Global exponential periodicity and stability of recurrent neural networks with multi-proportional delays

•Different from the prior works, here proportional delays are unbounded and time-varying.•Periodicity existing results of delay neural networks cannot be applied to the system in the paper.•The advantage is that the network's running time can be controlled by the network allowed delays.•Delay differential inequality is established, which is not (generalized) Halanay inequality.•The nonlinear activation functions are not necessarily differentiable, bounded, monotonic.

In this paper, a class of recurrent neural networks with multi-proportional delays is studied. The nonlinear transformation transforms a class of recurrent neural networks with multi-proportional delays into a class of recurrent neural networks with constant delays and time-varying coefficients. By constructing Lyapunov functional and establishing the delay differential inequality, several delay-dependent and delay-independent sufficient conditions are derived to ensure global exponential periodicity and stability of the system. And several examples and their simulations are given to illustrate the effectiveness of obtained results.