Hybrid Impulsive Neural Networks with Interval-Uncertain Weights

Abstract

Neural networks have emerged as a powerful illustrative diagram for the brain. Unveiling the mechanism of neural-dynamic evolution is one of the crucial steps toward understanding how the brain works and evolves. Inspired by the universal existence of impulses in many real systems, this chapter introduces a class of hybrid neural networks with impulses, time-delays and interval uncertainties, and studies its global dynamic evolution by robust interval analysis. The hybrid neural networks incorporate both continuous-time implementation and impulsive jump in mutual activations, where time-delays and interval uncertainties are represented simultaneously. By constructing a Banach contraction mapping, the existence and uniqueness of the equilibrium of the hybrid neural network model are proved and analyzed in detail. Based on nonsmooth Lyapunov functions and delayed impulsive differential equations, new criteria are derived for ensuring the global robust exponential stability of the hybrid neural networks. Convergence analysis together with illustrative examples show the effectiveness of the theoretical results.