Titlebook: Delay-Coupled Complex Systems; and Applications to Valentin Flunkert Book 2011 Springer-Verlag Berlin Heidelberg 2011 Complex networks.Con

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IntroductionDelays are ubiquitous in nature and occur, for instance, in coupled systems, in biological processes, neural systems, or in control problems. Time delays arise in these systems due to finite signal propagation and processing speeds, latency effects or are introduced deliberately via external control loops.

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CounterexampleIn this section we will construct a counterexample to the odd-number theorem, i.e., a system with an odd-number orbit, where the orbit can be stabilized by time-delayed feedback control. The counterexample consists of the normal form of a subcritical Hopf bifurcation

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Lang Kobayashi Laser EquationsCoupled semiconductor lasers will be the main application of chaos synchronization that we consider. We will therefore now introduce the dynamical laser equations

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Necessary Conditions for Synchronization of LasersPerfect synchronization is only possible if the SM is invariant. There are other forms of . such as . occurring, for instance, when the systems are non-identical, but we will restrict our analysis to perfect synchronization and a very weak form of generalized synchronization in lasers.

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BubblingThe stability of a synchronized state is determined by the largest transversal Lyapunov exponent (TLE) arising from the particular dynamics in the SM and the variational equation associated with transverse perturbations, as we have discussed in ..

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