Pramana

, Volume 64, Issue 4, pp 465–482 | Cite as

Collective dynamics of delay-coupled limit cycle oscillators

  • Abhijit Sen
  • Ramana Dodla
  • George L. Johnston

Abstract

Coupled limit cycle oscillators with instantaneous mutual coupling offer a useful but idealized mathematical paradigm for the study of collective behavior in a wide variety of biological, physical and chemical systems. In most real-life systems however the interaction is not instantaneous but is delayed due to finite propagation times of signals, reaction times of chemicals, individual neuron firing periods in neural networks etc. We present a brief overview of the effect of time-delayed coupling on the collective dynamics of such coupled systems. Simple model equations describing two oscillators with a discrete time-delayed coupling as well as those describing linear arrays of a large number of oscillators with time-delayed global or local couplings are studied. Analytic and numerical results pertaining to time delay induced changes in the onset and stability of amplitude death and phase-locked states are discussed. A number of recent experimental and theoretical studies reveal interesting new directions of research in this field and suggest exciting future areas of exploration and applications.

Keywords

Coupled oscillators time delay Hopf bifurcation amplitude death, synchronization, phase locking 

PACS Nos

05.45.+b 87.10+e 

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Copyright information

© Indian Academy of Sciences 2005

Authors and Affiliations

  • Abhijit Sen
    • 1
  • Ramana Dodla
    • 2
  • George L. Johnston
    • 3
  1. 1.Institute for Plasma Research, BhatGandhinagarIndia
  2. 2.Center for Neural ScienceNew York UniversityNew YorkUSA
  3. 3.EduTron Corp.WinchesterUSA

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