Quasi-Multisynchronization and Quasi-Monosynchronization of Delayed Neural Networks With Parameter Mismatch via Impulsive Control

This article focus on the quasi-multisynchronization and quasi-monosynchronization of delayed neural networks (DNNs) with parameter mismatch via impulsive control. At first, a kind of actication functions (AFs) is proposed and multistability/monostability criteria of DNNs are given. By judging 2<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> algebraic inequalities, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i>-neuron DNNs with this kind of AFs can produce 2<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>n</i></sup> locally stable equilibrium points (EPs) or one globally stable EP. In addition, a kind of impulsive controller is designed. Impulsive control strategy proposed in this paper can save the bandwidth and reduce the communication cost compared with continuous-time control strategy. Moreover, the concept of quasi-multisynchronization of DNNs is proposed for the first time and sufficient conditions are given to ensure quasi-multisynchronization and quasi-monosynchronization of DNNs by building the comparison system and using the Lagrange method of variation of parameters. Under this control method, a monostable system can become a multistable system, which means that the storage capacity (SC) of DNNs is improved. Lastly, two examples are illustrated to testify the validity of the proposed theory and method.