Systematic experimental exploration of bifurcations with noninvasive control

Area of Science:

• Nonlinear dynamics and control systems
• Experimental physics
• Bifurcation theory

Background:

• Investigating complex dynamics in physical systems is challenging.
• Existing noninvasive control methods have limitations, such as odd-number constraints.
• Understanding bifurcations is crucial for predicting system behavior.

Purpose of the Study:

• To present a general method for systematically investigating nonlinear experimental dynamics.
• To overcome the odd-number limitation in popular noninvasive control schemes.
• To demonstrate the application of the novel control method in a physical experiment.

Main Methods:

• Development of a general method for nonlinear dynamics investigation.
• Overcoming odd-number limitations in time-delayed and washout-filtered feedback control.
• Experimental tracing of a resonance surface using the developed noninvasive control.

Main Results:

• A novel noninvasive control method was successfully developed and applied.
• The odd-number limitation of existing control schemes was overcome.
• The resonance surface of a nonlinear oscillator was experimentally mapped near instability.

Conclusions:

• The presented method offers a robust approach for studying nonlinear systems.
• The developed control strategy enhances the investigation of equilibria and periodic orbits.
• This work provides new insights into bifurcations in periodically forced nonlinear oscillators.