Chaotic and pseudochaotic attractors of perturbed fractional oscillator

We consider a nonlinear oscillator of the Duffing type with fractional derivative of the order 1 < 2. In this system replacement of the regular derivative by the fractional one leads to decaying solutions. The main feature of the system is that decay is asymptotically the powerwise situation that appears in different applications. Perturbed by a periodic force, the system exhibits chaotic motion called fractional chaotic attractor (FCA). The FCA is compared to the regular chaotic attractor that exists in the periodically forced Duffing oscillator. The properties of the FCA are discussed and the pseudochaotic case is demonstrated numerically for the case of the dying attractor. We call pseudochaos the case when the randomness exists with zero Lyapunov exponent, i.e., the dispersion of initially close trajectories is subexponential. (C) 2006 American Institute of Physics.