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

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Valentin FlunkertReports important progress in the control of complex dynamics.Gives fundamental insights into the interplay of delay and synchronization.Nominated as an outstanding contribution by the Technical Unive

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Springer Theseshttp://image.papertrans.cn/d/image/264940.jpg

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Odd-Number Orbits Close to a Fold Bifurcationcritical Hopf bifurcation can be stabilized by time-delayed feedback control. Although this is a very generic example, the question arises whether this situation close to the Hopf bifurcation is special or if odd-number orbits born from other bifurcations can be stabilized, too.

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Stabilization with Symmetric Feedback Matricesents as it corresponds to the situation, where one measures a variable and applies the control signal to the dynamical equation of the same variable. We will now discuss a method to overcome this problem, i.e., to stabilize the UPO with symmetric feedback matrices.

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Application to Laser Systemse seminal paper of Lang and Kobayashi. Various delayed feedback methods have since then been used, such as all-optical feedback, phase-conjugate feedback, optoelectronic feedback, polarization rotated feedback and filtered feedback .

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K. Marzusch,S. Pildner von Steinburg(UPOs) and unstable steady states in dynamical systems. It has since then been successfully applied to a plethora of different systems, for instance, to spatially extended systems and even noise-driven systems for reviews see E. Schöll (2008)