Global exponential stability of neural networks with non-smooth and impact activations

In this paper, we consider a model of impulsive recurrent neural networks with piecewise constant argument. The dynamics are presented by differential equations with discontinuities such as impulses at fixed moments and piecewise constant argument of generalized type. Sufficient conditions ensuring the existence, uniqueness and global exponential stability of the equilibrium point are obtained. By employing Green’s function we derive new result of existence of the periodic solution. The global exponential stability of the solution is investigated. Examples with numerical simulations are given to validate the theoretical results.

► We model an impulsive recurrent neural networks with piecewise constant argument of generalized type.
► We obtain sufficient conditions ensuring the existence, uniqueness and global exponential stability of the equilibrium point.
► By employing Green’s function we derive new result of existence of the periodic solution.
► The global exponential stability of the solution is investigated.
► Examples with numerical simulations are given to validate the theoretical results.