Jinde Cao

In this paper, two related problems, global asymptotic stability (GAS) and global robust stability (GRS) of neural networks with time delays, are studied. First, GAS of delayed neural networks is discussed based on Lyapunov method and linear matrix inequality. New criteria are given to ascertain the GAS of delayed neural networks. In the designs and applications of neural networks, it is necessary to consider the deviation effects of bounded perturbations of network parameters. In this case, a d

Both exponential stability and periodic oscillatory solution of bidirectional associative memory (BAM) networks with axonal signal transmission delays are considered by constructing suitable Lyapunov functional and some analysis techniques. Some simple sufficient conditions are given ensuring the global exponential stability and the existence of periodic oscillatory solutions of BAM with delays. These conditions are presented in terms of system parameters and have important leading significance

In this paper, based on the invariant principle of functional differential equations, a simple, analytical, and rigorous adaptive feedback scheme is proposed for the synchronization of almost all kinds of coupled identical neural networks with time-varying delay, which can be chaotic, periodic, etc. We do not assume that the concrete values of the connection weight matrix and the delayed connection weight matrix are known. We show that two coupled identical neural networks with or without time-v

In this paper, we propose and study a general array model of coupled delayed neural networks with hybrid coupling, which is composed of constant coupling, discrete-delay coupling, and distributed-delay coupling. Based on the Lyapunov functional method and Kronecker product properties, several sufficient conditions are established to ensure global exponential synchronization based on the design of the coupling matrices, the inner linking matrices, and/or some free matrices representing the relati

Based on the Lyapunov stability theorem as well as some facts about the positive definiteness and inequality of matrices, a new sufficient condition is presented for the existence of a unique equilibrium point and its global asymptotic stability for delayed CNNs. This condition imposes constraints on the feedback matrices independent of the delay parameter. This condition is less restrictive than that given in earlier references.

By employing the Lyapunov-Krasovskii functional and linear matrix inequality (LMI) approach, the problem of global asymptotical stability is studied for recurrent neural networks with both discrete time-varying delays and distributed time-varying delays. Some sufficient conditions are given for checking the global asymptotical stability of recurrent neural networks with mixed time-varying delay. The proposed LMI result is computationally efficient as it can be solved numerically using standard c

In this paper, the global exponential stability and periodicity of a class of recurrent neural networks with time delays are addressed by using Lyapunov functional method and inequality techniques. The delayed neural network includes the well-known Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks as its special cases. New criteria are found to ascertain the global exponential stability and periodicity of the recurrent neural networks with time del