Synchronization behaviors in Goodwin oscillator networks driven by external periodic signals

In this paper, we present a systematic approach based on harmonic balance method to study the induced oscillations in a class of Goodwin oscillator networks forced by external periodic signals. Analytical expressions on the dependence of the phases and amplitudes of network oscillations to those of forcing inputs are revealed. Based on those expressions, we further show that under some specific conditions, the amplitude and phase shift of synchronized oscillations in networks of Goodwin oscillators monotonically depend on the amplitude of exciting inputs. The theoretical results are then illustrated through some examples.