Dynamical effects of noise on nonlinear systems
Author
Duman, Özer
Advisor
Volpe, Giovanni
Date
2014Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
Randomness and nonlinear dynamics consitute the most essential part of many
events in nature. Therefore, a better and comprehensive understanding of them
is a crucial step in describing natural phenomena as well as the prospect of predicting
their future outcome. Besides the interest from a fundamental point of
view, it is also useful in a wide variety of applications requiring delicate and careful
use of energy. Especially recent advances in micro- and nano-scale technology
requires harnessing the underlying noise itself as it is relatively hard to exert
forces without damaging the system at that scale. The main aim of this work
is to study the effects of noise on nonlinear dynamics. We show that the interplay
between noise, nonlinearity and nonequilibrium conditions leads to a finite
drift with the potential to change the dynamics of the system completely in a
predictable and tunable fashion. We report that the noise-induced drift disrupts
the phase space of a 2-D nonlinear system by shifting the fixed point by a finite
amount which may result in dramatic alterations over the temporal behavior of
the system. We track such alterations to several multi-dimensional model systems
from ecology, soft matter and statistical physics. In a 2-D ecological model
describing two species competing for the same resource, it is found that the system
switches between coexistence and extinction states depending on the shift
due to the noise-induced drift whereas for an aggregate of Brownian particles, it
is shown that noise-induced drift selectively shifts the probability distribution in
certain geometries which can be used in the realization of a microparticle sorter
in the mould of Feynman ratchets. In the case of the aggregate consisting of microswimmers,
tunable anomalous diffusion depending on the confinement length
is reported.
Keywords
Stochastic differential equationsStochastic differential delay equations
Nonlinear dynamics
Diffusion processes
Brownian motion
Microswimmers