Predicting bifurcation points via extreme learning machine methods trained on time-series datasets and parameters in...

Area of Science:

• Dynamical Systems and Chaos Theory
• Computational Intelligence
• Nonlinear Dynamics

Background:

• Bifurcation points are critical in understanding system behavior.
• Traditional methods struggle with complex systems and long periodic solutions.
• Accurate identification of bifurcation points is essential for system analysis.

Purpose of the Study:

• To propose a novel data-driven method for identifying bifurcation points.
• To enhance the analysis of discrete dynamical systems using Extreme Learning Machine with input parameter channels (ELM-IPC).
• To demonstrate the method's efficacy on complex systems.

Main Methods:

• Utilizing Extreme Learning Machine with input parameter channels (ELM-IPC) trained on time-series data.
• Aligning original parameter spaces with ELM-IPC derived parameter spaces via input parameter channels.
• Applying the method to the Hénon map and coupled Hénon map systems.

Main Results:

• The ELM-IPC method accurately identifies bifurcation points in discrete dynamical systems.
• The method successfully handles parameter spaces with coexisting solutions.
• Effectively detects bifurcation points in systems with periodic solutions exceeding a period of 100.

Conclusions:

• The proposed ELM-IPC method offers a robust data-driven approach for bifurcation point analysis.
• This technique advances the study of complex discrete dynamical systems.
• Enables accurate characterization of system dynamics in challenging parameter regimes.