Global µ-stability of neutral-type impulsive complex-valued BAM neural networks with leakage delay and unbounded time-varying delays

Abstract

This paper investigates the existence and uniqueness of the equilibrium point and its global µ-stability for neutral-type impulsive complex-valued bidirectional associative memory neural networks with leakage delay and unbounded time-varying delays, by considering two types of Lipschitz conditions to be satisfied by the activation functions. The homeomorphism lemma is used to obtain a sufficient condition for the existence and uniqueness of the equilibrium point. Sufficient delay-dependent conditions both in terms of complex-valued and real-valued linear matrix inequalities which ensure the global µ-stability of the equilibrium point are obtained by constructing appropriate Lyapunov–Krasovskii functionals with simple, double, and triple integral terms, and using the free weighting matrix method, simple and double complex-valued Jensen inequalities, the complex-valued reciprocally convex combination inequality, and the complex-valued Wirtiger-based integral inequality. Lastly, two numerical examples are provided to illustrate the effectiveness of the obtained theoretical results.