Existence and global exponential stability of periodic solution of two-neuron networks with time-varying delays

This paper is concerned with a delay differential system {ẋ(t)=−a1(t)x(t)+b1(t)f1(x(t−τ1(t)),y(t−τ2(t)))+I1(t),ẏ(t)=−a2(t)y(t)+b2(t)f2(x(t−τ3(t)),y(t−τ4(t)))+I2(t). Such a differential system can be regarded as a model of a two-neuron artificial neural network with delayed feedback. Some interesting results are obtained for the existence and exponential stability of the periodic solution for the system. Our approach is based on the continuation theorem of the coincidence degree, a priori estimates, and differential inequalities.