Global exponential stability of delayed complex-valued neural networks with discontinuous activation functions

Abstract

This paper studies the global exponential stability of delayed complex-valued neural networks with discontinuous activation functions. By introducing the complex-valued Filippov differential inclusion, we construct the framework of studying the dynamical behaviors of complex-valued neural networks with discontinuous bivariate activation functions. By employing the Leray–Schauder alternative theorem and choosing an appropriate Lyapunov function, we prove the global exponential stability of delayed complex-valued neural networks with discontinuous activation functions. The numerical example provided shows the effectiveness of the obtained results.