BIFURCATIONS OF EQUILIBRIA IN A DISCRETE RAYLEIGH-DUFFING OSCILLATOR

摘要

The discrete Rayleigh-Duffing oscillator described by difference equations is very common in several mechanical problems and reflects a combination of hysteretic and self-oscillatory behavior which will lead to extraordinarily similar dynamical phenomena. In this paper, through investigating the equivalent planar mapping, the types of hyperbolic fixed points of a discrete Rayleigh-Duffing oscillator are completely discussed. Moreover, by calculating the center manifold and normal form, the flip bifurcation and Neimark-Sacker bifurcation of this discrete model are first studied.

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