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Published on: February 22, 2018
Characterization of nonstationary chaotic systems
Ruth Serquina1, Ying-Cheng Lai, Qingfei Chen
1Department of Mathematics, MSU-Iligan Institute of Technology, the Philippines.
Summary
We present a new framework to characterize nonstationary dynamical systems using ensemble snapshots. This method extends fundamental nonlinear dynamics concepts like Lyapunov exponents and fractal dimensions to nonstationary systems.
Area of Science:
- Nonlinear dynamics
- Complex systems analysis
- Dynamical systems theory
Background:
- Standard nonlinear dynamics tools like Lyapunov exponents and fractal dimensions are primarily developed for stationary systems.
- Characterizing nonstationary dynamical systems remains a significant challenge in the field.
- Existing methods struggle to capture the evolving properties of nonstationary systems.
Purpose of the Study:
- To develop a novel framework for characterizing nonstationary dynamical systems.
- To extend the applicability of core nonlinear dynamics concepts to time-varying systems.
- To provide a method for analyzing the fractal properties of nonstationary systems.
Main Methods:
- Generating and analyzing ensemble snapshots from a large number of system trajectories.
- Defining Lyapunov exponents and fractal dimensions based on probability measures derived from ensemble snapshots.
- Investigating the validity of the Kaplan-Yorke formula for nonstationary systems.
Main Results:
- The proposed framework successfully characterizes nonstationary dynamical systems.
- Ensemble snapshots reveal underlying fractal properties of these systems.
- The fundamental Kaplan-Yorke formula remains largely valid for nonstationary systems.
Conclusions:
- A robust framework for characterizing nonstationary dynamical systems has been established.
- The study demonstrates the utility of ensemble snapshots in analyzing complex dynamics.
- Key theoretical results from nonlinear dynamics can be extended to nonstationary contexts.
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