Transport properties and bifurcation analysis in nonlinear dynamical systems
Bistable laser with long-delayed feedback: a scaling investigation
Scaling laws associated with a symmetry-break in the probability distribution func...
Grant number: | 17/14414-2 |
Support type: | Regular Research Grants |
Duration: | September 01, 2017 - August 31, 2019 |
Field of knowledge: | Physical Sciences and Mathematics - Physics - General Physics |
Principal researcher: | Edson Denis Leonel |
Grantee: | Edson Denis Leonel |
Home Institution: | Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil |
Abstract
The subject of scaling laws define the main research line investigation of the present project. In dynamical systems described either by differential equations or discrete mappings, quite often we find observables that are described by a power law. Examples include Lyapunov exponents, diffusion coefficient, quadratic mean velocity, periodic structures in the parameter plane producing objects called as shrimps, distance from the attractor, chaotic transient, among many others. When such measurable quantities are also scaling invariant, in other words, when they are invariant by a reduction or amplification, generally made via a control parameter or change in the initial condition, one can find a set of critical exponents that describe the dynamics of the observable by using scaling transformations. The main phenomenology to describe this property uses a set of scaling hypotheses as well as a generalized homogeneous function. From them it is possible to find an analytic relation for the exponents leading to a scaling law. Indeed, scaling laws are much useful in the characterization and definition of classes of universality and can be proved either using numerical simulations or analytic descriptions. Following this thematic, we shall investigate some dynamical systems that may exhibit chaos focusing in the characterization of chaotic seas, chaotic transport, transition from integrability to no integrability, time dependent billiards among others. (AU)
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