A numerical study of large amplitude motion on a chain of coupled nonlinear oscillators

1979 ◽  
Vol 70 (1) ◽  
pp. 26 ◽  
Author(s):  
Timothy J. Rolfe ◽  
Stuart A. Rice ◽  
John Dancz
Keyword(s):  
Large Amplitude ◽  
Numerical Study ◽  
Nonlinear Oscillators ◽  
Coupled Nonlinear Oscillators ◽  
A Chain ◽  
Large Amplitude Motion

PHASE SYNCHRONIZATION AND CHAOS SUPPRESSION IN A SET OF TWO COUPLED NONLINEAR OSCILLATORS

2002 ◽  
Vol 12 (10) ◽  
pp. 2105-2122 ◽  
Author(s):  
J. M. GONZALEZ-MIRANDA
Keyword(s):  
Phase Synchronization ◽  
Numerical Study ◽  
Three Dimensional ◽  
Nonlinear Oscillators ◽  
Fourier Space ◽  
Chaotic State ◽  
Chaos Suppression ◽  
Bifurcation Phenomena ◽  
Coupled Nonlinear Oscillators ◽  
Mutual Induction

A numerical study of the dynamics of two mutually coupled nonlinear oscillators, at least one of them being in a chaotic state, is presented. Each of these oscillators is described as a three-dimensional autonomous flux. The phase of the oscillations, the Lyapunov spectrum and the bifurcation diagram are studied as functions of the coupling strength. When this is increased the two systems entrain, starting to oscillate in phase; then, for further increase, chaos suppression occurs. The study of different cases shows a rich phenomenology which includes multistability, and several bifurcation phenomena. The transitions to chaos suppression and phase synchronization are studied and interpreted in Fourier space on the base of a simple mechanism of mutual induction of motions by means of the coupling.

Forcing of coupled nonlinear oscillators: studies of intersegmental coordination in the lamprey locomotor central pattern generator

1990 ◽  
Vol 64 (3) ◽  
pp. 862-871 ◽  
Author(s):  
T. L. Williams ◽  
K. A. Sigvardt ◽  
N. Kopell ◽  
G. B. Ermentrout ◽  
M. P. Remler
Keyword(s):  
Central Pattern Generator ◽  
Coupled Oscillators ◽  
Nonlinear Oscillators ◽  
Pattern Generator ◽  
Fictive Locomotion ◽  
Frequency Range ◽  
Intersegmental Coordination ◽  
Coupled Nonlinear Oscillators ◽  
Phase Lags ◽  
A Chain

1. This paper reports the results of an investigation of the basic mechanisms underlying intersegmental coordination in lamprey locomotion, by the use of a combined mathematical and biological approach. 2. Mathematically, the lamprey central pattern generator (CPG) is described as a chain of coupled nonlinear oscillators; experimentally, entrainment of fictive locomotion by imposed movement has been investigated. Interpretation of the results in the context of the theory has allowed conclusions to be drawn about the nature of ascending and descending coupling in the lamprey spinal CPG. 3. Theory predicts and data show that 1) the greater the number of oscillators in the chain, the smaller is the entrainment frequency range and 2) it is possible to entrain both above and below the rest frequency at one end but only above or below at the other end. 4. In the context of the experimental results, the theory indicates the following: 1) ascending coupling sets the intersegmental phase lags, whereas descending coupling changes the frequency of the coupled oscillators; 2) there are differences in the ascending and descending coupling other than strength; and it also suggests that 3) coupling slows down the oscillators.

scholarly journals Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators

2016 ◽  
Vol 325 ◽  
pp. 25-40 ◽  
Author(s):  
M. Duanmu ◽  
N. Whitaker ◽  
P.G. Kevrekidis ◽  
A. Vainchtein ◽  
J.E. Rubin
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Nonlinear Oscillators ◽  
Wave Solutions ◽  
Coupled Nonlinear Oscillators ◽  
A Chain

Frequency Clustering in a Chain of Weakly Coupled Oscillators

1997 ◽  
Vol 52 (8-9) ◽  
pp. 578-580 ◽  
Author(s):  
Thomas Kirner ◽  
Otto E. Rössler
Keyword(s):  
Numerical Simulation ◽  
Small Intestine ◽  
Coupled Oscillators ◽  
Nonlinear Oscillators ◽  
Conduction System ◽  
Linear Parameter ◽  
Weakly Coupled ◽  
Coupled Nonlinear Oscillators ◽  
A Chain ◽  
Frequency Gradient

Abstract A numerical simulation of a chain of diffusively coupled nonlinear oscillators with a linear parameter gradient exhibits clusters of frequencies. The intention was to investigate the frequency-gradient in the stimulus conduction system of the heart. The phenomenon generalizes earlier findings on “frequency plateaus” described in the 1960's by Nicholas Diamant as a model of small-intestine transport. This “waxing and waining” phenomenon is a version of chaos. Thus, subtle chaos in the heart and waxing and waining type chaos in the intestine may be related.

scholarly journals Experimental Observation of the Amplitude Death Effect in Two Coupled Nonlinear Oscillators

2000 ◽  
Vol 84 (23) ◽  
pp. 5312-5315 ◽  
Author(s):  
R. Herrero ◽  
M. Figueras ◽  
J. Rius ◽  
F. Pi ◽  
G. Orriols
Keyword(s):  
Experimental Observation ◽  
Nonlinear Oscillators ◽  
Amplitude Death ◽  
Coupled Nonlinear Oscillators
Sign in / Sign up

Export Citation Format

Share Document