Multisynchronization of Coupled Heterogeneous Genetic Oscillator Networks via Partial Impulsive Control

This paper focuses on the collective dynamics of multisynchronization among heterogeneous genetic oscillators under a partial impulsive control strategy. The coupled nonidentical genetic oscillators are modeled by differential equations with uncertainties. The definition of multisynchronization is proposed to describe some more general synchronization behaviors in the real. Considering that each genetic oscillator consists of a large number of biochemical molecules, we design a more manageable impulsive strategy for dynamic networks to achieve multisynchronization. Not all the molecules but only a small fraction of them in each genetic oscillator are controlled at each impulsive instant. Theoretical analysis of multisynchronization is carried out by the control theory approach, and a sufficient condition of partial impulsive controller for multisynchronization with given error bounds is established. At last, numerical simulations are exploited to demonstrate the effectiveness of our results.