scholarly journals On the Period-Adding Phenomena at the Frequency Locking in a One-Dimensional Mapping

1982 ◽  
Vol 68 (2) ◽  
pp. 669-672 ◽  
Author(s):  
K. Kaneko
Keyword(s):  
Frequency Locking ◽  
One Dimensional ◽  
Dimensional Mapping

scholarly journals On The Correlation between Properties of One-Dimensional Mappings of Control Functions and Chaos in a Special Type Delay Differential Equation

2017 ◽  
Vol 12 (2) ◽  
pp. 385-397 ◽  
Author(s):  
В.А. Лихошвай ◽  
V.A. Likhoshvai
Keyword(s):  
Differential Equation ◽  
Chaotic Dynamics ◽  
Molecular Genetic ◽  
Numerical Examples ◽  
One Dimensional ◽  
Control Functions ◽  
Delayed Argument ◽  
The One ◽  
Delay Differential ◽  
Dimensional Mapping

A differential equation of a special form, which contains two control functions f and g and one delayed argument, is analyzed. This equation has a wide application in biology for the description of dynamic processes in population, physiological, metabolic, molecular-genetic, and other applications. Specific numerical examples show the correlation between the properties of the one-dimensional mapping, which is generated by the ratio f /g, and the presence of chaotic dynamics for such equation. An empirical criterion is formulated that allows one to predict the presence of a chaotic potential for a given equation by the properties of the one-dimensional mapping f /g.

Deterministic hopping in a Josephson circuit described by a one-dimensional mapping

1985 ◽  
Vol 31 (4) ◽  
pp. 2509-2519 ◽  
Author(s):  
Robert F. Miracky ◽  
Michel H. Devoret ◽  
John Clarke
Keyword(s):  
One Dimensional ◽  
Dimensional Mapping

Error-detective one-dimensional mapping

2017 ◽  
Author(s):  
Yun Zhang ◽  
Shihao Zhou
Keyword(s):  
One Dimensional ◽  
Dimensional Mapping

scholarly journals ASYMPTOTIC DYNAMICS OF A CLASS OF COUPLED OSCILLATORS DRIVEN BY WHITE NOISES

2013 ◽  
Vol 13 (04) ◽  
pp. 1350002 ◽  
Author(s):  
WENXIAN SHEN ◽  
ZHONGWEI SHEN ◽  
SHENGFAN ZHOU
Keyword(s):  
Coupled Oscillators ◽  
Practical Importance ◽  
Second Order ◽  
Random Attractor ◽  
Coupling Coefficients ◽  
Horizontal Curve ◽  
Frequency Locking ◽  
One Dimensional ◽  
Asymptotic Dynamics ◽  
White Noises

This paper is devoted to the study of the asymptotic dynamics of a class of coupled second order oscillators driven by white noises. It is shown that any system of such coupled oscillators with positive damping and coupling coefficients possesses a global random attractor. Moreover, when the damping and the coupling coefficients are sufficiently large, the global random attractor is a one-dimensional random horizontal curve regardless of the strength of the noises, and the system has a rotation number, which implies that the oscillators in the system tend to oscillate with the same frequency eventually and therefore the so-called frequency locking is successful. The results obtained in this paper generalize many existing results on the asymptotic dynamics for a single second order noisy oscillator to systems of coupled second order noisy oscillators. They show that coupled damped second order oscillators with large damping have similar asymptotic dynamics as the limiting coupled first order oscillators as the damping goes to infinite and also that coupled damped second order oscillators have similar asymptotic dynamics as their proper space continuous counterparts, which are of great practical importance.

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