scholarly journals RECURRING ANTI-PHASE SIGNALS IN COUPLED NONLINEAR OSCILLATORS: CHAOTIC OR RANDOM TIME SERIES?

1993 ◽  
Vol 03 (03) ◽  
pp. 773-778 ◽  
Author(s):  
KWOK YEUNG TSANG ◽  
IRA B. SCHWARTZ
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Lyapunov Exponents ◽  
Nonlinear Oscillator ◽  
Nonlinear Oscillators ◽  
Random Time ◽  
High Dimensional ◽  
Coupled Nonlinear Oscillators ◽  
New Type

We discovered the existence of a new type of high-dimensional attractor in coupled nonlinear oscillator systems. Due to the presence of neutrally stable directions on the attractor, there can be noise-driven phase space diffusion. Recurring anti-phase states are observed as coherent portions of the time series. The observed time series looks coherent for a while, then incoherent, and then coherent again. Although the time series “looks” chaotic, the Lyapunov exponents are not positive.

Nonlinear Dynamics in the Ultradian Rhythm of Desmodium motorium

1995 ◽  
Vol 50 (12) ◽  
pp. 1113-1116 ◽  
Author(s):  
Jyh-Phen Chen ◽  
Wolfgang Engelmann ◽  
Gerold Baier
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Nonlinear Oscillators ◽  
Ultradian Rhythm ◽  
Ultradian Rhythms ◽  
Lateral Leaflet ◽  
Homoclinic Chaos ◽  
Coupled Nonlinear Oscillators

Abstract The dynamics of the lateral leaflet movement of Desmodium motorium is studied. Simple periodic, quasiperiodic and aperiodic time series are observed. The long-scale dynamics may either be uniform or composed of several prototypic oscillations (one of them reminiscent of homoclinic chaos). Diffusively coupled nonlinear oscillators may account for the variety of ultradian rhythms.

Lyapunov exponents of random time series

1996 ◽  
Vol 54 (2) ◽  
pp. 2122-2124 ◽  
Author(s):  
Toshiyuki Tanaka ◽  
Kazuyuki Aihara ◽  
Masao Taki
Keyword(s):  
Time Series ◽  
Lyapunov Exponents ◽  
Random Time

scholarly journals Complex dynamics and synchronization of delayed-feedback nonlinear oscillators

2010 ◽  
Vol 368 (1911) ◽  
pp. 343-366 ◽  
Author(s):  
Thomas E. Murphy ◽  
Adam B. Cohen ◽  
Bhargava Ravoori ◽  
Karl R. B. Schmitt ◽  
Anurag V. Setty ◽  
...  
Keyword(s):  
Lyapunov Exponents ◽  
Coupled Oscillators ◽  
Control Method ◽  
Complex Dynamics ◽  
Digital Signal ◽  
Nonlinear Oscillators ◽  
Delayed Feedback ◽  
High Dimensional ◽  
Electro Optic ◽  
Wide Range

We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electro-optic modulation and fibre-optic transmission, with feedback and filtering implemented through real-time digital signal processing. We consider two such oscillators that are coupled to one another, and we identify the conditions under which they will synchronize. By examining the rates of divergence or convergence between two coupled oscillators, we quantify the maximum Lyapunov exponents or transverse Lyapunov exponents of the system, and we present an experimental method to determine these rates that does not require a mathematical model of the system. Finally, we demonstrate a new adaptive control method that keeps two oscillators synchronized, even when the coupling between them is changing unpredictably.

scholarly journals Multivariate time series prediction of high dimensional data based on deep reinforcement learning

2021 ◽  
Vol 256 ◽  
pp. 02038
Author(s):  
Xin Ji ◽  
Haifeng Zhang ◽  
Jianfang Li ◽  
Xiaolong Zhao ◽  
Shouchao Li ◽  
...  
Keyword(s):  
Time Series ◽  
Reinforcement Learning ◽  
Phase Space ◽  
Time Series Prediction ◽  
Multivariate Time Series ◽  
High Dimensional Data ◽  
Prediction Method ◽  
Conditional Entropy ◽  
High Dimensional ◽  
Low Dimensional

In order to improve the prediction accuracy of high-dimensional data time series, a high-dimensional data multivariate time series prediction method based on deep reinforcement learning is proposed. The deep reinforcement learning method is used to solve the time delay of each variable and mine the data characteristics. According to the principle of maximum conditional entropy, the embedding dimension of the phase space is expanded, and a multivariate time series model of high-dimensional data is constructed. Thus, the conversion of reconstructed coordinates from low-dimensional to high-dimensional can be kept relatively stable. The strong independence and low redundancy of the final reconstructed phase space construct an effective model input vector for multivariate time series forecasting. Numerical experiments of classical multivariable chaotic time series show that the method proposed in this paper has better forecasting effect, which shows the forecasting effectiveness of this method.

Time series prediction using Lyapunov exponents in embedding phase space

2004 ◽  
Vol 30 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Jun Zhang ◽  
K.C. Lam ◽  
W.J. Yan ◽  
Hang Gao ◽  
Yuan Li
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Lyapunov Exponents ◽  
Time Series Prediction

Analysis of positive Lyapunov exponents from random time series

1998 ◽  
Vol 111 (1-4) ◽  
pp. 42-50 ◽  
Author(s):  
Toshiyuki Tanaka ◽  
Kazuyuki Aihara ◽  
Masao Taki
Keyword(s):  
Time Series ◽  
Lyapunov Exponents ◽  
Random Time

Predicting Limit Cycle Boundaries Deep Inside Parameter Space of a 2D Biochemical Nonlinear Oscillator Using Renormalization Group

2021 ◽  
Vol 31 (11) ◽  
pp. 2150162
Author(s):  
Ayan Dutta ◽  
Jyotipriya Roy ◽  
Dhruba Banerjee
Keyword(s):  
Renormalization Group ◽  
Phase Space ◽  
Limit Cycle ◽  
Parameter Space ◽  
Nonlinear Oscillator ◽  
Nonlinear Oscillators ◽  
Bifurcation Curve ◽  
Recent Past ◽  
Perturbative Renormalization ◽  
Biochemical Oscillator

Formation and study of periodic orbits in phase space in the case of nonlinear oscillators have been a topic of much interest in the recent past. In the current work, a method to go deep inside the limit cycle zone on one side of the bifurcation curve of a 2D non-Lienard biochemical oscillator has been introduced. It is discussed how such an introduction facilitates predicting the boundaries of limit cycles at various points of parameter space, nearly accurately, by the use of perturbative Renormalization Group. Sel’kov model of Glycolytic oscillator has been chosen as the base model to introduce the method.

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