Dynamics analysis of a class of planar systems with time-varying delays

This paper formulates and studies a model of planar systems. The model can well describe many practical architectures of delayed neural networks, which is generalization of some existing neural networks under a time-varying environment. Without assuming the smoothness, monotonicity and boundedness of the activation functions, the existence and global exponential stability of its periodic solutions are investigated. Some explicit and conclusive results are established. Our approach is based on the continuation theorem of the coincidence degree, a priori estimates, and differential inequalities.