| Title |
Sudėtingos netiesinės sistemos veikiamos spalvoto ir ne Gauso išorinio triukšmo / |
| Translation of Title |
Complex nonlinear systems affected by colored and non-Gaussian external noise. |
| Authors |
Kazakevičius, Rytis |
| Full Text |
|
| Pages |
39 |
| Keywords [eng] |
anomalous diffusion ; non-homogeneous media ; 1/f noise ; colored noise ; Levy noise |
| Abstract [eng] |
Transport properties in complex systems are usually characterized by the dependence on time of the variance. If the variance exhibits a non-linear growth on time, such a process is called anomalous diffusion. Starting from Langevin equations describing motion of a Brownian particle in heterogeneous media, in this thesis we have derived stochastic differential equation (SDE) generating signals with 1/f spectrum together with power-law steady-state distribution. In addition, we showed that the set of two nonlinearly coupled SDEs generates signals with power-law spectrum in a wide range of frequencies together with the almost arbitrary steady-state distribution. By using proposed equation we have studied the influence of external potentials on anomalous diffusion and obtained analytic expressions for the transition probability as well as for the first and the second moments. We have demonstrated that the existence of colored noise leads to an additional restriction of the diffusion seen as exponential cut-off of the distribution of particle positions and narrower range of frequencies where 1/f noise occurs. Additionally we have generalized proposed nonlinear SDE driven by Gaussian noise by replacing the Gaussian noise with a more general Levy stable noise. We have proposed time-fractional Fokker-Planck equation describing the subdiffusion of particles in an inhomogeneous medium. |
| Dissertation Institution |
Vilniaus universitetas. |
| Type |
Summaries of doctoral thesis |
| Language |
Lithuanian |
| Publication date |
2017 |
