CORRELATION DIMENSION OF DISSIPATIVE CONTINUOUS DYNAMICAL SYSTEMS STOCHASTICALLY EXCITED BY TEMPORAL INPUTS

2002 ◽  
Author(s):  
KAZUTOSHI GOHARA ◽  
JUN NISHIKAWA
Keyword(s):  
Dynamical Systems ◽  
Correlation Dimension

scholarly journals Correlation Dimension Detects Causal Links in Coupled Dynamical Systems

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 818 ◽  
Author(s):  
Anna Krakovská
Keyword(s):  
Dynamical Systems ◽  
Correlation Dimension ◽  
Dominant Role ◽  
Causal Analysis ◽  
Weak Links ◽  
Causal Relationships ◽  
Autoregressive Processes ◽  
State Spaces ◽  
Deterministic Dynamics

It is becoming increasingly clear that causal analysis of dynamical systems requires different approaches than, for example, causal analysis of interconnected autoregressive processes. In this study, a correlation dimension estimated in reconstructed state spaces is used to detect causality. If deterministic dynamics plays a dominant role in data then the method based on the correlation dimension can serve as a fast and reliable way to reveal causal relationships between and within the systems. This study demonstrates that the method, unlike most other causal approaches, detects causality well, even for very weak links. It can also identify cases of uncoupled systems that are causally affected by a hidden common driver.

scholarly journals Chaos and Complexity Dynamics of Evolutionary Systems

2020 ◽  
Author(s):  
Lal Mohan Saha
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Chaotic Motion ◽  
Correlation Dimension ◽  
Nonlinear Dynamical Systems ◽  
Chaotic Attractors ◽  
Tabular Form ◽  
Bifurcation Diagrams ◽  
Nonlinear Dynamical

Chaotic phenomena and presence of complexity in various nonlinear dynamical systems extensively discussed in the context of recent researches. Discrete as well as continuous dynamical systems both considered here. Visualization of regularity and chaotic motion presented through bifurcation diagrams by varying a parameter of the system while keeping other parameters constant. In the processes, some perfect indicator of regularity and chaos discussed with appropriate examples. Measure of chaos in terms of Lyapunov exponents and that of complexity as increase in topological entropies discussed. The methodology to calculate these explained in details with exciting examples. Regular and chaotic attractors emerging during the study are drawn and analyzed. Correlation dimension, which provides the dimensionality of a chaotic attractor discussed in detail and calculated for different systems. Results obtained presented through graphics and in tabular form. Two techniques of chaos control, pulsive feedback control and asymptotic stability analysis, discussed and applied to control chaotic motion for certain cases. Finally, a brief discussion held for the concluded investigation.

Sign in / Sign up

Export Citation Format

Share Document