Synchronization of chaotic systems, a patently nonlinear
phenomenon, has emerged as a highly active interdisciplinary
research topic at the interface of physics, biology, applied
mathematics and engineering sciences. In this connection,
time-delay systems described by delay differential equations have
developed as particularly
suitable tools for modeling specific dynamical systems. Indeed,
time-delay is ubiquitous in many physical systems, for example due
switching speeds of amplifiers in electronic circuits, finite
lengths of vehicles in traffic flows, finite signal propagation
times in biological networks and circuits, and quite generally
whenever memory effects are relevant.
This monograph presents the basics of chaotic time-delay systems
and their synchronization with an emphasis on the effects of
time-delay feedback which give rise to new collective
Special attention is devoted to scalar chaotic/hyperchaotic
systems, and some higher order models, occurring in different
branches of science and technology as well as to the
synchronization of their coupled versions.
Last but not least, the presentation as a whole strives for a
balance between the necessary mathematical description of the
and the detailed presentation of real-world applications.
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