Complex Time-Delay Systems: Theory and ApplicationsFatihcan M. Atay 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. |
Contents
1 | |
From Oscillators to Networks | 45 |
3 Delay Effects on Output Feedback Control of DynamicalSystems | 63 |
From Simple Models to Lasers and Neural Systems | 85 |
5 Finite Propagation Speeds in Spatially Extended Systems | 151 |
6 Stochastic DelayDifferential Equations | 177 |
Other editions - View all
Common terms and phrases
amplitude death anti-phase asymptotically stable Atay behavior card(S+ chaos characteristic equation chimera closed-loop complex computing condition consider constant converges corresponding coupled oscillators curves defined delay differential equations delay values delayed feedback control delayed neural networks denotes density distributed delay domain of control drivers dynamical systems eigenvalues equilibrium exists feedback gain finite fixed point Floquet multipliers frequency function Hopf bifurcation in-phase 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 delay propagation speed purely imaginary eigenvalues Pyragas region roots satisfies Schöll SDDEs Sect simulations spatial stability analysis stationary steady stochastic synchronization Theorem threshold time-delayed feedback control traffic dynamics traffic flow transcritical bifurcation unstable wave number zero Ωτ