit for the core circuit. Therefore, the accuracy of the approximation vector for relaxation may be improved and the number of relaxation steps may be greatly reduced. Core nodes are determined automatically by reflecting the circuit structure, then the overlapping level is determined automatically. We show that this method has good performance for simulating large scale circuits, and that it is faster than the nonlinear direct method which is used in standard circuit simulators.

This paper obtains some new results about the existence, uniqueness, and global asymptotic stability of the equilibrium of a nonlinear continuous neural network, under a sufficient condition weaker than ones presented in the literature. The avobe obtained results can also imply the existing ones about avsolute stability of nonlinear continuous neural networks

This paper describes an innovative, high-speed optical backboard bus composed of an optical star coupler, optical-transmitter modules, optical-receiver modules, and optical multi-mode glass fibers. A highly efficient optical coupling structure with an aspherical lens and a laser diode was designed to achieve a coupling efficiency of 90%, enabling distribution of optical signals at up to 1 Gb/s to 50 function boards. Embedded optical fibers in a printed circuit board were used to achieve precise control of the optical propagation delay times and permit a high packaging density. We developed small laser-diode and photo-diode modules suitable for optical coupling with the embedded fibers. A fabricated prototype optical backboard bus controlled by a controller IC mounted on a function board was able to successfully distribute high-speed optical signals to function boards with a high packaging density.

In this letter, we obtain the absolute exponential stability result of neural networks with globally Lipschitz continuous, increasing and bounded activation functions under a sufficient condition which can unify some relevant sufficient ones for absolute stability in the literature. The obtained absolute exponential stability result generalizes the existing ones about absolute stability of neural networks. Moreover, it is demonstrated, by a mathematically rigorous proof, that the network time constant is inversely proportional to the global exponential convergence rate of the network trajectories to the unique equilibrium. A numerical simulation example is also presented to illustrate the analysis results.

This letter points out that while a class of conditions presented in Matsuoka K. [1] are truly sufficient for absolute stability of neural networks, the proof of the sufficiency given in [1] is not sound. As a remark, a mathematically rigorous proof of the sufficiency of the class of conditions for absolute stability of neural networks is provided.

In this paper, we prove that for a class of nonsymmetric neural networks with connection matrices T having nonnegative off-diagonal entries, -T is an M-matrix is a necessary and sufficient condition for absolute exponential stability of the network belonging to this class. While this result extends the existing one of absolute stability in Forti, et al., its proof given in this paper is simpler, which is completed by an approach different from one used in Forti, et al. The most significant consequence is that the class of nonsymmetric neural networks with connection matrices T satisfying -T is an M-matrix is the largest class of nonsymmetric neural networks that can be employed for embedding and solving optimization problem with global exponential rate of convergence to the optimal solution and without the risk of spurious responses. An illustrating numerical example is also given.