Entrainment Analysis in Goodwin-Type Nonlinear Oscillator Networks Driven by External Periodic Signals

摘要

In this paper, we present a systematic approach based on harmonic balance method to study the entrained oscillations in a class of Goodwin-type oscillator networks forced by external periodic signals consisting of high order harmonics. First, a necessary condition and a conjecture for entrainment of network oscillations are presented. Next, the authors reveal an estimation for the profile of entrained oscillations in one situation and the monotone dependence of the amplitude and phase shift of entrained oscillations to the external input in other contexts. The theoretical results are then illustrated through some examples including a practical model for circadian rhythm in Neurospora crassa.