Complex Time-Delay Systems: Theory and Applications
Fatihcan M. Atay
Springer Science & Business Media, Mar 24, 2010 - Science - 328 pages
One of the major contemporary challenges in both physical and social sciences is modeling, analyzing, and understanding the self-organization, evolution, behavior, and eventual decay of complex dynamical systems ranging from cell assemblies to the human brain to animal societies. The multi-faceted problems in this domain require a wide range of methods from various scienti?c disciplines. There is no question that the inclusion of time delays in complex system models considerably enriches the challenges presented by the problems. Although this inclusion often becomes inevitable as real-world applications demand more and more realistic m- els, the role of time delays in the context of complex systems so far has not attracted the interest it deserves. The present volume is an attempt toward ?lling this gap. There exist various useful tools for the study of complex time-delay systems. At the forefront is the mathematical theory of delay equations, a relatively mature ?eld in many aspects, which provides some powerful techniques for analytical inquiries, along with some other tools from statistical physics, graph theory, computer science, dynamical systems theory, probability theory, simulation and optimization software, and so on. Nevertheless, the use of these methods requires a certain synergy to address complex systems problems, especially in the presence of time delays.
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amplitude death anti-phase asymptotically stable Atay behavior card(S+ chaos characteristic equation chimera closed-loop complex computing consider constant converges corresponding coupled oscillators curves deﬁned deﬁnition delay differential equations delayed feedback control delayed neural networks denotes density distributed delay domain of control drivers dynamical systems eigenvalues equilibrium exists exponential feedback gain ﬁeld ﬁnite ﬁring ﬁrst ﬁxed point Floquet multipliers ﬂuctuations frequency function global Hopf bifurcation in-phase inﬁnite inﬂuence interaction kernel laser Lemma Lett limit cycle linear Lyapunov Lyapunov exponent matrix neurons noise noise-induced non-local nonlinear obtain parameter periodic orbits periodic solution phase Phys plane positive problem Proof propagation speed Pyragas region roots Schöll simulations spatial stability analysis stationary steady stochastic sufﬁcient conditions synchronization Theorem threshold time-delayed feedback control trafﬁc dynamics trafﬁc ﬂow transcritical bifurcation unstable wave number zero