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.

Quantized stabilization of wireless networked control systems with packet losses.

This paper considers stabilization of discrete-time linear systems, where wireless networks exist for transmitting the sensor and controller information. Based on Markov jump systems, we show that the coarsest quantizer that stabilizes the WNCS is logarithmic in the sense of mean square quadratic stability and the stabilization of this system can be transformed into the robust stabilization of an equivalent uncertain system. Moreover, a method of optimal quantizer/controller design in terms of linear matrix inequality is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.

Impulsive Multiconsensus of Second-Order Multiagent Networks Using Sampled Position Data.

A multiconsensus problem of multiagent networks is solved in this paper, where multiconsensus refers to that the states of multiple agents in each subnetwork asymptotically converge to an individual consistent value when there exist information exchanges among subnetworks. A distributed impulsive protocol is proposed to achieve multiconsensus of second-order multiagent networks in terms of three categories: 1) stationary multiconsensus; 2) the first dynamic multiconsensus; and 3) the second dynamic multiconsensus. This impulsive protocol utilizes only sampled position data and is implemented at sampling instants. For those three categories of multiconsensus, the control parameters in the impulsive protocol are designed, respectively. Moreover, necessary and sufficient conditions are derived, under which each multiconsensus can be reached asymptotically. Several simulations are finally provided to demonstrate the effectiveness of the obtained theoretical results.

Stability and bifurcation analysis of new coupled repressilators in genetic regulatory networks with delays.

The genetic regulatory networks are complex dynamic systems which reflect various kinetic behaviors of living things. In this paper, a new structure of coupled repressilators is introduced to exploit the underlying functions. The new coupled repressilator model consists of two identical repressilators inhibiting each other directly. The coupling delays are taken into account. The existence of a unique equilibrium for this system is verified firstly, then the stability criteria for equilibrium are analyzed without and with coupling delays. The different functions on equilibrium and its stability played by related biochemical parameters in the structure including maximal transcription rate, coupling strength, the decay rate ratio between proteins and mRNAs, and coupling delays are discussed. At last, several numerical simulations are made to demonstrate our results.