A frequency-domain-based master stability function for synchronization in nonlinear periodic oscillators

SUMMARY An efficient methodology to study conditions for stable in-phase synchronization in networks of periodic identical nonlinear oscillators is proposed. The problem of investigating synchronization properties on periodic trajectories is reduced to an eigenvalue problem by means of the joint application of master stability function and harmonic balance techniques. The proposed method permits to exploit the periodicity of trajectories, reducing computational time with respect to traditional time-domain approaches (which were designed to deal with generic attractors) and good accuracy. In addition, such method can easily deal with networks of nonlinear periodic oscillators described by differential-algebraic equations, and then both static and dynamic coupling could be studied. Copyright © 2011 John Wiley & Sons, Ltd.