Energy-based analysis of frequency entrainment described by van der Pol and PLL equations

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This paper is devoted to an analysis of frequency entrainment described by van der Pol and PLL equations. The frequency entrainment stems from two different types of self-sustained oscillations, and the mechanism of entrainment has not been fully understood. The use of an energy balance relation is proposed in this paper to analyze the frequency entrainment. The energy balance relation is equivalent to the energy conservation law of dynamical systems which contain dissipation and input terms. This paper numerically and theoretically investigates the frequency entrainment via energy balance relation and response curves. They provide characteristic features of dc component, harmonic amplitude, phase difference, and supplied energy by driving oscillatory force. The obtained results show that the frequency entrainment described by the two equations have different features of supplied energy.
2006-12-06