Finite-difference model of the fractional oscillator of Van der Pol

Abstract

The algorithm of numerical modeling of self-oscillating system, defined by the equation of motion with fractional order derivative is offered. To discretize in time the equation of motion method is used the invariance of impulse response of linear resonators in combination with the formulas of the fractional differential transforms of discrete harmonic functions. The example of modeling of process of establishing self-oscillations in the fractional oscillator is given. Discusses the transformation of the finite-difference computational algorithm in the object of nonlinear dynamics in discrete time. Are provided spectral and correlation characteristics of chaotic self-oscillations of the fractional oscillator of Van der Pol in discrete time.

Keywords

• нелинейная динамика
• fractional differentiation
• van der pol equation
• numerical modeling
• discrete time nonlinear dynamics