Detecting weak phase locking in chaotic system with dual attractors and ill-defined phase structure

Area of Science:

• Nonlinear Dynamics and Chaos Theory
• Statistical Physics
• Complex Systems Analysis

Background:

• Phase locking is a fundamental phenomenon in complex systems, often observed in coupled oscillators and chaotic systems.
• Detecting phase locking in systems with intricate attractor structures, such as chaotic systems, presents significant analytical challenges.
• Existing methods may struggle with the complexity of chaotic attractors, necessitating novel quantitative approaches.

Purpose of the Study:

• To develop and validate a quantitative approach for detecting phase locking in chaotic systems.
• To investigate the route to weak phase locking by analyzing stroboscopic points.
• To compare the statistical detection of phase locking onset with Lyapunov exponent calculations.

Main Methods:

• A quantitative approach utilizing the stroboscopic method was employed to analyze phase locking.
• The study focused on analyzing stroboscopic points to understand the transition to weak phase locking.
• Lyapunov exponents were calculated to determine critical coupling strengths for phase locking.

Main Results:

• The developed statistical approach successfully detected the onset of weak phase locking in the chaotic system.
• The critical coupling strength derived from the statistical method showed strong agreement with values calculated using Lyapunov exponents.
• The Arnold tongue diagram was utilized to provide a detailed visualization of the phase locking intensity structure.

Conclusions:

• The stroboscopic method provides a robust quantitative framework for detecting phase locking in complex chaotic systems.
• The agreement between statistical detection and Lyapunov exponent calculations validates the proposed approach.
• The Arnold tongue diagram effectively illustrates the intricate details of phase locking phenomena in these systems.