Desynchronizing two oscillators while stimulating and observing only one

Area of Science:

• Nonlinear dynamics
• Complex systems
• Oscillator theory

Background:

• Synchronization is common in nature and technology.
• Undesired synchrony often requires external intervention for disruption.
• Controlling synchrony in coupled oscillators is a significant challenge.

Purpose of the Study:

• To investigate desynchronization of two coupled self-sustained oscillators using phase-specific external pulses.
• To analyze the scenario where only one oscillator can be stimulated and only one can be monitored.
• To develop a theoretical framework for understanding and controlling oscillator desynchronization.

Main Methods:

• Utilized a system of two coupled Rayleigh oscillators.
• Applied short, phase-specific pulses to one oscillator to induce desynchronization.
• Employed phase approximation to formulate the problem using a mathematical map.
• Derived exact expressions for phase-isostable coordinates.
• Analyzed time series data to extract phase response information.

Main Results:

• Demonstrated successful induction of desynchrony in coupled Rayleigh oscillators via targeted pulsing.
• Established a theoretical framework relating coupled and uncoupled oscillator responses.
• Showed that phase response information can be obtained from time series data.
• Identified differences in observation between stimulated and unstimulated oscillators.

Conclusions:

• Phase-specific pulsing is an effective method for desynchronizing coupled oscillators, even with restricted access.
• The developed theoretical model accurately describes the desynchronization process.
• Observational perspective (stimulated vs. unstimulated) influences the analysis of oscillator dynamics.