NDLI: Quasiperiodic and exponential transient phase waves and their bifurcations in a ring of unidirectionally coupled parametric oscillators

Content Provider	Springer Nature Link
Author	Horikawa, Yo Kitajima, Hiroyuki
Copyright Year	2012
Abstract	Phase waves rotating in a ring of unidirectionally coupled parametric oscillators are studied. The system has a pair of spatially uniform stable periodic solutions with a phase difference and an unstable quasiperiodic traveling phase wave solution. They are generated from the origin through a period doubling bifurcation and the Neimark–Sacker bifurcation, respectively. In transient states, phase waves rotating in a ring are generated, the duration of which increases exponentially with the number of oscillators (exponential transients). A power law distribution of the duration of randomly generated phase waves and the noise-sustained propagation of phase waves are also shown. These properties of transient phase waves are well described with a kinematical equation for the propagation of wave fronts. Further, the traveling phase wave is stabilized through a pitchfork bifurcation and changes into a standing wave through pinning. These bifurcations and exponential transient rotating waves are also shown in an autonomous system with averaging and a coupled map model, and they agree with each other.
Starting Page	1079
Ending Page	1094
Page Count	16
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	70
Issue Number	2
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2012-07-12
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Parametric oscillator Quasiperiodic oscillation Traveling phase wave Exponential transient Noise-sustained propagation Mechanical Engineering Automotive Engineering Mechanics Vibration, Dynamical Systems, Control
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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