Robust design against frequency variation for amplitude death in delay-coupled oscillators

Area of Science:

• Nonlinear dynamics and control systems engineering.
• Complex networks and systems theory.

Background:

• Amplitude death is crucial for suppressing unwanted oscillations in engineering.
• Oscillation frequency variations in systems like dc microgrids and airfoils challenge amplitude death stability.
• Existing methods often lack robustness against significant frequency fluctuations.

Purpose of the Study:

• To propose a novel design procedure for inducing amplitude death in delay-coupled oscillators that is robust against frequency variations.
• To analytically determine the frequency band for amplitude death and identify factors influencing its robustness.
• To provide a design applicable to diverse network topologies.

Main Methods:

• Analytical derivation of the frequency band for amplitude death in delay-coupled oscillators.
• Investigation of the impact of coupling strength, connection delay, and network topology (minimum eigenvalue of the adjacency matrix) on frequency robustness.
• Numerical simulations to validate the proposed design procedure and its stability under frequency variations.

Main Results:

• The frequency bandwidth for amplitude death is maximized when coupling strength is inversely proportional to connection delay.
• Network topology, specifically the minimum eigenvalue of the normalized adjacency matrix, influences the robustness of the frequency band.
• Bipartite networks demonstrate limited robustness to frequency variations.
• The proposed design procedure ensures stable amplitude death despite substantial frequency variations.

Conclusions:

• A robust design procedure for amplitude death in frequency-varying delay-coupled oscillators has been successfully developed.
• The findings offer practical implications for stabilizing systems like dc microgrids, airfoil systems, and thermoacoustic systems.
• The method's applicability across various network topologies highlights its versatility in complex systems engineering.