Parameter space of experimental chaotic circuits with high-precision control parameters.

Area of Science:

• Nonlinear dynamics
• Experimental physics
• Circuit theory

Background:

• Chua's circuit is a fundamental nonlinear electronic circuit used to study chaotic behavior.
• Understanding the complex dynamics within chaotic systems requires precise experimental data.
• Previous studies have theoretically predicted structures like 'shrimps' in chaotic systems.

Purpose of the Study:

• To experimentally confirm the existence of spiral cascade structures and scaling relationships of shrimps in Chua's circuit.
• To demonstrate a technological development for creating and studying chaotic circuits with high-resolution parameter spaces.
• To provide a comprehensive characterization of Chua's circuit behaviors.

Main Methods:

• Construction of a stable and reliable Chua's circuit component.
• Acquisition of long-term experimental data (approximately 21 weeks) with high resolution.
• Estimation of Lyapunov exponents for rigorous circuit characterization.

Main Results:

• Experimental confirmation of spiral cascade structures in Chua's circuit.
• Observation of 'shrimps' as stable islands within chaotic parameter spaces.
• Verification of an exponential decay in shrimp sizes with attractor period, consistent with quadratic family maps.

Conclusions:

• The developed technology enables reliable, long-term data acquisition for chaotic circuit analysis.
• Experimental evidence validates theoretical predictions of complex structures within Chua's circuit.
• The findings contribute to a deeper understanding of chaos theory and its experimental manifestations.