Search results for "Attractor"
showing 10 items of 162 documents
Dynamics of a minimal consumer network with bi -directional influence
2018
Abstract We study the dynamics of a model of interdependent consumer behavior defined by a family of two-dimensional noninvertible maps. This family belongs to a class of coupled logistic maps with different nonlinearity parameters and coupling terms that depend on one variable only. In our companion paper we considered the case of independent consumers as well as the case of uni-directionally connected consumers. The present paper aims at describing the dynamics in the case of a bi-directional connection. In particular, we investigate the bifurcation structure of the parameter plane associated with the strength of coupling between the consumers, focusing on the mechanisms of qualitative tr…
On boundaries of attractors in dynamical systems
2021
Abstract Fractal geometry is one of the beautiful and challenging branches of mathematics. Self similarity is an important property, exhibited by most of the fractals. Several forms of self similarity have been discussed in the literature. Iterated Function System (IFS) is a mathematical scheme to generate fractals. There are several variants of IFSs such as condensation IFS, countable IFS, etc. In this paper, certain properties of self similar sets, using the concept of boundary are discussed. The notion of boundaries like similarity boundary and dynamical boundary are extended to condensation IFSs. The relationships and measure theoretic properties of boundaries in dynamical systems are a…
Random bit generation through polarization chaos in nonlinear optical fibers
2017
Nowadays, cryptographic applications are becoming of paramount importance in order to guarantee ultimately secure communications. Performances of classical and quantum key distribution and encryption algorithms are strongly dependent on the used Random Number Generator (RNG). A good RNG must produce unpredictable, unreproducible and unbiased sequences of numbers. For this reason, many true random number generators relying on chaotic physical phenomena, such as chaotic oscillations of high-bandwidth lasers [1, 2] or polarization chaos from a VCSEL diode [3], have been developed. In this work, we propose a RNG implementation based on a different physical mechanism than the ones previously use…
Coexistence of periods in a bifurcation
2012
Abstract A particular type of order-to-chaos transition mediated by an infinite set of coexisting neutrally stable limit cycles of different periods is studied in the Varley–Gradwell–Hassell population model. We prove by an algebraic method that this kind of transition can only happen for a particular bifurcation parameter value. Previous results on the structure of the attractor at the transition point are here simplified and extended.
Complex Dynamics in a Harmonically Excited Lennard-Jones Oscillator: Microcantilever-Sample Interaction in Scanning Probe Microscopes1
1998
In this paper we model the microcantilever-sample interaction in an atomic force microscope (AFM) via a Lennard-Jones potential and consider the dynamical behavior of a harmonically forced system. Using nonlinear analysis techniques on attracting limit sets, we numerically verify the presence of chaotic invariant sets. The chaotic behavior appears to be generated via a cascade of period doubling, whose occurrence has been studied as a function of the system parameters. As expected, the chaotic attractors are obtained for values of parameters predicted by Melnikov theory. Moreover, the numerical analysis can be fruitfully employed to analyze the region of the parameter space where no theoret…
Higher-order coupled quintessence
2010
We study a coupled quintessence model in which the interaction with the dark-matter sector is a function of the quintessence potential. Such a coupling can arise from a field dependent mass term for the dark-matter field. The dynamical analysis of a standard quintessence potential coupled with the interaction explored here shows that the system possesses a late-time accelerated attractor. In light of these results, we perform a fit to the most recent Supernovae Ia, Cosmic Microwave Background, and Baryon Acoustic Oscillation data sets. Constraints arising from weak equivalence principle violation arguments are also discussed.
Secondary gravitational anisotropies in open universes
1998
The applicability of the potential approximation in the case of open universes is tested. Great Attractor-like structures are considered in the test. Previous estimates of the Cosmic Microwave background anisotropies produced by these structures are analyzed and interpreted. The anisotropies corresponding to inhomogeneous ellipsoidal models are also computed. It is proved that, whatever the spatial symmetry may be, Great Attractor-like objects with extended cores (radius $\sim 10h^{-1}$),located at redshift $z=5.9$ in an open universe with density parameter $\Omega_{0}=0.2$, produce secondary gravitational anisotropies of the order of $10^{-5}$ on angular scales of a few degrees. This aniso…
Polarization and modal attractors in conservative counterpropagating four-wave interaction
2005
An experimental and theoretical study of the resonant four-wave interaction scheme in the counterpropagating configuration reveals the existence of a novel attraction process in Hamiltonian systems. We show analytically that it is the specificity of the boundary conditions inherent in the counterpropagating configuration that makes attraction dynamics possible in spite of the reversible nature of the four-wave interaction. In the context of optics, this novel dynamical feature could be the basic mechanism of a universal polarizer performing total polarization conversion of unpolarized light with, in principle, 100% efficiency.
The great attractor and the COBE quadrupole
2008
A nonlinear model for the Great Attractor is built. It is based on the Tolman-Bondi solution of the Einstein equations. The angular temperature distribution of the Cosmic Microwave Background produced by the Great Attractor is numerically obtained. Several realizations of the Great Attractor are studied. In all the cases, the distance from the Great Attractor to the Local Group is ≈ 43h−1 Mpc, the density contrast reduces to a half of the central value at a radius of 9h−1 Mpc ⪯ Rc ⪯ 14h−1 Mpc, and the dipole due to the infall towards the inhomogeneity center is 1.33 × 10−3 ⪯ D ⪯ 1.8 × 10−3. A complete arbitrary background is assumed; the density parameter, Σ and the reduced Hubble constant,…
The imprints of the Great Attractor and the Virgo cluster on the microwave background
1993
A fully non-linear model based on the Tolman-Bondi solution of the Einstein equations is used to describe the Great Attractor and the Virgo cluster. The background is a Friedmann-Robertson-Walker universe, and the inhomogeneity develops from physically motivated initial profiles of the energy density and the peculiar velocity. Accurate numerical integrations of the field equations of the null geodesics are carried out, and thus the angular temperature distribution of the microwave background produced by the chosen overdensities is found. The observer is located in the Local Group. The quadrupole Q produced by each overdensity is computed and divided into two parts: the relativistic Doppler …