The influence of delayed coupling and feedback on dynamical systems has been investigated for several decades. However, the early studies were mostly restricted to a few systems, and powerful mathematical and computational tools to treat these systems were lacking. In recent years, more and more systems are being recognized to be influenced by or to be describable via delayed coupling. Moreover, the application of delay systems to a spectrum of applications is being pursued, ranging from encrypted communication to system control. An important aspect is that now tools have become available that allow one to study delay systems experimentally, via numerical simulations and via analytic treatment in an unprecedentedly detailed and, even more importantly, coherent manner. Therefore, in recent years, dynamical systems with delays have evolved as a major topic in nonlinear sciences.
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