Finite time synchronization of complex dynamical networks.

*(Chinese. English summary)* Zbl 1212.93008
Summary: Complex networks are everywhere. Synchronization is a very important nonlinear phenomenon which universally exists in nature. Over the last decade, many researchers have further investigated the synchronization of complex dynamical networks, including identical synchronization, clustering synchronization, partial synchronization, etc. The characterization of the synchronization speed of complex dynamical networks in most known results is asymptotic. That is, complex networks can realize synchronization only when the time $t$ tends to infinity. However, there are few results reported on how long complex networks can reach synchronization. Based on two kinds of typical complex dynamical networks with nonlinear coupling, this paper further explores the finite-time synchronization of complex dynamical networks. In detail, under some suitable conditions, it is proved that the above complex dynamical networks can realize accurate synchronization within finite-time. Moreover, a typical numerical simulation is then given to validate the effectiveness of the proposed criteria for finite-time synchronization. It should be especially pointed out that the finite-time synchronization successfully overcomes the difficulty of infinite synchronization time. The above results have some important practical meaning for real-world engineering applications.

##### MSC:

93A30 | Mathematical modelling of systems |

90B10 | Network models, deterministic (optimization) |

93C10 | Nonlinear control systems |

93A15 | Large scale systems |