Collective dynamics of delay-coupled limit cycle oscillators |
| |
Authors: | Abhijit Sen Ramana Dodla George L Johnston |
| |
Institution: | (1) Institute for Plasma Research, Bhat, 382 428 Gandhinagar, India;(2) Center for Neural Science, New York University, 10003 New York, NY, USA;(3) EduTron Corp., 5 Cox Road, 01890 Winchester, MA, USA |
| |
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 |
本文献已被 SpringerLink 等数据库收录! |
|