High-resolution parameter space of an experimental chaotic circuit

Area of Science:

• Nonlinear dynamics
• Experimental circuits
• Chaos theory

Background:

• Complex periodic structures are fundamental in nonlinear systems.
• Understanding their organization in parameter space is crucial for predicting system behavior.
• Previous studies often lacked the resolution to detail these structures.

Purpose of the Study:

• To report a high-resolution codimension-two parameter space of an experimental chaotic circuit.
• To investigate the abundance and organization of complex periodic structures.
• To corroborate experimental findings with numerical dynamical model investigations.

Main Methods:

• Utilizing a 0.5 mV step dc voltage source for high-resolution control parameter adjustment.
• Mapping the codimension-two parameter space of an experimental chaotic circuit.
• Performing numerical investigations on the corresponding dynamical model.

Main Results:

• A detailed high-resolution parameter space exhibiting abundant complex periodic structures was generated.
• These structures were observed to organize in a period-adding bifurcation cascade.
• The cascade was found to accumulate into a chaotic region.
• Numerical simulations corroborated new features observed in the experimental parameter space.

Conclusions:

• High-resolution parameter space mapping is effective for revealing intricate dynamics in chaotic circuits.
• Period-adding bifurcations represent a key mechanism for the emergence of chaos from periodic behavior.
• The experimental results align with theoretical predictions from the dynamical model, validating the findings.