PHENOMENON OF ASYMMETRY OF INTERNAL TIME, TAKING INTO ACCOUNT THE INSTABILITY AND IRREVERSIBILITY OF PROCESSES IN THE THEORY OF FORECASTING THE STATE OF COMPLEX DYNAMICAL SYSTEMS

2019 ◽  
Author(s):  
V. A. Ostreykovskiy ◽  
◽  
S. A. Lysenkova ◽  
E. N. Shevchenko ◽  
◽  
...  
Keyword(s):  
Dynamical Systems ◽  
The State ◽  
Complex Dynamical Systems ◽  
Internal Time

scholarly journals Stability threshold approach for complex dynamical systems

2015 ◽  
Vol 18 (1) ◽  
pp. 013004 ◽  
Author(s):  
Vladimir V Klinshov ◽  
Vladimir I Nekorkin ◽  
Jürgen Kurths
Keyword(s):  
Dynamical Systems ◽  
Complex Dynamical Systems ◽  
Stability Threshold ◽  
Threshold Approach

scholarly journals Phase Synchronization Is the Amplified Result by the Hilbert Transform

2015 ◽  
Vol 2015 ◽  
pp. 1-3 ◽  
Author(s):  
Ming-Chi Lu ◽  
Hsing-Chung Ho ◽  
Chen-An Chan ◽  
Chia-Ju Liu ◽  
Jiann-Shing Lih ◽  
...  
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Hilbert Transform ◽  
Phase Synchronization ◽  
Nonlinear Dynamical Systems ◽  
The State ◽  
Nonlinear Dynamical ◽  
Large Correlation ◽  
Current Usage ◽  
The Hilbert Transform

We investigate the interplay between phase synchronization and amplitude synchronization in nonlinear dynamical systems. It is numerically found that phase synchronization intends to be established earlier than amplitude synchronization. Nevertheless, amplitude synchronization (or the state with large correlation between the amplitudes) is crucial for the maintenance of a high correlation between two time series. A breakdown of high correlation in amplitudes will lead to a desynchronization of two time series. It is shown that these unique features are caused essentially by the Hilbert transform. This leads to a deep concern and criticism on the current usage of phase synchronization.

scholarly journals Data based identification and prediction of nonlinear and complex dynamical systems

2016 ◽  
Vol 644 ◽  
pp. 1-76 ◽  
Author(s):  
Wen-Xu Wang ◽  
Ying-Cheng Lai ◽  
Celso Grebogi
Keyword(s):  
Dynamical Systems ◽  
Complex Dynamical Systems
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