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.