Biomedical subjects

A A Stanislavsky

Publications and source records attributed to A A Stanislavsky.

5 recordsLinked to original sources

PubMed2006

Chaotic and pseudochaotic attractors of perturbed fractional oscillator.

We consider a nonlinear oscillator of the Duffing type with fractional derivative of the order 1<alpha<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.

Journal Article↗

PubMed2006

Long-term memory contribution as applied to the motion of discrete dynamical systems.

We consider the evolution of logistic maps under long-term memory. The memory effects are characterized by one parameter, alpha. If it equals to zero, any memory is absent. This leads to the ordinary discrete dynamical systems. For alpha=1 the memory becomes full, and each subsequent state of the corresponding discrete system accumulates all past states with the same weight just as the ordinary integral of first order does in the continuous space. The case with 0 0.15 the memory effects win over chaos.

Algorithms↗

PubMed2004

Fractional oscillator.

We consider a fractional oscillator which is a generalization of the conventional linear oscillator in the framework of fractional calculus. It is interpreted as an ensemble average of ordinary harmonic oscillators governed by a stochastic time arrow. The intrinsic absorption of the fractional oscillator results from the full contribution of the harmonic oscillator ensemble: these oscillators differ a little from each other in frequency so that each response is compensated by an antiphase response of another harmonic oscillator. This allows one to draw a parallel in the dispersion analysis for media described by a fractional oscillator and an ensemble of ordinary harmonic oscillators with damping. The features of this analysis are discussed.

Journal Article↗

PubMed2003

Fractional dynamics from the ordinary Langevin equation.

We consider the usual Langevin equation depending on an internal time. This parameter is substituted by a first passage time of a self-similar Markov process. Then the Gaussian process is parent, and the hitting time process is directing. The probability to find the resulting process at the real time is defined by the integral relationship between the probability densities of the parent and directing processes. The corresponding master equation becomes the fractional Fokker-Planck equation. We show that the resulting process has non-Markovian properties, all its moments are finite, the fluctuation-dissipation relation and the H-theorem hold.

Journal Article↗

PubMed2000

Memory effects and macroscopic manifestation of randomness.

It is shown that due to memory effects the complex behavior of components in a stochastic system can be transmitted to macroscopic evolution of the system as a whole. Within the Markov approximation widely used in ordinary statistical mechanics, memory effects are neglected. As a result, a time-scale separation between the macroscopic and the microscopic level of description exists, the macroscopic differential picture is not a consequence of microscopic nondifferentiable dynamics. On the other hand, the presence of complete memory in a system means that all its components have the same behavior. If the memory function has no characteristic time scales, the correct description of the macroscopic evolution of such systems has to be in terms of the fractional calculus.

Markov Chains↗