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Chaos

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https://www.readbyqxmd.com/read/28576112/periodic-nonlinear-sliding-modes-for-two-uniformly-magnetized-spheres
#1
Boyd F Edwards, John M Edwards
A uniformly magnetized sphere slides without friction along the surface of a second, identical sphere that is held fixed in space, subject to the magnetic force and torque of the fixed sphere and the normal force. The free sphere has two stable equilibrium positions and two unstable equilibrium positions. Two small-amplitude oscillatory modes describe the sliding motion of the free sphere near each stable equilibrium, and an unstable oscillatory mode describes the motion near each unstable equilibrium. The three oscillatory modes remain periodic at finite amplitudes, one bifurcating into mixed modes and circumnavigating the free sphere at large energies...
May 2017: Chaos
https://www.readbyqxmd.com/read/28576111/generalized-synchronization-between-chimera-states
#2
Ralph G Andrzejak, Giulia Ruzzene, Irene Malvestio
Networks of coupled oscillators in chimera states are characterized by an intriguing interplay of synchronous and asynchronous motion. While chimera states were initially discovered in mathematical model systems, there is growing experimental and conceptual evidence that they manifest themselves also in natural and man-made networks. In real-world systems, however, synchronization and desynchronization are not only important within individual networks but also across different interacting networks. It is therefore essential to investigate if chimera states can be synchronized across networks...
May 2017: Chaos
https://www.readbyqxmd.com/read/28576110/improving-the-pseudo-randomness-properties-of-chaotic-maps-using-deep-zoom
#3
Jeaneth Machicao, Odemir M Bruno
A generalized method is proposed to compose new orbits from a given chaotic map. The method provides an approach to examine discrete-time chaotic maps in a "deep-zoom" manner by using k-digits to the right from the decimal separator of a given point from the underlying chaotic map. Interesting phenomena have been identified. Rapid randomization was observed, i.e., chaotic patterns tend to become indistinguishable when compared to the original orbits of the underlying chaotic map. Our results were presented using different graphical analyses (i...
May 2017: Chaos
https://www.readbyqxmd.com/read/28576109/construction-of-rational-solutions-of-the-real-modified-korteweg-de-vries-equation-from-its-periodic-solutions
#4
Qiuxia Xing, Lihong Wang, Dumitru Mihalache, Kuppuswamy Porsezian, Jingsong He
In this paper, we consider the real modified Korteweg-de Vries (mKdV) equation and construct a special kind of breather solution, which can be obtained by taking the limit λj → λ1 of the Lax pair eigenvalues used in the n-fold Darboux transformation that generates the order-n periodic solution from a constant seed solution. Further, this special kind of breather solution of order n can be used to generate the order-n rational solution by taking the limit λ1 → λ0, where λ0 is a special eigenvalue associated with the eigenfunction ϕ of the Lax pair of the mKdV equation...
May 2017: Chaos
https://www.readbyqxmd.com/read/28576108/calculation-of-hamilton-energy-and-control-of-dynamical-systems-with-different-types-of-attractors
#5
Jun Ma, Fuqiang Wu, Wuyin Jin, Ping Zhou, Tasawar Hayat
Strange attractors can be observed in chaotic and hyperchaotic systems. Most of the dynamical systems hold a finite number of attractors, while some chaotic systems can be controlled to present an infinite number of attractors by generating infinite equilibria. Chaos can also be triggered in some dynamical systems that can present hidden attractors, and the attractors in these dynamical systems find no equilibria and the basin of attraction is not connected with any equilibrium (the equilibria position meets certain restriction function)...
May 2017: Chaos
https://www.readbyqxmd.com/read/28576107/experimental-analysis-of-density-fingering-instability-modified-by-precipitation
#6
L Binda, C El Hasi, A Zalts, A D'Onofrio
We analyze the effect of precipitate formation on the development of density induced hydrodynamic instabilities. In this case, the precipitate is BaCO3, obtained by reaction of CO2 with aqueous BaCl2. CO2(g) dissolution increases the local density of the aqueous phase, triggering Rayleigh-Taylor instabilities and BaCO3 formation. It was observed that at first the precipitate was formed at the finger front. As the particles became bigger, they began to fall down from the front. These particles were used as tracers using PIV technique to visualize the particle streamlines and to obtain the velocity of that movement...
May 2017: Chaos
https://www.readbyqxmd.com/read/28576106/electrical-resonance-of-amphotericin-b-channel-activity-in-lipidic-membranes
#7
Karla S Récamier, Iván Ortega-Blake, P Parmananda
In our previous work [J. Membrane Biol. 237, 31 (2010)], we showed the dependence of the time average conductance of Nystatin channels as a function of the applied potential. Specifically, it was observed that greater potential induced enhanced channel activity. This indicates that the supramolecular structure could be stabilized by a large field, possibly by giving a preferential orientation to the monomers. In the present work, we entertain the notion that the process of pore formation in the lipidic membranes has an underlying deterministic component...
May 2017: Chaos
https://www.readbyqxmd.com/read/28576105/on-the-influence-of-additive-and-multiplicative-noise-on-holes-in-dissipative-systems
#8
Orazio Descalzi, Carlos Cartes, Helmut R Brand
We investigate the influence of noise on deterministically stable holes in the cubic-quintic complex Ginzburg-Landau equation. Inspired by experimental possibilities, we specifically study two types of noise: additive noise delta-correlated in space and spatially homogeneous multiplicative noise on the formation of π-holes and 2π-holes. Our results include the following main features. For large enough additive noise, we always find a transition to the noisy version of the spatially homogeneous finite amplitude solution, while for sufficiently large multiplicative noise, a collapse occurs to the zero amplitude solution...
May 2017: Chaos
https://www.readbyqxmd.com/read/28576104/systematic-search-for-wide-periodic-windows-and-bounds-for-the-set-of-regular-parameters-for-the-quadratic-map
#9
Zbigniew Galias
An efficient method to find positions of periodic windows for the quadratic map f(x)=ax(1-x) and a heuristic algorithm to locate the majority of wide periodic windows are proposed. Accurate rigorous bounds of positions of all periodic windows with periods below 37 and the majority of wide periodic windows with longer periods are found. Based on these results, we prove that the measure of the set of regular parameters in the interval [3,4] is above 0.613960137. The properties of periodic windows are studied numerically...
May 2017: Chaos
https://www.readbyqxmd.com/read/28576103/topological-characterization-and-early-detection-of-bifurcations-and-chaos-in-complex-systems-using-persistent-homology
#10
Khushboo Mittal, Shalabh Gupta
Early detection of bifurcations and chaos and understanding their topological characteristics are essential for safe and reliable operation of various electrical, chemical, physical, and industrial processes. However, the presence of non-linearity and high-dimensionality in system behavior makes this analysis a challenging task. The existing methods for dynamical system analysis provide useful tools for anomaly detection (e.g., Bendixson-Dulac and Poincare-Bendixson criteria can detect the presence of limit cycles); however, they do not provide a detailed topological understanding about system evolution during bifurcations and chaos, such as the changes in the number of subcycles and their positions, lifetimes, and sizes...
May 2017: Chaos
https://www.readbyqxmd.com/read/28576102/a-critical-comparison-of-lagrangian-methods-for-coherent-structure-detection
#11
Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, George Haller
We review and test twelve different approaches to the detection of finite-time coherent material structures in two-dimensional, temporally aperiodic flows. We consider both mathematical methods and diagnostic scalar fields, comparing their performance on three benchmark examples: the quasiperiodically forced Bickley jet, a two-dimensional turbulence simulation, and an observational wind velocity field from Jupiter's atmosphere. A close inspection of the results reveals that the various methods often produce very different predictions for coherent structures, once they are evaluated beyond heuristic visual assessment...
May 2017: Chaos
https://www.readbyqxmd.com/read/28576101/the-stability-of-fixed-points-for-a-kuramoto-model-with-hebbian-interactions
#12
Jared C Bronski, Yizhang He, Xinye Li, Yue Liu, Danielle Rae Sponseller, Seth Wolbert
We consider a variation of the Kuramoto model with dynamic coupling, where the coupling strengths are allowed to evolve in response to the phase difference between the oscillators, a model first considered by Ha, Noh, and Park. We demonstrate that the fixed points of this model, as well as their stability, can be completely expressed in terms of the fixed points and stability of the analogous classical Kuramoto problem where the coupling strengths are fixed to a constant (the same for all edges). In particular, for the "all-to-all" network, where the underlying graph is the complete graph, the problem reduces to the problem of understanding the fixed points and stability of the all-to-all Kuramoto model with equal edge weights, a problem that is well understood...
May 2017: Chaos
https://www.readbyqxmd.com/read/28576100/isochronous-dynamics-in-pulse-coupled-oscillator-networks-with-delay
#13
Pan Li, Wei Lin, Konstantinos Efstathiou
We consider a network of identical pulse-coupled oscillators with delay and all-to-all coupling. We demonstrate that the discontinuous nature of the dynamics induces the appearance of isochronous regions-subsets of the phase space filled with periodic orbits having the same period. For each fixed value of the network parameters, such an isochronous region corresponds to a subset of initial states on an appropriate surface of section with non-zero dimensions such that all periodic orbits in this set have qualitatively similar dynamical behaviour...
May 2017: Chaos
https://www.readbyqxmd.com/read/28576099/solitons-and-their-stability-in-the-nonlocal-nonlinear-schr%C3%A3-dinger-equation-with-pt-symmetric-potentials
#14
Zichao Wen, Zhenya Yan
We report localized nonlinear modes of the self-focusing and defocusing nonlocal nonlinear Schrödinger equation with the generalized PT-symmetric Scarf-II, Rosen-Morse, and periodic potentials. Parameter regions are presented for broken and unbroken PT-symmetric phases of linear bounded states and the linear stability of the obtained solitons. Moreover, we numerically explore the dynamical behaviors of solitons and find stable solitons for some given parameters.
May 2017: Chaos
https://www.readbyqxmd.com/read/28576098/generation-of-multi-scroll-attractors-without-equilibria-via-piecewise-linear-systems
#15
R J Escalante-González, E Campos-Cantón, Matthew Nicol
In this paper, we present a new class of dynamical system without equilibria which possesses a multiscroll attractor. It is a piecewise-linear system which is simple, stable, displays chaotic behavior and serves as a model for analogous non-linear systems. We test for chaos using the 0-1 Test for Chaos from Gottwald and Melbourne [SIAM J. Appl. Dyn. Syst. 8(1), 129-145 (2009)].
May 2017: Chaos
https://www.readbyqxmd.com/read/28576097/effects-of-partial-time-delays-on-phase-synchronization-in-watts-strogatz-small-world-neuronal-networks
#16
Xiaojuan Sun, Matjaž Perc, Jürgen Kurths
In this paper, we study effects of partial time delays on phase synchronization in Watts-Strogatz small-world neuronal networks. Our focus is on the impact of two parameters, namely the time delay τ and the probability of partial time delay pdelay, whereby the latter determines the probability with which a connection between two neurons is delayed. Our research reveals that partial time delays significantly affect phase synchronization in this system. In particular, partial time delays can either enhance or decrease phase synchronization and induce synchronization transitions with changes in the mean firing rate of neurons, as well as induce switching between synchronized neurons with period-1 firing to synchronized neurons with period-2 firing...
May 2017: Chaos
https://www.readbyqxmd.com/read/28576096/an-initial-boundary-value-problem-for-the-integrable-spin-1-gross-pitaevskii-equations-with-a-4-%C3%A3-4-lax-pair-on-the-half-line
#17
Zhenya Yan
We extend the idea of the Fokas unified transform to investigate the initial-boundary value problem for the integrable spin-1 Gross-Pitaevskii equations with a 4 × 4 Lax pair on the half-line. The solution of this system can be expressed in terms of the solution of a 4 × 4 matrix Riemann-Hilbert (RH) problem formulated in the complex k-plane. The relevant jump matrices of the RH problem can be explicitly found using the two spectral functions s(k) and S(k), which can be defined by the initial data, the Dirichlet-Neumann boundary data at x = 0...
May 2017: Chaos
https://www.readbyqxmd.com/read/28576095/synchronization-of-moving-oscillators-in-three-dimensional-space
#18
Soumen Majhi, Dibakar Ghosh
We investigate the macroscopic behavior of a dynamical network consisting of a time-evolving wiring of interactions among a group of random walkers. We assume that each walker (agent) has an oscillator and show that depending upon the nature of interaction, synchronization arises where each of the individual oscillators are allowed to move in such a random walk manner in a finite region of three dimensional space. Here, the vision range of each oscillator decides the number of oscillators with which it interacts...
May 2017: Chaos
https://www.readbyqxmd.com/read/28576094/frequency-and-phase-synchronization-in-large-groups-low-dimensional-description-of-synchronized-clapping-firefly-flashing-and-cricket-chirping
#19
Edward Ott, Thomas M Antonsen
A common observation is that large groups of oscillatory biological units often have the ability to synchronize. A paradigmatic model of such behavior is provided by the Kuramoto model, which achieves synchronization through coupling of the phase dynamics of individual oscillators, while each oscillator maintains a different constant inherent natural frequency. Here we consider the biologically likely possibility that the oscillatory units may be capable of enhancing their synchronization ability by adaptive frequency dynamics...
May 2017: Chaos
https://www.readbyqxmd.com/read/28456181/comb-like-turing-patterns-embedded-in-hopf-oscillations-spatially-localized-states-outside-the-2-1-frequency-locked-region
#20
Paulino Monroy Castillero, Arik Yochelis
A generic mechanism for the emergence of spatially localized states embedded in an oscillatory background is demonstrated by using a 2:1 frequency locking oscillatory system. The localization is of Turing type and appears in two space dimensions as a comb-like state in either π phase shifted Hopf oscillations or inside a spiral core. Specifically, the localized states appear in absence of the well known flip-flop dynamics (associated with collapsed homoclinic snaking) that is known to arise in the vicinity of Hopf-Turing bifurcation in one space dimension...
April 2017: Chaos
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