Dynamics of fuzzy genetic regulatory networks with leakage and mixed delays in doubly-measure pseudo-almost periodic environment

Abstract

The study of dynamics behaviors of genetic regulatory networks (GRNs) is essential for the understanding of living organisms at both molecular and cellular levels. This paper deals with a class of fuzzy genetic regulatory networks (FGRNs) with time varying-delays in leakage terms, time-varying discrete delays, unbounded distributed delays, and doubly-measure pseudo-almost periodic parameters. Based on the doubly-measure pseudo-almost periodic theory, exponential dichotomy, differential inequality, and the Banach fixed point theorem, we establish some sufficient conditions to support the existence and global exponential stability of doubly-measure pseudo-almost periodic solutions for the considered model. A numerical example along with a graphical illustration are presented to support our main results. The results of this paper are new and extend existing GRNs models using almost periodic and weighted pseudo-almost periodic functions to support a wider range of regulatory processes.