Quantifying the degree of locking in weakly forced stochastic systems

Area of Science:

• Nonlinear Dynamics
• Laser Physics
• Control Theory

Background:

• Controlling stochastic nonlinear systems with small signals is crucial for many applications.
• Existing methods for quantifying signal locking lack precision.
• Semiconductor lasers with optical feedback exhibit random spiking, posing a control challenge.

Purpose of the Study:

• To develop a precise method for quantifying signal locking in stochastic nonlinear systems.
• To investigate the control of optical spike emission in a semiconductor laser using electric perturbations.
• To demonstrate the general applicability of the proposed method to other stochastic systems.

Main Methods:

• Utilized a semiconductor laser with optical feedback operating in a spiking regime.
• Quantified spike locking using success rate (SR) and false positive rate (FPR).
• Employed receiver operating characteristic (ROC) curve analysis (SR vs. FPR) to assess control effectiveness.

Main Results:

• The ROC curve analysis precisely identified parameter regions for full control of laser spikes.
• Demonstrated that optimal parameters allow the laser to emit exactly one spike per perturbation.
• Successfully applied ROC analysis to a stochastic bistable system under square-wave forcing, identifying best locking parameters.

Conclusions:

• ROC curve analysis provides a robust and generalizable method for quantifying signal locking in stochastic nonlinear systems.
• This approach offers a significant improvement over traditional spectral or correlation analyses.
• The findings have broad implications for controlling complex dynamical systems in various scientific and engineering fields.