Introduction to chaos

Abstract

Chaos is a fascinating phenomenon that has been observed in nature (weather and climate, dynamics of satellites in the solar system, time evolution of the magnetic field of celestial bodies, and population growth in ecology) and laboratory (electrical circuits, lasers, chemical reactions, fluid dynamics, mechanical systems, and magneto-mechanical devices). Chaotic behavior has also found numerous applications in electrical and communication engineering, information and communication technologies, biology and medicine. This was mainly due to the wideband character of the chaotic signals, easy experimental control of chaos and all that being achieved with an inexpensive lab realization of either the electric circuits or corresponding algorithms if only number series were in focus. Communication and signal processing applications of chaos, as areas of permanent interest, were roughly established since 1990, after the theories of chaos synchronization and chaos controlwere worked out in more details. Today, sound engineering applications of quasi random sequence generation, modeling of communication channels using chaos, chaotic cryptography, digital image encoding, and chaotic transport phenomena in complex networks all represent areas of permanent research with commercially viable engineering solutions [Kocarev et al 2009]. © 2011 Springer-Verlag Berlin Heidelberg.