scholarly journals Devil's staircase route to chaos in a forced relaxation oscillator

1994 ◽  
Vol 44 (1) ◽  
pp. 109-128 ◽  
Author(s):  
Lluis Alsedà ◽  
Antonio Falcó
Keyword(s):  
Relaxation Oscillator ◽  
Devil's Staircase ◽  
Devil’S Staircase ◽  
Route To Chaos

scholarly journals On the Amplitude of External Perturbation and Chaos via Devil's Staircase — Stability of Attractors

2015 ◽  
Vol 25 (11) ◽  
pp. 1550145 ◽  
Author(s):  
Sadataka Furui ◽  
Tomoyuki Takano
Keyword(s):  
Electric Current ◽  
External Perturbation ◽  
Sinusoidal Oscillation ◽  
Hidden Attractors ◽  
Devil's Staircase ◽  
Frequency Dependent ◽  
Farey Sequences ◽  
Devil’S Staircase ◽  
Chaotic Circuits ◽  
Route To Chaos

We designed a chaotic memristive circuit proposed by Chua and Muthuswamy, and analyzed the behavior of the voltage of the capacitor, electric current in the inductor and the voltage of the memristor by adding an external sinusoidal oscillation of a type γω cos ωt to [Formula: see text], when [Formula: see text] is expressed by y(t)/C, and studied Devil's staircase route to chaos. We compared the frequency of the driving oscillation fs and the frequency of the response fd in the window and assigned W = fs/fd to each window. When capacitor C = 1.0, we observe stable attractors of Farey sequences [Formula: see text], which can be interpreted as hidden attractors, while when C = 1.2, we observe disturbed attractors. Frequency dependent stability of chaotic circuits due to octonions is discussed.

STABLE OSCILLATIONS AND DEVIL'S STAIRCASE IN THE VAN DER POL OSCILLATOR

2000 ◽  
Vol 10 (01) ◽  
pp. 155-164 ◽  
Author(s):  
T. GILBERT ◽  
R. W. GAMMON
Keyword(s):  
Rotation Number ◽  
Variable Parameter ◽  
Relaxation Oscillator ◽  
Van Der Pol Oscillator ◽  
Driving Frequency ◽  
Devil's Staircase ◽  
Van Der Pol ◽  
Devil’S Staircase ◽  
Staircase Structure ◽  
Parameter Values

A forced van der Pol relaxation oscillator is studied experimentally in the regime of stable oscillations. The variable parameter is chosen to be the driving frequency. For a range of parameter values, we show that the rotation number varies continuously from 0 to 1. This work provides experimental evidence that period-adding bifurcations to chaos previously reported by Kennedy and Chua are intimately connected to the existence of a regime of stable oscillations where the rotation number shows a Devil's-staircase structure.

NMR spectra and relaxation in incommensurate systems in the presence of a devil's staircase

1985 ◽  
Vol 46 (7) ◽  
pp. 1205-1209 ◽  
Author(s):  
R. Blinc ◽  
S. Žumer ◽  
D.C. Ailion ◽  
J. Nicponski
Keyword(s):  
Nmr Spectra ◽  
Devil's Staircase ◽  
Devil’S Staircase

Phenomenology of a Devil's Staircase

1992 ◽  
Vol 3 (2) ◽  
pp. 231-250
Author(s):  
D. G. Sannikov
Keyword(s):  
Devil's Staircase ◽  
Devil’S Staircase

Devil's-staircase behavior of a simple spin model

1981 ◽  
Vol 24 (5) ◽  
pp. 2744-2750 ◽  
Author(s):  
E. B. Rasmussen ◽  
S. J. Knak Jensen
Keyword(s):  
Spin Model ◽  
Devil's Staircase ◽  
Devil’S Staircase

A multiple devil's staircase in a discontinuous map

1997 ◽  
Vol 231 (3-4) ◽  
pp. 152-158 ◽  
Author(s):  
Shi-Xian Qu ◽  
Shunguang Wu ◽  
Da-Ren He
Keyword(s):  
Devil's Staircase ◽  
Devil’S Staircase ◽  
Discontinuous Map

scholarly journals Devil's staircase for nonconvex interactions

2000 ◽  
Vol 50 (3) ◽  
pp. 307-311 ◽  
Author(s):  
J Jędrzejewski ◽  
J Miękisz
Keyword(s):  
Devil's Staircase ◽  
Devil’S Staircase ◽  
Nonconvex Interactions
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