Complex Time-Delay Systems

1. Front Matter

   Pages i-xii

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2. Amplitude Death, Synchrony, and Chimera States in Delay Coupled Limit Cycle Oscillators

   • Abhijit Sen, Ramana Dodla, George L. Johnston, Gautam C. Sethia

   Pages 1-43

3. Delay-Induced Stability: From Oscillators to Networks

   • Fatihcan M. Atay

   Pages 45-62

4. Delay Effects on Output Feedback Control of Dynamical Systems

   • Silviu-Iulian Niculescu, Wim Michiels, Keqin Gu, Chaouki T. Abdallah

   Pages 63-84

5. Time-Delayed Feedback Control: From Simple Models to Lasers and Neural Systems

   • Eckehard Schöll, Philipp Hövel, Valentin Flunkert, Markus A. Dahlem

   Pages 85-150

6. Finite Propagation Speeds in Spatially Extended Systems

   • Axel Hutt

   Pages 151-176

7. Stochastic Delay-Differential Equations

   • André Longtin

   Pages 177-195

8. Global Convergent Dynamics of Delayed Neural Networks

   • Wenlian Lu, Tianping Chen

   Pages 197-262

9. Stability and Hopf Bifurcation for a First-Order Delay Differential Equation with Distributed Delay

   • Fabien Crauste

   Pages 263-296

10. Deterministic Time-Delayed Traffic Flow Models: A Survey

    • Rifat Sipahi, Silviu-Iulian Niculescu

    Pages 297-322

11. Back Matter

    Pages 323-325

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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.

• Chimera
• bifurcation
• complex system
• complex systems
• complexity
• delayed neural networks
• stochastic delay-differential equations
• time-delay systems
• time-delayed control and feedback
• information and communication, circuits

• Wissenschaften, MPI für Mathematik in den, Leipzig, Germany

  Fatihcan M. Atay

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