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This brief presents two new results on the global stability of cellular neural networks with delay (DCCN's). First, a sufficient condition for the uniqueness and global asymptotic stability of the equilibrium point is given. Then, a sufficient condition for the existence of a stable equilibrium point in the total saturation region is obtained. The significance of the conditions is that the stability properties of the equilibrium point are not affected by the delay parameter. These conditions are also weaker than some previously given for global stability of DCNN's. Index Terms - Cellular neural networks, complete stability, global asymptotic stability, stable equilibrium points.

In this paper, we study the equilibrium set of cellular neural networks (CNN's). We establish new conditions for the stability of equilibria in delayed cellular neural networks (DCNN's), and we also study the topology of the equilibrium set - whether equilibria are isolated. Index Terms - Equilibria and generic properties.

In this brief, it is shown that one-dimensional Josephson junction arrays can be mapped onto sworks under some restrictions. Analytic expressions to the stability of equilibria of these arrays are derived and applied to the behavior of vortex solutions. Relations between these static solutions and a particular solution of a partial differential equation are shown. By means of the theory of Hamiltonian systems a qualitative theory for Josephson junction arrays is derived and applied in numerical simulations.

Complete stability of cellular neural networks and their associated dynamical system precludes the possibility of any periodic or chaotic behavior and is an important property to establish. In this paper complete stability of the opposite-sign cellular neural network is established provided that the template values fall within the range (p - 1)/2 < s < p - 1. The results in this paper extend the parameter range from previously known results.

In this paper, we present a sufficient condition for absolute stability of a larger class of dynamical neural networks. It is shown that the H-matrix condition on the interconnection matrix ensures the existence, uniqueness and global asymptotic stability (GAS) of the equilibrium point with respect to slope-limited activation functions. Index Terms--Absolute stability, neural networks.

In this paper, a sufficient condition is presented for the uniqueness and global asymptotic stability of the equilibrium point for delayed cellular neural networks (DCNN's). This condition imposes constraints on the feedback matrices independently of the delay parameter. This result is also discussed from the point of view of its relationship to earlier results. Index Terms--Delayed cellular neural network, global stability.

This letter points out that a statement in the above letter, saying that the sufficiency part of absolute stability result on neural networks in the above letter (Theorem 2.1) includes the sufficiency part of the absolute stability result in Forti et al. [1], is not correct under the stated conditions. On the other hand, it is shown that the sufficiency part of absolute stability result in Forti et al. [1] is included by the sufficiency part of a conjecture stated in the above letter (Conjecture 3.3). Index Terms - Absolute stability, neural networks.