Reconstructing bifurcation diagrams only from time-series data generated by electronic circuits in discrete-time...

Area of Science:

• Dynamical Systems and Chaos Theory
• Nonlinear Dynamics
• Electronic Circuit Analysis

Background:

• Bifurcation-diagram reconstruction analyzes system attractors by observing limited data across parameter variations.
• Existing methods primarily focus on continuous-time systems, limiting applications to discrete-time physical phenomena.
• Real-world engineering and physics often involve discrete-time systems with observable attractors.

Purpose of the Study:

• To reconstruct bifurcation diagrams from time-series data of discrete-time dynamical systems generated by electronic circuits.
• To investigate the robustness of bifurcation-diagram reconstruction against dynamical and observational noise.
• To validate the method by comparing Lyapunov exponents with numerical and experimental data.

Main Methods:

• Utilizing time-series data from electronic circuits operating in discrete-time dynamical regimes.
• Employing an extreme learning machine (ELM) as a time-series predictor for its generalization capabilities.
• Perturbing generated datasets with both dynamical and observational noise to simulate real-world conditions.

Main Results:

• Successfully reconstructed bifurcation diagrams from noisy time-series data of discrete-time electronic circuits.
• Demonstrated the robustness of the extreme learning machine-based reconstruction against introduced noise.
• Quantitative verification showed consistency between reconstructed and numerically/experimentally generated Lyapunov exponents.

Conclusions:

• Bifurcation-diagram reconstruction is feasible for discrete-time dynamical systems using electronic circuit data.
• The extreme learning machine offers a noise-resilient approach for analyzing complex dynamical behaviors in physical systems.
• This method expands the applicability of bifurcation analysis to a broader range of engineering and scientific problems.