2ストローク振動子のリミットサイクルの数値解析

概要

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It is well known by the Poincare-Bendixson theorem that the long term behaviour of orbits of autonomous oscillators of the second order takes limit cycles in the phase plane, which is one of the most representative features of nonlinear oscillations in the Nonlinear Dynamical Systems and Chaos Engineering. The classical limit cycles given by the Rayleigh equation and the van der Pol equation consist of the four strokes due to nonlinear characteristic functions with symmetry. In comparison with such four-stroke oscillators usually found in literature, we study numerically the two-stroke oscillators provided by Le Corbeiller, which are expressed by nonlinear characteristic functions with dissymmetry. The criteria to distinguish the two-stroke oscillators from the four-stroke or other oscillators are discussed based on a model oscillator whose characteristic function looses the symmetry with changing values of the parameter involved. Such two-stroke oscillators may be applied to the breathing, the legged locomotion of animals and the flutter of birds and insects.
沼津工業高等専門学校の論文
2008-01-31