Exponential Synchronization of Delayed Switching Genetic Oscillator Networks via Mode-Dependent Partial Impulsive Control

This paper investigates the global exponential synchronization problem of switching genetic oscillator networks with time-varying delays by using a newly-designed partial impulsive control scheme. This scheme is only required to control partial molecules of each gene node, different from the traditional pinning impulsive control scheme, in which all the molecules of the chosen nodes are assumed to be under control. Besides, both the number of controlled molecules and the impulsive strength of the presented control scheme are mode-dependent, either identical or different with respect to different topologies. Based on the Lyapunov stability theory and comparison principle, the sufficient criteria for guaranteeing the exponential synchronization of genetic oscillator networks with finite arbitrarily switching topologies are established. Finally, two illustrative examples are presented to verify the main results.