A nonlinear memductance induced intermittent and anti-phase synchronization

Area of Science:

• Nonlinear dynamics
• Complex systems
• Network science

Background:

• Coupled oscillators are fundamental in various scientific fields.
• Understanding dynamic coupling is crucial for complex system behavior.
• Nonlinear memductance offers a novel mechanism for dynamic interactions.

Purpose of the Study:

• To introduce a model for oscillators coupled via mean-field nonlinear memductance.
• To investigate how dynamic nonlinearity influences oscillator coupling.
• To explore synchronization and anti-synchronization phenomena in such systems.

Main Methods:

• Development of a mathematical model for mean-field coupled oscillators.
• Incorporation of nonlinear memductance to induce dynamic coupling.
• Analysis of system behavior under varying forcing frequencies and coupling strengths.
• Validation through numerical simulations.

Main Results:

• Nonlinear memductance creates dynamic coupling, altering interaction direction over time.
• Observed synchronization and anti-synchronization manifolds based on system parameters.
• Identified anti-phase and intermittent synchronization patterns.
• Demonstrated a transition from intermittent to complete synchronization via anti-phase synchronization with increasing coupling.

Conclusions:

• The proposed model effectively captures complex dynamics in coupled oscillators.
• Dynamic coupling driven by nonlinear memductance offers new insights into synchronization phenomena.
• Findings have significant implications for understanding neuronal network dynamics and collective behavior.