The problem of synchronization of chaotic systems has been in the literature for over 30 years, andit has been thoroughly studied although not exhaustively. More or less at the same time appeared the possibility of controlling chaotic motion which was firstly applied to the control of chaotic orbits. Synchronization of systems of many chaotic elements became a necessity due to the possibility of using them in encrypted communications, since they would provide high dimensionality chaos. This area of research has been quite productive because of the richness of processes that will synchronize rather complex systems. But, in spite of that, all systems known synchronize asymptotically. Recently we showed that a couple of chaotic systems can be synchronized in a finite time, not necessarily losing their chaotic dynamics. In this project we attempt to continue this type of study to search of the possibility to apply it to finite time synchrony of networks, with applications to several systems such as networks of neurons during an epileptic seizure.
News published in Agência FAPESP Newsletter about the scholarship: