Complex Time-Delay Systems pp 1-43

Part of the Understanding Complex Systems book series (UCS) | Cite as

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

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

Abstract

In this chapter we will discuss the effects of time delay on the collective states of a model mathematical system composed of a collection of coupled limit cycle oscillators. Such an assembly of coupled nonlinear oscillators serves as a useful paradigm for the study of collective phenomena in many physical, chemical, and biological systems and has therefore led to a great deal of theoretical and experimental work in the past [1–6]. Examples of practical applications of such models include simulating the interactions of arrays of Josephson junctions [7, 8], semiconductor lasers [9, 10], charge density waves [11], phase-locking of relativistic magnetrons [12], Belousov–Zhabotinskii reactions in coupled Brusselator models [2, 13–15], and neural oscillator networks for circadian pacemakers [16].

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Abhijit Sen
    • 1
  • Ramana Dodla
    • 2
  • George L. Johnston
    • 3
  • Gautam C. Sethia
    • 1
  1. 1.Institute for Plasma Research, BhatGandhinagarIndia
  2. 2.Department of BiologyUniversity of Texas at San AntonioSan AntonioUSA
  3. 3.EduTron Corp.WinchesterUSA

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