Dynamics of Delayed Neural Networks with Impulses
Xiaodi Li · Journal of Applied & Computational Mathematics · 2012
Although there are many important results dealing with the static attractors (i.e., equilibrium points) of various NNs, experimental and theoretical studies have revealed that periodic attractors (i.e., stationary oscillation) in NNs is also a very interesting dynamic behavior as many biological and cognitive activities (e.g., heartbeat, respiration, mastication, locomotion, and memorization) exhibit periodicity. Persistent oscillation, such as limit cycles (periodic orbits), represents a common feature of neural firing patterns produced by dynamic interplay between cellular and synaptic mechanisms. Moreover, stationary oscillations in NNs have found many applications such as associative memories, pattern recognition, machine learning, and robot motion control etc. Investigation of stationary oscillations on NNs is indispensable for practical design and engineering applications of network models. Also, an equilibrium point can be viewed as a special periodic attractor of neural networks with arbitrary period. In this sense, the analysis of periodic attractor of neural networks may be considered to be more general than that of equilibrium point. In addition, there are