The Anishchenko–Astakhov Oscillator of Chaotic Self-Sustained Oscillations

Abstract

In general form, self-sustained oscillatory systems with one degree of freedom are described by the equation

$$\displaystyle{ \ddot{x} +\varPhi (x,\boldsymbol{\alpha })\dot{x} +\varPsi (x,\boldsymbol{\alpha }) = 0\;, }$$

(11.1)

where x is a variable oscillating periodically, $\varPhi (x,\boldsymbol{\alpha })$ and $\varPsi (x,\boldsymbol{\alpha })$ are nonlinear functions characterizing the action of forces providing periodic self-sustained oscillations, and $\boldsymbol{\alpha }$ is a vector of parameters $(\alpha _{1},\alpha _{2},\ldots,\alpha _{n})$.