GLOBAL EXPONENTIAL STABILITY AND PERIODIC OSCILLATIONS OF REACTION–DIFFUSION BAM NEURAL NETWORKS WITH PERIODIC COEFFICIENTS AND GENERAL DELAYS
Abstract
For a large class of reaction–diffusion bidirectional associative memory (RDBAM) neural networks with periodic coefficients and general delays, several new delay-dependent or delay-independent sufficient conditions ensuring the existence and global exponential stability of a unique periodic solution are given, by constructing suitable Lyapunov functionals and employing some analytic techniques such as Poincaré mapping. The presented conditions are easily verifiable and useful in the design and applications of RDBAM neural networks. Moreover, the employed analytic techniques do not require the symmetry of the bidirectional connection weight matrix, the boundedness, monotonicity and differentiability of activation functions of the network. In several ways, the results generalize and improve those established in the current literature.
This work was partially supported by the National Natural Science Foundation of China under Grant 10471059, the Natural Science Foundation of Jiangsu Province under Grant BK2001024, the Foundation for University Key Teachers of the Ministry of Education of China, and the Hong Kong Research Grants Council under Grant CityU 1115/03E.
