Oscillating dynamics of Lotka–Volterra neural networks with time-varying delays and distributed delays

This paper is concerned with the dynamical behaviors of doubly weighted Stepanov-like pseudo almost automorphic solution of Lotka–Volterra neural networks with time-varying delays and infinite distributed delays. Based on the Banach’s fixed point theorem, exponential dichotomy of linear differential equations, doubly weighted Stepanov-like pseudo almost automorphic functions theory and constructing a suitable Lyapunov functional, a set of sufficient criteria that guarantee the existence, uniqueness and S p -globally exponential stability of unique positive ( μ , ν ) -Stepanov like pseudo almost automorphic solution are discussed. Moreover, numerical simulations are carried out to illustrate the validity of the theoretical results.