turkmath.org

Impulsive neural networks have been enormously developed issuing from the fact that in implementation of electronic networks, the state of the networks is subject to instantaneous perturbations and experiences abrupt change at certain moments, which may be caused by switching phenomenon, frequency change or other sudden noises. On the other hand, studies on neural dynamical systems not only involve stability and periodicity, but also involve other dynamic behaviors such as almost periodicity, chaos and bifurcation. If one considers long-term dynamical behaviors, the periodic parameters often turn out to experience certain perturbations, that is, parameters become periodic up to a small error. Thus, almost periodic oscillatory behavior is considered to be more accordant with reality. Although it is of great importance in real life applications, the generalization to almost periodicity has been rarely studied in the literature. In this talk, we address a new model of neural networks related to the discontinuity phenomena which is called impulsive recurrent neural networks with variable moments of time. Sufficient conditions for existence and uniqueness of exponentially stable almost periodic solution are investigated. An example is given to illustrate our theoretical results. Equations with non- fixed moments of discontinuity create a great number of opportunities for theoretical inquiry as well as theoretical challenges. The proposed new involvements have an important role for the real world problems.