Importance of Chaos Synchronization on Technology and Science

In this chapter the authors talk about importance of chaos synchronization on technology and science. This chapter is developed in three sections. In the former the authors tackle the subject related with the so-called the synchronized state in the sense of identical synchronization. It is done via robust nonlinear observer design, considering corrupted measurements and model uncertainties, coupling uncertainty estimators with nonlinear state observers. The second part treats the subject related to the applications to chaos communications, that is to say, an application of chaos theory which is aimed to provide security in the transmission of information performed through telecommunications technologies, speaking roughly at the transmitter, a message is added on to a chaotic signal and then, the message is masked in the chaotic signal. As it carries the information, the chaotic signal is also called chaotic carrier. This is done via control theory and is a particular case of chaos synchronization. Finally, in the latter section the authors talk about application to synchronization of biological systems that is to say, the intercellular Ca²+ waves have been seen like a mechanism by means of which a group of cells can communicate with one another and coordinate a multicellular response to a local event. Recently, it has been observed in a variety of systems that calcium signals can also propagate from one cell to another and thereby serve as a means of intercellular communication. The desire to understand the biophysical mechanisms of cellular dynamics has lead to introduce feedback control laws in some biological systems. Departing from the above ideas, this section explores links between feedback control schemes, with an external input, and intracellular calcium functions for coordination and control.