Stability Analysis of a Class of Neural Networks with State-Dependent State Delay

Abstract

The differential equations with state-dependent delay are very important equations because they can describe some problems in the real world more accurately. Due to the complexity of state-dependent delay, it also brings challenges to the research. The value of delay varying with the state is the difference between state-dependent delay and time-dependent delay. It is impossible to know exactly in advance how far historical state information is needed, and then the problem of state-dependent delay is more complicated compared with time-dependent delay. The dominating work of this paper is to solve the stability problem of neural networks equipped with state-dependent state delay. We use the purely analytical method to deduce the sufficient conditions for local exponential stability of the zero solution. Finally, a few numerical examples are presented to prove the availability of our results.