New results on network of neurons with delayed feedback: Periodical switching of excitation and inhibition

Considered is a class of periodic delay differential equationx˙(t)=−a(t)x(t)+b(t)f(x(t−τ(t)))+I(t). Such a differential system can be regarded as a model of an isolated neuron in a periodic environment and also appears in several other applications. By means of the continuation theorem and inequalities analysis, we not only obtain some sufficient conditions ensuring the existence and global exponential stability of the periodic solution but also estimate the exponentially convergence rate. Our results are less restrictive than previously known criteria and can be applied to neural networks with a broader range of activation functions.