In-phase and mixed-phase measure synchronization of camphor rotors

Area of Science:

• Physics
• Nonlinear Dynamics
• Complex Systems

Background:

• Synchronization is a fundamental phenomenon in coupled dynamical systems.
• Yukawa interaction describes a specific type of attractive or repulsive force.
• Understanding synchronization in mechanical systems like rotors is crucial for various applications.

Purpose of the Study:

• To investigate the synchronization dynamics of two rotors coupled via Yukawa interaction.
• To derive and validate the analytical conditions for measure synchronization.
• To explore the role of initial conditions and coupling parameters in synchronization.

Main Methods:

• Numerical simulations were performed to model rotor synchronization.
• Analytical derivations were used to establish conditions for synchronization.
• Experimental validation was conducted using coupled camphor-infused rotors.

Main Results:

• The study reports the observation of both in-phase and mixed-phase measure synchronizations.
• An analytical condition for synchronization was successfully derived and verified.
• Experimental results confirmed the findings from numerical and analytical approaches.

Conclusions:

• The research successfully demonstrates and validates measure synchronization in coupled rotors under Yukawa interaction.
• Both the critical coupling parameter and initial conditions are essential for determining the measure synchronization region in conservative systems.