Quasiperiodic Oscillator with Two Independent Frequencies

Abstract

Quasiperiodic oscillations are widespread in nature and are an important subject of research in the natural sciences. Their peculiarity lies in the fact that they include two or more independent frequencies in the oscillation spectrum:

$$\displaystyle{ x(t) = x\big[\phi _{1}(t),\phi _{2}(t),\ldots,\phi _{p}(t)\big]\;, }$$

(12.1)

where ϕ _i (t) = ω _i t, i = 1, 2, …, p. As a result, x(t) in (12.1) is 2π-periodic in each argument ϕ _i (t), but the quasiperiodic process itself is, in the general case, non-periodic, i.e., x(t) ≠ x(t + T ₀).