Multisynchronization of Delayed Coupled Neural Networks With General Activation Functions via Impulsive Control.

Abstract

This article studies the multisynchronization of delayed coupled neural networks (DCNNs) with general activation functions (AFs) via impulsive control. At first, a kind of AFs is proposed, and the $\boldsymbol {n}$ -neuron subnetwork with this kind of AFs can produce $\boldsymbol {(p+1)^{n}}$ locally stable equilibrium points (EPs) or periodic orbits (POs) by judging $\boldsymbol {2n(p+1)}$ algebraic inequalities and a nonsingular $\boldsymbol {M}$ -matrix. Compared with some specific AFs, such as the Sigmoid AFs or the saturated AFs, the AFs proposed in this article are more general. In addition, a kind of impulsive controller is designed. Compared with a continuous-time control strategy, the impulsive control strategy proposed in this article can reduce the communication cost and save bandwidth. Moreover, sufficient conditions are given to ensure both dynamical multisynchronization (DMS) and static multisynchronization (SMS) of DCNNs by building the comparison system and using the Lagrange method of variation of parameters. Lastly, an example is illustrated to testify to the validity of the obtained results.