Synchronization in relaxation oscillator networks with conduction delays

Area of Science:

• Dynamical Systems
• Network Science
• Computational Neuroscience

Background:

• Locally coupled networks of relaxation oscillators are fundamental in modeling various biological and physical systems.
• Achieving synchrony, particularly zero phase-lag synchrony, in such networks with conduction delays remains a significant challenge.

Purpose of the Study:

• To propose and analyze a novel mechanism for achieving zero phase-lag synchrony in locally coupled networks of relaxation oscillators with excitatory connections and conduction delays.
• To provide analytical insights into selecting system parameters for rapid synchrony.
• To demonstrate the robustness and applicability of the proposed mechanism.

Main Methods:

• Analysis of a two-coupled-oscillator system to derive phase compression rates.
• Derivation of conditions for selecting nullclines to induce synchrony.
• Numerical simulations of locally coupled networks with conduction delays.

Main Results:

• Identified a mechanism for zero phase-lag synchrony based on differential rates of motion along nullclines.
• Derived analytical criteria for choosing nullclines to achieve rapid synchrony.
• Demonstrated through simulations that the mechanism is effective in larger networks and robust to parameter variations and initial conditions.

Conclusions:

• The proposed mechanism enables rapid zero phase-lag synchrony in networks of relaxation oscillators with conduction delays.
• The choice of nullclines is critical for inducing synchrony.
• The findings offer a new approach for designing and controlling synchronized behavior in complex oscillatory networks.