Regular and Chaotic Regimes in Scalar Field Cosmology
Directory of Open Access Journals (Sweden)
Alexey V. Toporensky
2006-03-01
Full Text Available A transient chaos in a closed FRW cosmological model with a scalar field is studied. We describe two different chaotic regimes and show that the type of chaos in this model depends on the scalar field potential. We have found also that for sufficiently steep potentials or for potentials with large cosmological constant the chaotic behavior disappears.
Quantization rules for strongly chaotic systems
International Nuclear Information System (INIS)
Aurich, R.; Bolte, J.
1992-09-01
We discuss the quantization of strongly chaotic systems and apply several quantization rules to a model system given by the unconstrained motion of a particle on a compact surface of constant negative Gaussian curvature. We study the periodic-orbit theory for distinct symmetry classes corresponding to a parity operation which is always present when such a surface has genus two. Recently, several quantization rules based on periodic orbit theory have been introduced. We compare quantizations using the dynamical zeta function Z(s) with the quantization condition cos(π N(E)) = 0, where a periodix-orbit expression for the spectral staircase N(E) is used. A general discussion of the efficiency of periodic-orbit quantization then allows us to compare the different methods. The system dependence of the efficiency, which is determined by the topological entropy τ and the mean level density anti d(E), is emphasized. (orig.)
Chaotic secure communication based on strong tracking filtering
International Nuclear Information System (INIS)
Li Xiongjie; Xu Zhengguo; Zhou Donghua
2008-01-01
A scheme for implementing secure communication based on chaotic maps and strong tracking filter (STF) is presented, and a modified STF algorithm with message estimation is developed for the special requirement of chaotic secure communication. At the emitter, the message symbol is modulated by chaotic mapping and is output through a nonlinear function. At the receiver, the driving signal is received and the message symbol is recovered dynamically by the STF with estimation of message symbol. Simulation results of Holmes map demonstrate that when message symbols are binary codes, STF can effectively recover the codes of the message from the noisy chaotic signals. Compared with the extended Kalman filter (EKF), STF has a lower bit error rate
Negative mobility of a Brownian particle: Strong damping regime
Słapik, A.; Łuczka, J.; Spiechowicz, J.
2018-02-01
We study impact of inertia on directed transport of a Brownian particle under non-equilibrium conditions: the particle moves in a one-dimensional periodic and symmetric potential, is driven by both an unbiased time-periodic force and a constant force, and is coupled to a thermostat of temperature T. Within selected parameter regimes this system exhibits negative mobility, which means that the particle moves in the direction opposite to the direction of the constant force. It is known that in such a setup the inertial term is essential for the emergence of negative mobility and it cannot be detected in the limiting case of overdamped dynamics. We analyse inertial effects and show that negative mobility can be observed even in the strong damping regime. We determine the optimal dimensionless mass for the presence of negative mobility and reveal three mechanisms standing behind this anomaly: deterministic chaotic, thermal noise induced and deterministic non-chaotic. The last origin has never been reported. It may provide guidance to the possibility of observation of negative mobility for strongly damped dynamics which is of fundamental importance from the point of view of biological systems, all of which in situ operate in fluctuating environments.
Mallory, Kristina; van Gorder, Robert A.
We study chaotic behavior of solutions to the bilinear system of Lorenz type developed by Celikovsky and Vanecek [1994] through an application of competitive modes. This bilinear system of Lorenz type is one possible canonical form holding the Lorenz equation as a special case. Using a competitive modes analysis, which is a completely analytical method allowing one to identify parameter regimes for which chaos may occur, we are able to demonstrate a number of parameter regimes which admit a variety of distinct chaotic behaviors. Indeed, we are able to draw some interesting conclusions which relate the behavior of the mode frequencies arising from writing the state variables for the Celikovsky-Vanecek model as coupled oscillators, and the types of emergent chaotic behaviors observed. The competitive modes analysis is particularly useful if all but one of the model parameters are fixed, and the remaining free parameter is used to modify the chaos observed, in a manner analogous to a bifurcation parameter. Through a thorough application of the method, we are able to identify several parameter regimes which give new dynamics (such as specific forms of chaos) which were not observed or studied previously in the Celikovsky-Vanecek model. Therefore, the results demonstrate the advantage of the competitive modes approach for detecting new parameter regimes leading to chaos in third-order dynamical systems.
The chaotic regime of D-term inflation
Energy Technology Data Exchange (ETDEWEB)
Buchmüller, W. [DESY, Notkestrasse 85, 22607 Hamburg (Germany); Domcke, V. [SISSA/INFN, Via Bonomea 265, 34136 Trieste (Italy); Schmitz, K., E-mail: wilfried.buchmueller@desy.de, E-mail: valerie.domcke@sissa.it, E-mail: kai.schmitz@ipmu.jp [Kavli IPMU (WPI), University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa (Japan)
2014-11-01
We consider D-term inflation for small couplings of the inflaton to matter fields. Standard hybrid inflation then ends at a critical value of the inflaton field that exceeds the Planck mass. During the subsequent waterfall transition the inflaton continues its slow-roll motion, whereas the waterfall field rapidly grows by quantum fluctuations. Beyond the decoherence time, the waterfall field becomes classical and approaches a time-dependent minimum, which is determined by the value of the inflaton field and the self-interaction of the waterfall field. During the final stage of inflation, the effective inflaton potential is essentially quadratic, which leads to the standard predictions of chaotic inflation. The model illustrates how the decay of a false vacuum of GUT-scale energy density can end in a period of 'chaotic inflation'.
The chaotic regime of D-term inflation
Energy Technology Data Exchange (ETDEWEB)
Buchmueller, W. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Domcke, V. [SISSA/INFN, Triest (Italy); Schmitz, K. [Kavli IPMU (WPI), Kashiwa (Japan)
2014-08-15
We consider D-term inflation for small couplings of the inflaton to matter fields. Standard hybrid inflation then ends at a critical value of the inflaton field that exceeds the Planck mass. During the subsequent waterfall transition the inflaton continues its slow-roll motion, whereas the waterfall field rapidly grows by quantum fluctuations. Beyond the decoherence time, the waterfall field becomes classical and approaches a time-dependent minimum, which is determined by the value of the inflaton field and the self-interaction of the waterfall field. During the final stage of inflation, the effective inflaton potential is essentially quadratic, which leads to the standard predictions of chaotic inflation. The model illustrates how the decay of a false vacuum of GUT-scale energy density can end in a period of 'chaotic inflation'.
The chaotic regime of D-term inflation
International Nuclear Information System (INIS)
Buchmueller, W.; Domcke, V.; Schmitz, K.
2014-08-01
We consider D-term inflation for small couplings of the inflaton to matter fields. Standard hybrid inflation then ends at a critical value of the inflaton field that exceeds the Planck mass. During the subsequent waterfall transition the inflaton continues its slow-roll motion, whereas the waterfall field rapidly grows by quantum fluctuations. Beyond the decoherence time, the waterfall field becomes classical and approaches a time-dependent minimum, which is determined by the value of the inflaton field and the self-interaction of the waterfall field. During the final stage of inflation, the effective inflaton potential is essentially quadratic, which leads to the standard predictions of chaotic inflation. The model illustrates how the decay of a false vacuum of GUT-scale energy density can end in a period of 'chaotic inflation'.
The chaotic regime of D-term inflation
International Nuclear Information System (INIS)
Buchmüller, W.; Domcke, V.; Schmitz, K.
2014-01-01
We consider D-term inflation for small couplings of the inflaton to matter fields. Standard hybrid inflation then ends at a critical value of the inflaton field that exceeds the Planck mass. During the subsequent waterfall transition the inflaton continues its slow-roll motion, whereas the waterfall field rapidly grows by quantum fluctuations. Beyond the decoherence time, the waterfall field becomes classical and approaches a time-dependent minimum, which is determined by the value of the inflaton field and the self-interaction of the waterfall field. During the final stage of inflation, the effective inflaton potential is essentially quadratic, which leads to the standard predictions of chaotic inflation. The model illustrates how the decay of a false vacuum of GUT-scale energy density can end in a period of 'chaotic inflation'
The chaotic regime of D-term inflation
Buchmüller, W.; Domcke, V.; Schmitz, K.
2014-11-01
We consider D-term inflation for small couplings of the inflaton to matter fields. Standard hybrid inflation then ends at a critical value of the inflaton field that exceeds the Planck mass. During the subsequent waterfall transition the inflaton continues its slow-roll motion, whereas the waterfall field rapidly grows by quantum fluctuations. Beyond the decoherence time, the waterfall field becomes classical and approaches a time-dependent minimum, which is determined by the value of the inflaton field and the self-interaction of the waterfall field. During the final stage of inflation, the effective inflaton potential is essentially quadratic, which leads to the standard predictions of chaotic inflation. The model illustrates how the decay of a false vacuum of GUT-scale energy density can end in a period of `chaotic inflation'.
Dynamics of coherent states in regular and chaotic regimes of the non-integrable Dicke model
Lerma-Hernández, S.; Chávez-Carlos, J.; Bastarrachea-Magnani, M. A.; López-del-Carpio, B.; Hirsch, J. G.
2018-04-01
The quantum dynamics of initial coherent states is studied in the Dicke model and correlated with the dynamics, regular or chaotic, of their classical limit. Analytical expressions for the survival probability, i.e. the probability of finding the system in its initial state at time t, are provided in the regular regions of the model. The results for regular regimes are compared with those of the chaotic ones. It is found that initial coherent states in regular regions have a much longer equilibration time than those located in chaotic regions. The properties of the distributions for the initial coherent states in the Hamiltonian eigenbasis are also studied. It is found that for regular states the components with no negligible contribution are organized in sequences of energy levels distributed according to Gaussian functions. In the case of chaotic coherent states, the energy components do not have a simple structure and the number of participating energy levels is larger than in the regular cases.
Deformed GOE for systems with a few degrees of freedom in the chaotic regime
International Nuclear Information System (INIS)
Hussein, M.S.; Pato, M.P.
1990-01-01
New distribution laws for the energy level spacings and the eigenvector amplitudes, appropriate for systems with a few degrees of freedom in the chaotic regime, are derived by conveniently deforming the GOE. The cases of 2X2 and 3X3 matrices are fully worked out. Suggestions concerning the general case of matrices with large dimensions are made. (author)
Deformed GOE for systems with a few degrees of freedom in the chaotic regime
International Nuclear Information System (INIS)
Hussein, M.S.; Pato, M.P.
1990-03-01
New distribution laws for the energy level spacings and the eigenvector amplitudes, approapriate for systems with a few degrees of freedom in the chaotic regime, are derived by conveniently deforming the GOE. The cases of 2x2 and 3x3 matrices are fully worked out. Suggestions concerning the general case of matrices with large dimensions are made. (author) [pt
Gu, Yan; Wang, Jiao
1997-02-01
We study relaxation of an ensemble of cat maps with initially localized phase-space distributions. Calculations of the coarse-grained entropy Sɛ ( t) for both classical and quantum motions are presented. It is shown that, within the relaxation period, both classical and quantum entropies increase with a nearly constant rate which can be identified as the largest Lyapunov exponent of the classical cat. After an empirical relaxation time, the time behavior for two entropies becomes different. While the classical entropy increases to the equilibrium entropy Seqm and stays there, its quantum analogue fluctuates incessantly around a mean overlineSɛ which is less than Seqm. We regard the entropy difference ΔS = S eqm - overlineSɛ as a measure of nonergodicity of the quantum motion of strongly chaotic systems and investigate its dependence on the Planck constant h. For fixed initial phase-space distributions, numerical results suggest that there is a scaling law ΔSαhβ with β ≈ 0.72 in the semiclassical regime.
Simulation of weak and strong Langmuir collapse regimes
International Nuclear Information System (INIS)
Hadzievski, L.R.; Skoric, M.M.; Kono, M.; Sato, T.
1998-01-01
In order to check the validity of the self-similar solutions and the existence of weak and strong collapse regimes, direct two dimensional simulation of the time evolution of a Langmuir soliton instability is performed. Simulation is based on the Zakharov model of strong Langmuir turbulence in a weakly magnetized plasma accounting for the full ion dynamics. For parameters considered, agreement with self-similar dynamics of the weak collapse type is found with no evidence of the strong Langmuir collapse. (author)
International Nuclear Information System (INIS)
Tung Wenwen; Qi Yan; Gao, J.B.; Cao Yinhe; Billings, Lora
2005-01-01
In recent years it has been increasingly recognized that noise and determinism may have comparable but different influences on population dynamics. However, no simple analysis methods have been introduced into ecology which can readily characterize those impacts. In this paper, we study a population model with strong periodicity and both with and without noise. The noise-free model generates both quasi-periodic and chaotic dynamics for certain parameter values. Due to the strong periodicity, however, the generated chaotic dynamics have not been satisfactorily described. The dynamics becomes even more complicated when there is noise. Characterizing the chaotic and stochastic dynamics in this model thus represents a challenging problem. Here we show how the chaotic dynamics can be readily characterized by the direct dynamical test for deterministic chaos developed by [Gao JB, Zheng ZM. Europhys. Lett. 1994;25:485] and how the influence of noise on quasi-periodic motions can be characterized as asymmetric diffusions wandering along the quasi-periodic orbit. It is hoped that the introduced methods will be useful in studying other population models as well as population time series obtained both in field and laboratory experiments
Buoyancy-driven chaotic regimes during solute dispersion in pore networks
International Nuclear Information System (INIS)
Tsakiroglou, C.D.; Theodoropoulou, M.A.; Karoutsos, V.
2005-01-01
In an attempt to investigate gravity effects on solute dispersion at the scale of a pore network, single source-solute transport visualization experiments are performed on glass-etched pore networks of varying morphology and degree of pore-scale heterogeneities. The (lighter) low solute concentration aqueous solution flows steadily through the porous medium and the (heavier) high solute concentration solution is injected at a very low and constant flow rate through an inner port. The transient evolution of the solute concentration distribution over various regions of the pore network is determined at different scales by capturing and video-recording snapshots of the dispersion on PC, measuring automatically the spatial variation of the color intensity of the solution, and transforming the color intensities to solute concentrations. Without the action of gravity, the steady-state dispersion regime changes with Peclet (Pe) number, and the longitudinal and transverse dispersivities are estimated by fitting the experimental datasets to approximate analytic solutions of the advection-dispersion equation. Under the action of gravity, multiple of steady-state solute dispersion regimes is developed at each Pe value, and lobe-shaped instabilities of the solute concentration are observed across the pore network, as the downward flow of the denser (higher solute concentration) fluid is counterbalanced by the upward flow of the less dense (lower solute concentration) fluid. The steady-state dispersion regimes may be periodic, quasi-periodic or chaotic depending on the system parameters. The nature of the transient fluctuations of the average solute concentration is analyzed by identifying the periodicity of the fluctuations, determining the autocorrelation function and the statistical moments of the time series, and inspecting the FFT (fast Fourier transform) power spectra. It is found that the mixing zone tends to be stabilized at higher values of the Peclet (Pe) number
The Cornwall-Norton model in the strong coupling regime
International Nuclear Information System (INIS)
Natale, A.A.
1991-01-01
The Cornwall-Norton model is studied in the strong coupling regime. It is shown that the fermionic self-energy at large momenta behaves as Σ(p) ∼ (m 2 /p) ln (p/m). We verify that in the strong coupling phase the dynamically generated masses of gauge and scalar bosons are of the same order, and the essential features of the model remain intact. (author)
Periodic-orbit theory of the number variance Σ2(L) of strongly chaotic systems
International Nuclear Information System (INIS)
Aurich, R.; Steiner, F.
1994-03-01
We discuss the number variance Σ 2 (L) and the spectral form factor F(τ) of the energy levels of bound quantum systems whose classical counterparts are strongly chaotic. Exact periodic-orbit representations of Σ 2 (L) and F(τ) are derived which explain the breakdown of universality, i.e., the deviations from the predictions of random-matrix theory. The relation of the exact spectral form factor F(τ) to the commonly used approximation K(τ) is clarified. As an illustration the periodic-orbit representations are tested in the case of a strongly chaotic system at low and high energies including very long-range correlations up to L=700. Good agreement between 'experimental' data and theory is obtained. (orig.)
Spectator Effects during Leptogenesis in the Strong Washout Regime
Garbrecht, Bjorn
2014-01-01
By including spectator fields into the Boltzmann equations for Leptogenesis, we show that partially equilibrated spectator interactions can have a significant impact on the freeze-out value of the asymmetry in the strong washout regime. The final asymmetry is typically increased, since partially equilibrated spectators "hide" a part of the asymmetry from washout. We study examples with leptonic and non-leptonic spectator processes, assuming thermal initial conditions, and find up to 50% enhanced asymmetries compared to the limit of fully equilibrated spectators. Together with a comprehensive overview of the equilibration temperatures for various Standard Model processes, the numerical results indicate the ranges when the limiting cases of either fully equilibrated or negligible spectator fields are applicable and when they are not. Our findings also indicate an increased sensitivity to initial conditions and finite density corrections even in the strong washout regime.
Regular and chaotic motion of two dimensional electrons in a strong magnetic field
International Nuclear Information System (INIS)
Bar-Lev, Oded; Levit, Shimon.
1992-05-01
For two dimensional system of electrons in a strong magnetic field a standard approximation is the projection on a single Landau level. The resulting Hamiltonian is commonly treated semiclassically. An important element in applying the semiclassical approximation is the integrability of the corresponding classical system. We discuss the relevant integrability conditions and give a simple example of a non-integrable system-two interacting electrons in the presence of two impurities-which exhibits a coexistence of regular and chaotic classical motions. Since the inverse of the magnetic field plays the role of the Planck constant in these problems, one has the opportunity to control the 'closeness' of chaotic physical systems to the classical limit. (author)
Dynamics of levitated nanospheres: towards the strong coupling regime
International Nuclear Information System (INIS)
Monteiro, T S; Millen, J; Pender, G A T; Barker, P F; Marquardt, Florian; Chang, D
2013-01-01
The use of levitated nanospheres represents a new paradigm for the optomechanical cooling of a small mechanical oscillator, with the prospect of realizing quantum oscillators with unprecedentedly high quality factors. We investigate the dynamics of this system, especially in the so-called self-trapping regime, where one or more optical fields simultaneously trap and cool the mechanical oscillator. The determining characteristic of this regime is that both the mechanical frequency ω M and single-photon optomechanical coupling strength parameters g are a function of the optical field intensities, in contrast to usual set-ups where ω M and g are constant for the given system. We also measure the characteristic transverse and axial trapping frequencies of different sized silica nanospheres in a simple optical standing wave potential, for spheres of radii r = 20–500 nm, illustrating a protocol for loading single nanospheres into a standing wave optical trap that would be formed by an optical cavity. We use these data to confirm the dependence of the effective optomechanical coupling strength on sphere radius for levitated nanospheres in an optical cavity and discuss the prospects for reaching regimes of strong light–matter coupling. Theoretical semiclassical and quantum displacement noise spectra show that for larger nanospheres with r ∼> 100 nm a range of interesting and novel dynamical regimes can be accessed. These include simultaneous hybridization of the two optical modes with the mechanical modes and parameter regimes where the system is bistable. We show that here, in contrast to typical single-optical mode optomechanical systems, bistabilities are independent of intracavity intensity and can occur for very weak laser driving amplitudes. (paper)
Electronic Maxwell demon in the coherent strong-coupling regime
Schaller, Gernot; Cerrillo, Javier; Engelhardt, Georg; Strasberg, Philipp
2018-05-01
We consider an external feedback control loop implementing the action of a Maxwell demon. Applying control actions that are conditioned on measurement outcomes, the demon may transport electrons against a bias voltage and thereby effectively converts information into electric power. While the underlying model—a feedback-controlled quantum dot that is coupled to two electronic leads—is well explored in the limit of small tunnel couplings, we can address the strong-coupling regime with a fermionic reaction-coordinate mapping. This exact mapping transforms the setup into a serial triple quantum dot coupled to two leads. We find that a continuous projective measurement of the central dot occupation would lead to a complete suppression of electronic transport due to the quantum Zeno effect. In contrast, by using a microscopic detector model we can implement a weak measurement, which allows for closure of the control loop without transport blockade. Then, in the weak-coupling regime, the energy flows associated with the feedback loop are negligible, and dominantly the information gained in the measurement induces a bound for the generated electric power. In the strong coupling limit, the protocol may require more energy for operating the control loop than electric power produced, such that the whole device is no longer information dominated and can thus not be interpreted as a Maxwell demon.
The laser proton acceleration in the strong charge separation regime
International Nuclear Information System (INIS)
Nishiuchi, M.; Fukumi, A.; Daido, H.; Li, Z.; Sagisaka, A.; Ogura, K.; Orimo, S.; Kado, M.; Hayashi, Y.; Mori, M.; Bulanov, S.V.; Esirkepov, T.; Nemoto, K.; Oishi, Y.; Nayuki, T.; Fujii, T.; Noda, A.; Iwashita, Y.; Shirai, T.; Nakamura, S.
2006-01-01
We report the experimental results of proton acceleration as well as the simple one-dimensional model which explains our experimental data. The proton acceleration experiment is carried out with a TW short pulse laser irradiated on a tantalum thin-foil target (3 μm thickness) with an intensity of ∼3x10 18 Wcm -2 . Accelerated protons exhibit a typical energy spectrum with two quasi-Maxwellian components with a high energy cut-off. We can successfully explain the higher energy part as well as the cut off energy of the proton spectrum with the simple-one-dimensional model based on the strong charge separation regime, which is the extension of the model proposed originally by [M. Passoni et al., Phys. Rev. E 69 (2004) 026411
Mathematical structure of Rabi oscillations in the strong coupling regime
International Nuclear Information System (INIS)
Fujii, Kazuyuki
2003-01-01
In this paper, we generalize the Jaynes-Cummings Hamiltonian by making use of some operators based on Lie algebras su(1, 1) and su(2), and study a mathematical structure of Rabi floppings of these models in the strong coupling regime. We show that Rabi frequencies are given by matrix elements of generalized coherent operators (Fujii K 2002 Preprint quant-ph/0202081) under the rotating-wave approximation. In the first half, we make a general review of coherent operators and generalized coherent ones based on Lie algebras su(1, 1) and su(2). In the latter half, we carry out a detailed examination of Frasca (Frasca M 2001 Preprint quant-ph/0111134) and generalize his method, and moreover present some related problems. We also apply our results to the construction of controlled unitary gates in quantum computation. Lastly, we make a brief comment on application to holonomic quantum computation
Statistical properties of highly excited quantum eigenstates of a strongly chaotic system
International Nuclear Information System (INIS)
Aurich, R.; Steiner, F.
1992-06-01
Statistical properties of highly excited quantal eigenstates are studied for the free motion (geodesic flow) on a compact surface of constant negative curvature (hyperbolic octagon) which represents a strongly chaotic system (K-system). The eigenstates are expanded in a circular-wave basis, and it turns out that the expansion coefficients behave as Gaussian pseudo-random numbers. It is shown that this property leads to a Gaussian amplitude distribution P(ψ) in the semiclassical limit, i.e. the wavefunctions behave as Gaussian random functions. This behaviour, which should hold for chaotic systems in general, is nicely confirmed for eigenstates lying 10000 states above the ground state thus probing the semiclassical limit. In addition, the autocorrelation function and the path-correlation function are calculated and compared with a crude semiclassical Bessel-function approximation. Agreement with the semiclassical prediction is only found, if a local averaging is performed over roughly 1000 de Broglie wavelengths. On smaller scales, the eigenstates show much more structure than predicted by the first semiclassical approximation. (orig.)
CO2 laser with modulated losses: Theoretical models and experiments in the chaotic regime
International Nuclear Information System (INIS)
Pando L, C.L.; Meucci, R.; Ciofini, M.; Arecchi, F.T.
1993-04-01
We compare two different theoretical models for a CO 2 laser, namely the two-and four-level model, and show that the second one traces with much better accuracy the experimental behavior in the case of a chaotic dynamics due to time modulation of the cavity losses. Even though the two-level model provides a qualitative explanation of the chaotic dynamics, only the four-level one assures a quantitative fitting. We also show that, at the onset of chaos, the chaotic dynamics is low dimensional and can be described in terms of a noninvertible unidimensional map. (author). 12 refs, 8 figs, 2 tabs
Quantum eigenstates of a strongly chaotic system and the scar phenomenon
International Nuclear Information System (INIS)
Aurich, R.; Steiner, F.
1993-04-01
The quantum eigenstates of a strongly chaotic system (hyperbolic octagon) are studied with special emphasis on the scar phenomenon. The dynamics of a localized wavepacket is discussed which travels along a short periodic orbit yielding a test for the scar model developed by Heller. The autocorrelation function C(t) and the smeared weighted spectral density S τ (E) are in accordance with this model, but the conclusion that this implies the existence of scarred eigenstates is not confirmed. A random wavefunction model generates with the same probability intensity structures being localized near short periodic orbits as the wavefunctions obeying the Schroedinger equation. Although there are some eigenstates which are localized near a periodic orbit, the conclusion that their intensities differ significantly from the statistically expected ones cannot be drawn. Thus the scar phenomenon seems to be absent in the case of hyperbolic octagons. (orig.)
Low-dimensional chaotic attractors in drift wave turbulence
International Nuclear Information System (INIS)
Persson, M.; Nordman, H.
1991-01-01
Simulation results of toroidal η i -mode turbulence are analyzed using mathematical tools of nonlinear dynamics. Low-dimensional chaotic attractors are found in the strongly nonlinear regime while in the weakly interacting regime the dynamics is high dimensional. In both regimes, the solutions are found to display sensitive dependence on initial conditions, characterized by a positive largest Liapunov exponent. (au)
Coulomb Impurity Problem of Graphene in Strong Coupling Regime in Magnetic Fields.
Kim, S C; Yang, S-R Eric
2015-10-01
We investigate the Coulomb impurity problem of graphene in strong coupling limit in the presence of magnetic fields. When the strength of the Coulomb potential is sufficiently strong the electron of the lowest energy boundstate of the n = 0 Landau level may fall to the center of the potential. To prevent this spurious effect the Coulomb potential must be regularized. The scaling function for the inverse probability density of this state at the center of the impurity potential is computed in the strong coupling regime. The dependence of the computed scaling function on the regularization parameter changes significantly as the strong coupling regime is approached.
International Nuclear Information System (INIS)
Elyutin, P V; Rubtsov, A N
2008-01-01
The energy evolution of a quantum chaotic system under the perturbation that harmonically depends on time is studied for the case of large perturbation, in which the rate of transition calculated from the Fermi golden rule (FGR) is about or exceeds the frequency of perturbation. For this case, the models of the Hamiltonian with random non-correlated matrix elements demonstrate that the energy evolution retains its diffusive character, but the rate of diffusion increases slower than the square of the magnitude of perturbation, thus destroying the quantum-classical correspondence for the energy diffusion and the energy absorption in the classical limit ℎ → 0. The numerical calculation carried out for a model built from the first principles (the quantum analog of the Pullen-Edmonds oscillator) demonstrates that the evolving energy distribution, apart from the diffusive component, contains a ballistic one with the energy dispersion that is proportional to the square of time. This component originates from the chains of matrix elements with correlated signs and vanishes if the signs of matrix elements are randomized. The presence of the ballistic component formally extends the applicability of the FGR to the non-perturbative domain and restores the quantum-classical correspondence
Electrically tunable single-dot nanocavities in the weak and strong coupling regimes
DEFF Research Database (Denmark)
Laucht, Arne; Hofbauer, Felix; Angele, Jacob
2008-01-01
We report the design, fabrication and optical investigation of electrically tunable single quantum dot - photonic crystal defect nanocavities [1] operating in both the weak and strong coupling regimes of the light matter interaction. Unlike previous studies, where the dot-cavity spectral detuning...... of the emitted photons from a single-dot nanocavity in the weak and strong coupling regimes. New information is obtained on the nature of the dot-cavity coupling in the weak coupling regime and electrical control of zero dimensional polaritons is demonstrated for the first time. Vacuum Rabi splittings up to 2g...... electrical readout of the strongly coupled dot-cavity system using photocurrent methods will be discussed. This work is financially supported by the DFG via SFB 631 and by the German Excellence Initiative via the “Nanosystems Initiative Munich (NIM)”....
BGK-type models in strong reaction and kinetic chemical equilibrium regimes
International Nuclear Information System (INIS)
Monaco, R; Bianchi, M Pandolfi; Soares, A J
2005-01-01
A BGK-type procedure is applied to multi-component gases undergoing chemical reactions of bimolecular type. The relaxation process towards local Maxwellians, depending on mass and numerical densities of each species as well as common velocity and temperature, is investigated in two different cases with respect to chemical regimes. These cases are related to the strong reaction regime characterized by slow reactions, and to the kinetic chemical equilibrium regime where fast reactions take place. The consistency properties of both models are stated in detail. The trend to equilibrium is numerically tested and comparisons for the two regimes are performed within the hydrogen-air and carbon-oxygen reaction mechanism. In the spatial homogeneous case, it is also shown that the thermodynamical equilibrium of the models recovers satisfactorily the asymptotic equilibrium solutions to the reactive Euler equations
Photon and spin dependence of the resonance line shape in the strong coupling regime
Miyashita, Seiji; Shirai, Tatsuhiko; Mori, Takashi; De Raedt, Hans; Bertaina, Sylvain; Chiorescu, Irinel
2012-01-01
We study the quantum dynamics of a spin ensemble coupled to cavity photons. Recently, related experimental results have been reported, showing the existence of the strong coupling regime in such systems. We study the eigenenergy distribution of the multi-spin system (following the Tavis-Cummings
Dovzhenko, D S; Ryabchuk, S V; Rakovich, Yu P; Nabiev, I R
2018-02-22
Resonance interaction between a molecular transition and a confined electromagnetic field can reach the coupling regime where coherent exchange of energy between light and matter becomes reversible. In this case, two new hybrid states separated in energy are formed instead of independent eigenstates, which is known as Rabi splitting. This modification of the energy spectra of the system offers new possibilities for controlled impact on various fundamental properties of coupled matter (such as the rate of chemical reactions and the conductivity of organic semiconductors). To date, the strong coupling regime has been demonstrated in many configurations under different ambient conditions. However, there is still no comprehensive approach to determining parameters for achieving the strong coupling regime for a wide range of practical applications. In this review, a detailed analysis of various systems and corresponding conditions for reaching strong coupling is carried out and their advantages and disadvantages, as well as the prospects for application, are considered. The review also summarizes recent experiments in which the strong coupling regime has led to new interesting results, such as the possibility of collective strong coupling between X-rays and matter excitation in a periodic array of Fe isotopes, which extends the applications of quantum optics; a strong amplification of the Raman scattering signal from a coupled system, which can be used in surface-enhanced and tip-enhanced Raman spectroscopy; and more efficient second-harmonic generation from the low polaritonic state, which is promising for nonlinear optics. The results reviewed demonstrate great potential for further practical applications of strong coupling in the fields of photonics (low-threshold lasers), quantum communications (switches), and biophysics (molecular fingerprinting).
Study of the Higgs-Yukawa theory in the strong-Yukawa coupling regime
International Nuclear Information System (INIS)
Bulava, John; Gerhold, Philipp; Nagy, Attila; Deutsches Elektronen-Synchrotron; Hou, George W.S.; Smigielski, Brian; Jansen, Karl; Knippschild, Bastian; Univ. of Mainz; Lin, David C.J.; National Centre of Theoretical Sciences, Hsinchu; Nagai, Kei-Ichi; Ogawa, Kenji
2011-12-01
In this article, we present an ongoing lattice study of the Higgs-Yukawa model, in the regime of strong-Yukawa coupling, using overlap fermions. We investigated the phase structure in this regime by computing the Higgs vacuum expectation value, and by exploring the finite-size scaling behaviour of the susceptibility corresponding to the magnetisation. Our preliminary results indicate the existence of a second-order phase transition when the Yukawa coupling becomes large enough, at which the Higgs vacuum expectation value vanishes and the susceptibility diverges. (orig.)
Spontaneous dressed-state polarization in the strong driving regime of cavity QED.
Armen, Michael A; Miller, Anthony E; Mabuchi, Hideo
2009-10-23
We utilize high-bandwidth phase-quadrature homodyne measurement of the light transmitted through a Fabry-Perot cavity, driven strongly and on resonance, to detect excess phase noise induced by a single intracavity atom. We analyze the correlation properties and driving-strength dependence of the atom-induced phase noise to establish that it corresponds to the long-predicted phenomenon of spontaneous dressed-state polarization. Our experiment thus provides a demonstration of cavity quantum electrodynamics in the strong-driving regime in which one atom interacts strongly with a many-photon cavity field to produce novel quantum stochastic behavior.
de Oliveira, G. L.; Ramos, R. V.
2018-03-01
In this work, it is presented an optical scheme for quantum key distribution employing two synchronized optoelectronic oscillators (OEO) working in the chaotic regime. The produced key depends on the chaotic dynamic, and the synchronization between Alice's and Bob's OEOs uses quantum states. An attack on the synchronization signals will disturb the synchronization of the chaotic systems increasing the error rate in the final key.
Analog quantum simulation of the Rabi model in the ultra-strong coupling regime.
Braumüller, Jochen; Marthaler, Michael; Schneider, Andre; Stehli, Alexander; Rotzinger, Hannes; Weides, Martin; Ustinov, Alexey V
2017-10-03
The quantum Rabi model describes the fundamental mechanism of light-matter interaction. It consists of a two-level atom or qubit coupled to a quantized harmonic mode via a transversal interaction. In the weak coupling regime, it reduces to the well-known Jaynes-Cummings model by applying a rotating wave approximation. The rotating wave approximation breaks down in the ultra-strong coupling regime, where the effective coupling strength g is comparable to the energy ω of the bosonic mode, and remarkable features in the system dynamics are revealed. Here we demonstrate an analog quantum simulation of an effective quantum Rabi model in the ultra-strong coupling regime, achieving a relative coupling ratio of g/ω ~ 0.6. The quantum hardware of the simulator is a superconducting circuit embedded in a cQED setup. We observe fast and periodic quantum state collapses and revivals of the initial qubit state, being the most distinct signature of the synthesized model.An analog quantum simulation scheme has been explored with a quantum hardware based on a superconducting circuit. Here the authors investigate the time evolution of the quantum Rabi model at ultra-strong coupling conditions, which is synthesized by slowing down the system dynamics in an effective frame.
Nonlinear Brillouin amplification of finite-duration seeds in the strong coupling regime
International Nuclear Information System (INIS)
Lehmann, G.; Spatschek, K. H.
2013-01-01
Parametric plasma processes received renewed interest in the context of generating ultra-intense and ultra-short laser pulses up to the exawatt-zetawatt regime. Both Raman as well as Brillouin amplifications of seed pulses were proposed. Here, we investigate Brillouin processes in the one-dimensional (1D) backscattering geometry with the help of numerical simulations. For optimal seed amplification, Brillouin scattering is considered in the so called strong coupling (sc) regime. Special emphasis lies on the dependence of the amplification process on the finite duration of the initial seed pulses. First, the standard plane-wave instability predictions are generalized to pulse models, and the changes of initial seed pulse forms due to parametric instabilities are investigated. Three-wave-interaction results are compared to predictions by a new (kinetic) Vlasov code. The calculations are then extended to the nonlinear region with pump depletion. Generation of different seed layers is interpreted by self-similar solutions of the three-wave interaction model. Similar to Raman amplification, shadowing of the rear layers by the leading layers of the seed occurs. The shadowing is more pronounced for initially broad seed pulses. The effect is quantified for Brillouin amplification. Kinetic Vlasov simulations agree with the three-wave interaction predictions and thereby affirm the universal validity of self-similar layer formation during Brillouin seed amplification in the strong coupling regime
Semi-analytical fluid study of the laser wake field excitation in the strong intensity regime
Energy Technology Data Exchange (ETDEWEB)
Jovanović, D., E-mail: djovanov@ipb.ac.rs [Institute of Physics, University of Belgrade, Belgrade (Serbia); Fedele, R., E-mail: renato.fedele@na.infn.it [Dipartimento di Fisica, Universitá di Napoli Federico II, Napoli (Italy); INFN Sezione di Napoli, Napoli (Italy); Belić, M., E-mail: milivoj.belic@qatar.tamu.edu [Texas A & M University at Qatar, Doha (Qatar); De Nicola, S., E-mail: sergio.denicola@spin.cnr.it [Dipartimento di Fisica, Universitá di Napoli Federico II, Napoli (Italy); INFN Sezione di Napoli, Napoli (Italy); CNR-SPIN, Complesso Universitario di Monte S' Angelo, Napoli (Italy)
2016-09-01
We present an analytical and numerical study of the interaction of a multi-petawatt, pancake-shaped laser pulse with an unmagnetized plasma. The study has been performed in the ultrarelativistic regime of electron jitter velocities, in which the plasma electrons are almost completely expelled from the pulse region. The calculations are applied to a laser wake field acceleration scheme with specifications that may be available in the next generation of Ti:Sa lasers and with the use of recently developed pulse compression techniques. A set of novel nonlinear equations is derived using a three-timescale description, with an intermediate timescale associated with the nonlinear phase of the electromagnetic wave and with the spatial bending of its wave front. They describe, on an equal footing, both the strong and the moderate laser intensity regimes, pertinent to the core and to the edges of the pulse.
A theoretical model of strong and moderate El Niño regimes
Takahashi, Ken; Karamperidou, Christina; Dewitte, Boris
2018-02-01
The existence of two regimes for El Niño (EN) events, moderate and strong, has been previously shown in the GFDL CM2.1 climate model and also suggested in observations. The two regimes have been proposed to originate from the nonlinearity in the Bjerknes feedback, associated with a threshold in sea surface temperature (T_c ) that needs to be exceeded for deep atmospheric convection to occur in the eastern Pacific. However, although the recent 2015-16 EN event provides a new data point consistent with the sparse strong EN regime, it is not enough to statistically reject the null hypothesis of a unimodal distribution based on observations alone. Nevertheless, we consider the possibility suggestive enough to explore it with a simple theoretical model based on the nonlinear Bjerknes feedback. In this study, we implemented this nonlinear mechanism in the recharge-discharge (RD) ENSO model and show that it is sufficient to produce the two EN regimes, i.e. a bimodal distribution in peak surface temperature (T) during EN events. The only modification introduced to the original RD model is that the net damping is suppressed when T exceeds T_c , resulting in a weak nonlinearity in the system. Due to the damping, the model is globally stable and it requires stochastic forcing to maintain the variability. The sustained low-frequency component of the stochastic forcing plays a key role for the onset of strong EN events (i.e. for T>T_c ), at least as important as the precursor positive heat content anomaly (h). High-frequency forcing helps some EN events to exceed T_c , increasing the number of strong events, but the rectification effect is small and the overall number of EN events is little affected by this forcing. Using the Fokker-Planck equation, we show how the bimodal probability distribution of EN events arises from the nonlinear Bjerknes feedback and also propose that the increase in the net feedback with increasing T is a necessary condition for bimodality in the RD
Density-dependent electron scattering in photoexcited GaAs in strongly diffusive regime
DEFF Research Database (Denmark)
Mics, Zoltán; D’Angio, Andrea; Jensen, Søren A.
2013-01-01
In a series of systematic optical pump–terahertz probe experiments, we study the density-dependent electron scattering rate in photoexcited GaAs in the regime of strong carrier diffusion. The terahertz frequency-resolved transient sheet conductivity spectra are perfectly described by the Drude...... model, directly yielding the electron scattering rates. A diffusion model is applied to determine the spatial extent of the photoexcited electron-hole gas at each moment after photoexcitation, yielding the time-dependent electron density, and hence the density-dependent electron scattering time. We find...
Flouri, Eirini
2009-01-01
Chaotic home systems have been linked with children's adverse psychological and academic outcomes. But, as they represent a departure from the suburban ideal of space, order, and family cohesiveness and stability, they should also be linked with low support for survival values. Using longitudinal data from the 1970 British Cohort Study (BCS70)…
DEFF Research Database (Denmark)
Schäfer, Mirko; Greiner, Martin
2011-01-01
to chaotic strings. Inhomogeneous coupling weights as well as small-world perturbations of the ring-network structure are discussed. It is found that certain combinations of coupling and network disorder preserve the empirical relationship between chaotic strings and the weak and strong sector...
Engineering light emission of two-dimensional materials in both the weak and strong coupling regimes
Brotons-Gisbert, Mauro; Martínez-Pastor, Juan P.; Ballesteros, Guillem C.; Gerardot, Brian D.; Sánchez-Royo, Juan F.
2018-01-01
Two-dimensional (2D) materials have promising applications in optoelectronics, photonics, and quantum technologies. However, their intrinsically low light absorption limits their performance, and potential devices must be accurately engineered for optimal operation. Here, we apply a transfer matrix-based source-term method to optimize light absorption and emission in 2D materials and related devices in weak and strong coupling regimes. The implemented analytical model accurately accounts for experimental results reported for representative 2D materials such as graphene and MoS2. The model has been extended to propose structures to optimize light emission by exciton recombination in MoS2 single layers, light extraction from arbitrarily oriented dipole monolayers, and single-photon emission in 2D materials. Also, it has been successfully applied to retrieve exciton-cavity interaction parameters from MoS2 microcavity experiments. The present model appears as a powerful and versatile tool for the design of new optoelectronic devices based on 2D semiconductors such as quantum light sources and polariton lasers.
Lasing by driven atoms-cavity system in collective strong coupling regime.
Sawant, Rahul; Rangwala, S A
2017-09-12
The interaction of laser cooled atoms with resonant light is determined by the natural linewidth of the excited state. An optical cavity is another optically resonant system where the loss from the cavity determines the resonant optical response of the system. The near resonant combination of an optical Fabry-Pérot cavity with laser cooled and trapped atoms couples two distinct optical resonators via light and has great potential for precision measurements and the creation of versatile quantum optics systems. Here we show how driven magneto-optically trapped atoms in collective strong coupling regime with the cavity leads to lasing at a frequency red detuned from the atomic transition. Lasing is demonstrated experimentally by the observation of a lasing threshold accompanied by polarization and spatial mode purity, and line-narrowing in the outcoupled light. Spontaneous emission into the cavity mode by the driven atoms stimulates lasing action, which is capable of operating as a continuous wave laser in steady state, without a seed laser. The system is modeled theoretically, and qualitative agreement with experimentally observed lasing is seen. Our result opens up a range of new measurement possibilities with this system.
Reflection from the strong gravity regime in a lensed quasar at redshift z = 0.658.
Reis, R C; Reynolds, M T; Miller, J M; Walton, D J
2014-03-13
The co-evolution of a supermassive black hole with its host galaxy through cosmic time is encoded in its spin. At z > 2, supermassive black holes are thought to grow mostly by merger-driven accretion leading to high spin. It is not known, however, whether below z ≈ 1 these black holes continue to grow by coherent accretion or in a chaotic manner, though clear differences are predicted in their spin evolution. An established method of measuring the spin of black holes is through the study of relativistic reflection features from the inner accretion disk. Owing to their greater distances from Earth, there has hitherto been no significant detection of relativistic reflection features in a moderate-redshift quasar. Here we report an analysis of archival X-ray data together with a deep observation of a gravitationally lensed quasar at z = 0.658. The emission originates within three or fewer gravitational radii from the black hole, implying a spin parameter (a measure of how fast the black hole is rotating) of a = 0.87(+0.08)(-0.15) at the 3σ confidence level and a > 0.66 at the 5σ level. The high spin found here is indicative of growth by coherent accretion for this black hole, and suggests that black-hole growth at 0.5 ≤ z ≤ 1 occurs principally by coherent rather than chaotic accretion episodes.
Puebla, Ricardo; Casanova, Jorge; Plenio, Martin B.
2018-03-01
The dynamics of the quantum Rabi model (QRM) in the deep strong coupling regime is theoretically analyzed in a trapped-ion set-up. Recognizably, the main hallmark of this regime is the emergence of collapses and revivals, whose faithful observation is hindered under realistic magnetic dephasing noise. Here, we discuss how to attain a faithful implementation of the QRM in the deep strong coupling regime which is robust against magnetic field fluctuations and at the same time provides a large tunability of the simulated parameters. This is achieved by combining standing wave laser configuration with continuous dynamical decoupling. In addition, we study the role that amplitude fluctuations play to correctly attain the QRM using the proposed method. In this manner, the present work further supports the suitability of continuous dynamical decoupling techniques in trapped-ion settings to faithfully realize different interacting dynamics.
Optical Control of Mechanical Mode-Coupling within a MoS2 Resonator in the Strong-Coupling Regime.
Liu, Chang-Hua; Kim, In Soo; Lauhon, Lincoln J
2015-10-14
Two-dimensional (2-D) materials including graphene and transition metal dichalcogenides (TMDs) are an exciting platform for ultrasensitive force and displacement detection in which the strong light-matter coupling is exploited in the optical control of nanomechanical motion. Here we report the optical excitation and displacement detection of a ∼ 3 nm thick MoS2 resonator in the strong-coupling regime, which has not previously been achieved in 2-D materials. Mechanical mode frequencies can be tuned by more than 12% by optical heating, and they exhibit avoided crossings indicative of strong intermode coupling. When the membrane is optically excited at the frequency difference between vibrational modes, normal mode splitting is observed, and the intermode energy exchange rate exceeds the mode decay rate by a factor of 15. Finite element and analytical modeling quantifies the extent of mode softening necessary to control intermode energy exchange in the strong coupling regime.
LINKING TESTS OF GRAVITY ON ALL SCALES: FROM THE STRONG-FIELD REGIME TO COSMOLOGY
Energy Technology Data Exchange (ETDEWEB)
Baker, Tessa [Astrophysics, Denys Wilkinson Building, Keble Road, University of Oxford, Oxford, OX1 3RH (United Kingdom); Psaltis, Dimitrios [Astronomy Department, University of Arizona, 933 North Cherry Avenue., Tucson, AZ 85721 (United States); Skordis, Constantinos, E-mail: tessa.baker@astro.ox.ac.uk, E-mail: dpsaltis@email.arizona.edu, E-mail: skordis@ucy.ac.cy [School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD (United Kingdom)
2015-03-20
The current effort to test general relativity (GR) employs multiple disparate formalisms for different observables, obscuring the relations between laboratory, astrophysical, and cosmological constraints. To remedy this situation, we develop a parameter space for comparing tests of gravity on all scales in the universe. In particular, we present new methods for linking cosmological large-scale structure, the cosmic microwave background, and gravitational waves with classic PPN tests of gravity. Diagrams of this gravitational parameter space reveal a noticeable untested regime. The untested window, which separates small-scale systems from the troubled cosmological regime, could potentially hide the onset of corrections to GR.
Directory of Open Access Journals (Sweden)
William J Platt
Full Text Available Fire seasonality, an important characteristic of fire regimes, commonly is delineated using seasons based on single weather variables (rainfall or temperature. We used nonparametric cluster analyses of a 17-year (1993-2009 data set of weather variables that influence likelihoods and spread of fires (relative humidity, air temperature, solar radiation, wind speed, soil moisture to explore seasonality of fire in pine savanna-grassland landscapes at the Avon Park Air Force Range in southern Florida. A four-variable, three-season model explained more variation within fire weather variables than models with more seasons. The three-season model also delineated intra-annual timing of fire more accurately than a conventional rainfall-based two-season model. Two seasons coincided roughly with dry and wet seasons based on rainfall. The third season, which we labeled the fire season, occurred between dry and wet seasons and was characterized by fire-promoting conditions present annually: drought, intense solar radiation, low humidity, and warm air temperatures. Fine fuels consisting of variable combinations of pyrogenic pine needles, abundant C4 grasses, and flammable shrubs, coupled with low soil moisture, and lightning ignitions early in the fire season facilitate natural landscape-scale wildfires that burn uplands and across wetlands. We related our three season model to fires with different ignition sources (lightning, military missions, and prescribed fires over a 13-year period with fire records (1997-2009. Largest wildfires originate from lightning and military ignitions that occur within the early fire season substantially prior to the peak of lightning strikes in the wet season. Prescribed ignitions, in contrast, largely occur outside the fire season. Our delineation of a pronounced fire season provides insight into the extent to which different human-derived fire regimes mimic lightning fire regimes. Delineation of a fire season associated with
Platt, William J.; Orzell, Steve L.; Slocum, Matthew G.
2015-01-01
Fire seasonality, an important characteristic of fire regimes, commonly is delineated using seasons based on single weather variables (rainfall or temperature). We used nonparametric cluster analyses of a 17-year (1993–2009) data set of weather variables that influence likelihoods and spread of fires (relative humidity, air temperature, solar radiation, wind speed, soil moisture) to explore seasonality of fire in pine savanna-grassland landscapes at the Avon Park Air Force Range in southern Florida. A four-variable, three-season model explained more variation within fire weather variables than models with more seasons. The three-season model also delineated intra-annual timing of fire more accurately than a conventional rainfall-based two-season model. Two seasons coincided roughly with dry and wet seasons based on rainfall. The third season, which we labeled the fire season, occurred between dry and wet seasons and was characterized by fire-promoting conditions present annually: drought, intense solar radiation, low humidity, and warm air temperatures. Fine fuels consisting of variable combinations of pyrogenic pine needles, abundant C4 grasses, and flammable shrubs, coupled with low soil moisture, and lightning ignitions early in the fire season facilitate natural landscape-scale wildfires that burn uplands and across wetlands. We related our three season model to fires with different ignition sources (lightning, military missions, and prescribed fires) over a 13-year period with fire records (1997–2009). Largest wildfires originate from lightning and military ignitions that occur within the early fire season substantially prior to the peak of lightning strikes in the wet season. Prescribed ignitions, in contrast, largely occur outside the fire season. Our delineation of a pronounced fire season provides insight into the extent to which different human-derived fire regimes mimic lightning fire regimes. Delineation of a fire season associated with timing of
Storti, Mario A.; Nigro, Norberto M.; Paz, Rodrigo R.; Dalcín, Lisandro D.
2009-03-01
In this paper some results on the convergence of the Gauss-Seidel iteration when solving fluid/structure interaction problems with strong coupling via fixed point iteration are presented. The flow-induced vibration of a flat plate aligned with the flow direction at supersonic Mach number is studied. The precision of different predictor schemes and the influence of the partitioned strong coupling on stability is discussed.
Zhou, Ning; Yuan, Meng; Gao, Yuhan; Li, Dongsheng; Yang, Deren
2016-04-26
Strong coupling between semiconductor excitons and localized surface plasmons (LSPs) giving rise to hybridized plexciton states in which energy is coherently and reversibly exchanged between the components is vital, especially in the area of quantum information processing from fundamental and practical points of view. Here, in photoluminescence spectra, rather than from common extinction or reflection measurements, we report on the direct observation of Rabi splitting of approximately 160 meV as an indication of strong coupling between excited states of CdSe/ZnS quantum dots (QDs) and LSP modes of silver nanoshells under nonresonant nanosecond pulsed laser excitation at room temperature. The strong coupling manifests itself as an anticrossing-like behavior of the two newly formed polaritons when tuning the silver nanoshell plasmon energies across the exciton line of the QDs. Further analysis substantiates the essentiality of high pump energy and collective strong coupling of many QDs with the radiative dipole mode of the metallic nanoparticles for the realization of strong coupling. Our finding opens up interesting directions for the investigation of strong coupling between LSPs and excitons from the perspective of radiative recombination under easily accessible experimental conditions.
International Nuclear Information System (INIS)
Benisti, D.
2011-01-01
This manuscript provides a theoretical description, sometimes illustrated by experimental results, of several examples of field-matter interaction in various domains of physics, showing how the same basic concepts and theoretical methods may be used in very different physics situations. The issues addressed here are nonlinear field-matter interaction in plasma physics within the framework of classical mechanics (with a particular emphasis on wave-particle interaction), the linear analysis of beam-plasma instabilities in the relativistic regime, and the quantum description of laser-atom interaction, including quantum electrodynamics. Novel methods are systematically introduced in order to solve some very old problems, like the nonlinear counterpart of the Landau damping rate in plasma physics, for example. Moreover, our results directly apply to inertial confinement fusion, laser propagation in an atomic vapor, ion acceleration in a magnetized plasma and the physics of the Reversed Field Pinch for magnetic fusion. (author)
Energy deposition of heavy ions in the regime of strong beam-plasma correlations.
Gericke, D O; Schlanges, M
2003-03-01
The energy loss of highly charged ions in dense plasmas is investigated. The applied model includes strong beam-plasma correlation via a quantum T-matrix treatment of the cross sections. Dynamic screening effects are modeled by using a Debye-like potential with a velocity dependent screening length that guarantees the known low and high beam velocity limits. It is shown that this phenomenological model is in good agreement with simulation data up to very high beam-plasma coupling. An analysis of the stopping process shows considerably longer ranges and a less localized energy deposition if strong coupling is treated properly.
Metallization of a Rashba wire by a superconducting layer in the strong-proximity regime
Reeg, Christopher; Loss, Daniel; Klinovaja, Jelena
2018-04-01
Semiconducting quantum wires defined within two-dimensional electron gases and strongly coupled to thin superconducting layers have been extensively explored in recent experiments as promising platforms to host Majorana bound states. We study numerically such a geometry, consisting of a quasi-one-dimensional wire coupled to a disordered three-dimensional superconducting layer. We find that, in the strong-coupling limit of a sizable proximity-induced superconducting gap, all transverse subbands of the wire are significantly shifted in energy relative to the chemical potential of the wire. For the lowest subband, this band shift is comparable in magnitude to the spacing between quantized levels that arises due to the finite thickness of the superconductor (which typically is ˜500 meV for a 10-nm-thick layer of aluminum); in higher subbands, the band shift is much larger. Additionally, we show that the width of the system, which is usually much larger than the thickness, and moderate disorder within the superconductor have almost no impact on the induced gap or band shift. We provide a detailed discussion of the ramifications of our results, arguing that a huge band shift and significant renormalization of semiconducting material parameters in the strong-coupling limit make it challenging to realize a topological phase in such a setup, as the strong coupling to the superconductor essentially metallizes the semiconductor. This metallization of the semiconductor can be tested experimentally through the measurement of the band shift.
What occurs in the fragile-to-strong liquid transition regime?
DEFF Research Database (Denmark)
Yue, Yuanzheng; Hu, L.N.
The slow dynamics of glass-forming liquids is a complex subject of the condensed matter science. But the fragile-to-strong transition, which was observed not long ago [Ito, et al, Nature 1999], makes this subject even more complex since it is extremely challenging to directly probe the structural...
Photoinduced Electron Transfer in the Strong Coupling Regime: Waveguide-Plasmon Polaritons.
Zeng, Peng; Cadusch, Jasper; Chakraborty, Debadi; Smith, Trevor A; Roberts, Ann; Sader, John E; Davis, Timothy J; Gómez, Daniel E
2016-04-13
Reversible exchange of photons between a material and an optical cavity can lead to the formation of hybrid light-matter states where material properties such as the work function [ Hutchison et al. Adv. Mater. 2013 , 25 , 2481 - 2485 ], chemical reactivity [ Hutchison et al. Angew. Chem., Int. Ed. 2012 , 51 , 1592 - 1596 ], ultrafast energy relaxation [ Salomon et al. Angew. Chem., Int. Ed. 2009 , 48 , 8748 - 8751 ; Gomez et al. J. Phys. Chem. B 2013 , 117 , 4340 - 4346 ], and electrical conductivity [ Orgiu et al. Nat. Mater. 2015 , 14 , 1123 - 1129 ] of matter differ significantly to those of the same material in the absence of strong interactions with the electromagnetic fields. Here we show that strong light-matter coupling between confined photons on a semiconductor waveguide and localized plasmon resonances on metal nanowires modifies the efficiency of the photoinduced charge-transfer rate of plasmonic derived (hot) electrons into accepting states in the semiconductor material. Ultrafast spectroscopy measurements reveal a strong correlation between the amplitude of the transient signals, attributed to electrons residing in the semiconductor and the hybridization of waveguide and plasmon excitations.
Zhang, Yu-Yu; Chen, Xiang-You
2017-12-01
An unexplored nonperturbative deep strong coupling (npDSC) achieved in superconducting circuits has been studied in the anisotropic Rabi model by the generalized squeezing rotating-wave approximation. Energy levels are evaluated analytically from the reformulated Hamiltonian and agree well with numerical ones in a wide range of coupling strength. Such improvement ascribes to deformation effects in the displaced-squeezed state presented by the squeezed momentum variance, which are omitted in previous displaced states. The atom population dynamics confirms the validity of our approach for the npDSC strength. Our approach offers the possibility to explore interesting phenomena analytically in the npDSC regime in qubit-oscillator experiments.
International Nuclear Information System (INIS)
Casner, A.; Masse, L.; Liberatore, S.; Delorme, B.; Jacquet, L.; Loiseau, P.; Smalyuk, V. A.; Martinez, D.; Remington, B. A.
2012-01-01
As the control of the development of Rayleigh-Taylor-type hydrodynamic instabilities is crucial to achieve efficient implosions on the Laser Megajoule, and as the complexity of these instabilities requires an experimental validation of theoretical models and of the associated numerical simulations, the authors briefly present a proposition of experiments aimed at studying the strongly non linear Rayleigh-Taylor instability on the National Ignition Facility (NIF). This should allow a regime of competition between bubbles to be achieved for the first time in direct attack. They evoke the first experiment performed in March 2013
Strong-pinning regimes by spherical inclusions in anisotropic type-II superconductors
Energy Technology Data Exchange (ETDEWEB)
Willa, R.; Koshelev, A. E.; Sadovskyy, I. A.; Glatz, A.
2017-11-27
The current-carrying capacity of type-II superconductors is decisively determined by how well material defect structures can immobilize vortex lines. In order to gain deeper insights into intrinsic pinning mechanisms, we have explored the case of vortex trapping by randomly distributed spherical inclusions using large-scale simulations of the time-dependent Ginzburg-Landau equations. We find that for a small density of particles having diameters of two coherence lengths, the vortex lattice preserves its structure and the critical current jc decays with the magnetic field following a power-law B-a with a ~ 0:66, which is consistent with predictions of strong pinning theory. For higher density of particles and/or larger inclusions, the lattice becomes progressively more disordered and the exponent smoothly decreases down to a ~ 0:3. At high magnetic fields, all inclusions capture a vortex and the critical current decays faster than B-1 as would be expected by theory. In the case of larger inclusions with diameter of four coherence length, the magnetic-field dependence of the critical current is strongly affected by the ability of inclusions to capture multiple vortex lines. We found that at small densities, the fraction of inclusions trapping two vortex lines rapidly grows within narrow field range leading to a shallow peak in jc(B)-dependence within this range. With increasing inclusion density, this peak transforms into a plateau, which then smooths out. Using the insights gained from simulations, we determine the limits of applicability of strong pinning theory and provide different routes to describe vortex pinning beyond those bounds.
Strasberg, Philipp; Schaller, Gernot; Schmidt, Thomas L.; Esposito, Massimiliano
2018-05-01
We establish a theoretical method which goes beyond the weak-coupling and Markovian approximations while remaining intuitive, using a quantum master equation in a larger Hilbert space. The method is applicable to all impurity Hamiltonians tunnel coupled to one (or multiple) baths of free fermions. The accuracy of the method is in principle not limited by the system-bath coupling strength, but rather by the shape of the spectral density and it is especially suited to study situations far away from the wide-band limit. In analogy to the bosonic case, we call it the fermionic reaction coordinate mapping. As an application, we consider a thermoelectric device made of two Coulomb-coupled quantum dots. We pay particular attention to the regime where this device operates as an autonomous Maxwell demon shoveling electrons against the voltage bias thanks to information. Contrary to previous studies, we do not rely on a Markovian weak-coupling description. Our numerical findings reveal that in the regime of strong coupling and non-Markovianity, the Maxwell demon is often doomed to disappear except in a narrow parameter regime of small power output.
Indications of a ΔI=1/2 rule in the strong coupling regime
International Nuclear Information System (INIS)
Angus, I.G.
1988-01-01
The authors attempt to understand the ΔI = 1/2 pattern of the nonleptonic weak decays of the kaons. The calculation scheme employed is the Strong Coupling Expansion of lattice QCD. Kogut-Susskind fermions are used in the Hamiltonian formalism. They describe in detail the methods used to expedite this calculation, all of which was done by computer algebra. The final result is very encouraging. Even though an exact interpretation is clouded by the presence of irrelevant operators, and questions of lattice artifacts, a signal of the /d//I = 1/2 rule appears to be observable. With an appropriate choice of the one free parameter, enhancements greater than those observed experimentally can be obtained. The authors point out a number of surprising results which turn up in the course of the calculation
International Nuclear Information System (INIS)
Rimberg, A J; Blencowe, M P; Armour, A D; Nation, P D
2014-01-01
We propose a scheme involving a Cooper pair transistor (CPT) embedded in a superconducting microwave cavity, where the CPT serves as a charge tunable quantum inductor to facilitate ultra-strong coupling between photons in the cavity and a nano- to meso-scale mechanical resonator. The mechanical resonator is capacitively coupled to the CPT, such that mechanical displacements of the resonator cause a shift in the CPT inductance and hence the cavity's resonant frequency. The amplification provided by the CPT is sufficient for the zero point motion of the mechanical resonator alone to cause a significant change in the cavity resonance. Conversely, a single photon in the cavity causes a shift in the mechanical resonator position on the order of its zero point motion. As a result, the cavity-Cooper pair transistor coupled to a mechanical resonator will be able to access a regime in which single photons can affect single phonons and vice versa. Realizing this ultra-strong coupling regime will facilitate the creation of non-classical states of the mechanical resonator, as well as the means to accurately characterize such states by measuring the cavity photon field. (paper)
International Nuclear Information System (INIS)
Doron, E.; Smilanski, U.
1991-11-01
We discuss the spectra of quantized chaotic billiards from the point of view of scattering theory. We show that the spectral and resonance density functions both fluctuate about a common mean. A semiclassical treatment explains this in terms of classical scattering trajectories and periodic orbits of the poincare scattering map. This formalism is used to interpret recent experiments where the spectra of chaotic cavities where measured by microwave scattering. (author)
Second sound in a two-dimensional Bose gas: From the weakly to the strongly interacting regime
Ota, Miki; Stringari, Sandro
2018-03-01
Using Landau's theory of two-fluid hydrodynamics, we investigate first and second sounds propagating in a two-dimensional (2D) Bose gas. We study the temperature and interaction dependence of both sound modes and show that their behavior exhibits a deep qualitative change as the gas evolves from the weakly interacting to the strongly interacting regime. Special emphasis is placed on the jump of both sounds at the Berezinskii-Kosterlitz-Thouless transition, caused by the discontinuity of the superfluid density. We find that the excitation of second sound through a density perturbation becomes weaker and weaker as the interaction strength increases as a consequence of the decrease in the thermal expansion coefficient. Our results could be relevant for future experiments on the propagation of sound on the Bose-Einstein condensate (BEC) side of the BCS-BEC crossover of a 2D superfluid Fermi gas.
Hargart, F.; Roy-Choudhury, K.; John, T.; Portalupi, S. L.; Schneider, C.; Höfling, S.; Kamp, M.; Hughes, S.; Michler, P.
2016-12-01
In this work we present an extensive experimental and theoretical investigation of different regimes of strong field light-matter interaction for cavity-driven quantum dot (QD) cavity systems. The electric field enhancement inside a high-Q micropillar cavity facilitates exceptionally strong interaction with few cavity photons, enabling the simultaneous investigation for a wide range of QD-laser detuning. In case of a resonant drive, the formation of dressed states and a Mollow triplet sideband splitting of up to 45 μeV is measured for a mean cavity photon number ≤slant 1. In the asymptotic limit of the linear AC Stark effect we systematically investigate the power and detuning dependence of more than 400 QDs. Some QD-cavity systems exhibit an unexpected anomalous Stark shift, which can be explained by an extended dressed 4-level QD model. We provide a detailed analysis of the QD-cavity systems properties enabling this novel effect. The experimental results are successfully reproduced using a polaron master equation approach for the QD-cavity system, which includes the driving laser field, exciton-cavity and exciton-phonon interactions.
Bildirici, Melike; Sonustun, Fulya Ozaksoy; Sonustun, Bahri
2018-01-01
In the regards of chaos theory, new concepts such as complexity, determinism, quantum mechanics, relativity, multiple equilibrium, complexity, (continuously) instability, nonlinearity, heterogeneous agents, irregularity were widely questioned in economics. It is noticed that linear models are insufficient for analyzing unpredictable, irregular and noncyclical oscillations of economies, and for predicting bubbles, financial crisis, business cycles in financial markets. Therefore, economists gave great consequence to use appropriate tools for modelling non-linear dynamical structures and chaotic behaviors of the economies especially in macro and the financial economy. In this paper, we aim to model the chaotic structure of exchange rates (USD-TL and EUR-TL). To determine non-linear patterns of the selected time series, daily returns of the exchange rates were tested by BDS during the period from January 01, 2002 to May 11, 2017 which covers after the era of the 2001 financial crisis. After specifying the non-linear structure of the selected time series, it was aimed to examine the chaotic characteristic for the selected time period by Lyapunov Exponents. The findings verify the existence of the chaotic structure of the exchange rate returns in the analyzed time period.
Li, Xiaokai; Wang, Chuncheng; Yuan, Zongqiang; Ye, Difa; Ma, Pan; Hu, Wenhui; Luo, Sizuo; Fu, Libin; Ding, Dajun
2017-09-01
By combining kinematically complete measurements and a semiclassical Monte Carlo simulation we study the correlated-electron dynamics in the strong-field double ionization of Kr. Interestingly, we find that, as we step into the sequential-ionization regime, there are still signatures of correlation in the two-electron joint momentum spectrum and, more intriguingly, the scaling law of the high-energy tail is completely different from early predictions on the low-Z atom (He). These experimental observations are well reproduced by our generalized semiclassical model adapting a Green-Sellin-Zachor potential. It is revealed that the competition between the screening effect of inner-shell electrons and the Coulomb focusing of nuclei leads to a non-inverse-square central force, which twists the returned electron trajectory at the vicinity of the parent core and thus significantly increases the probability of hard recollisions between two electrons. Our results might have promising applications ranging from accurately retrieving atomic structures to simulating celestial phenomena in the laboratory.
Gangolf, Thomas; Blecher, Marius; Bolanos, Simon; Lancia, Livia; Marques, Jean-Raphael; Cerchez, Mirela; Prasad, Rajendra; Aurand, Bastian; Loiseau, Pascal; Fuchs, Julien; Willi, Oswald
2017-10-01
In the ongoing quest for novel techniques to obtain ever higher laser powers, plasma amplification has drawn much attention, benefiting from the fact that a plasma can sustain much higher energy densities than a solid state amplifier. As a plasma process, Stimulated Brillouin Backscattering in the strong coupling regime (sc-SBS) can be used to transfer energy from one laser pulse (pump) to another (seed), by a nonlinear ion oscillation forced by the pump laser. Here, we report on experimental results on amplification by sc-SBS using the ARCTURUS Ti:Sapphire multi-beam laser system at the University of Duesseldorf, Germany. Counter-propagating in a supersonic Hydrogen gas jet target, an ultrashort seed pulse with a pulse duration between 30 and 160 fs and an energy between 1 and 12 mJ was amplified by a high-energy pump pulse (1.7 ps, 700 mJ). For some of the measurements, the gas was pre-ionized with a separate laser pulse (780 fs, 460 mJ). Preliminary analysis shows that the amplification was larger for the longer seed pulses, consistent with theoretical predictions.
Maurer, J.; Willenberg, B.; Daněk, J.; Mayer, B. W.; Phillips, C. R.; Gallmann, L.; Klaiber, M.; Hatsagortsyan, K. Z.; Keitel, C. H.; Keller, U.
2018-01-01
We explore ionization and rescattering in strong mid-infrared laser fields in the nondipole regime over the full range of polarization ellipticity. In three-dimensional photoelectron momentum distributions (3D PMDs) measured with velocity map imaging spectroscopy, we observe the appearance of a sharp ridge structure along the major polarization axis. Within a certain range of ellipticity, the electrons in this ridge are clearly separated from the two lobes that commonly appear in the PMD with elliptically polarized laser fields. In contrast to the well-known lobes of direct electrons, the sharp ridge is created by Coulomb focusing of the softly recolliding electrons. These ridge electrons are directly related to a counterintuitive shift of the PMD peak opposite to the laser beam propagation direction when the dipole approximation breaks down. The ellipticity-dependent 3D PMDs give access to different ionization and recollision dynamics with appropriate filters in the momentum space. For example, we can extract information about the spread of the initial wave packet and the Coulomb momentum transfer of the rescattering electrons.
Eigenfunctions in chaotic quantum systems
Energy Technology Data Exchange (ETDEWEB)
Baecker, Arnd
2007-07-01
The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted. (orig.)
Eigenfunctions in chaotic quantum systems
International Nuclear Information System (INIS)
Baecker, Arnd
2007-01-01
The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted. (orig.)
Kumar, Santosh; Dietz, Barbara; Guhr, Thomas; Richter, Achim
2017-12-15
The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal cross sections in the Heidelberg approach, which is applicable to a wide range of quantum chaotic systems. Thus, eventually, we fully solve a problem that already arose more than half a century ago in compound-nucleus scattering. We compare our results with data from microwave and compound-nucleus experiments, particularly addressing the transition from isolated resonances towards the Ericson regime of strongly overlapping ones.
Weck, Philippe F.; Cochrane, Kyle R.; Root, Seth; Lane, J. Matthew D.; Shulenburger, Luke; Carpenter, John H.; Sjostrom, Travis; Mattsson, Thomas R.; Vogler, Tracy J.
2018-03-01
The shock Hugoniot for full-density and porous CeO2 was investigated in the liquid regime using ab initio molecular dynamics (AIMD) simulations with Erpenbeck's approach based on the Rankine-Hugoniot jump conditions. The phase space was sampled by carrying out NVT simulations for isotherms between 6000 and 100 000 K and densities ranging from ρ =2.5 to 20 g /cm3 . The impact of on-site Coulomb interaction corrections +U on the equation of state (EOS) obtained from AIMD simulations was assessed by direct comparison with results from standard density functional theory simulations. Classical molecular dynamics (CMD) simulations were also performed to model atomic-scale shock compression of larger porous CeO2 models. Results from AIMD and CMD compression simulations compare favorably with Z-machine shock data to 525 GPa and gas-gun data to 109 GPa for porous CeO2 samples. Using results from AIMD simulations, an accurate liquid-regime Mie-Grüneisen EOS was built for CeO2. In addition, a revised multiphase SESAME-type EOS was constrained using AIMD results and experimental data generated in this work. This study demonstrates the necessity of acquiring data in the porous regime to increase the reliability of existing analytical EOS models.
Chaotic scattering of two identical point vortex pairs revisited
DEFF Research Database (Denmark)
Tophøj, Laust Emil Hjerrild; Aref, Hassan
2008-01-01
A new numerical exploration suggests that the motion of two vortex pairs, with constituent vortices all of the same absolute circulation, displays chaotic scattering regimes. The mechanisms leading to chaotic scattering are different from the “slingshot effect” identified by Price [Phys. Fluids A...
International Nuclear Information System (INIS)
Wei Jun; Liao Xiaofeng; Wong, Kwok-wo; Xiang Tao
2006-01-01
Based on the study of some previously proposed chaotic encryption algorithms, we found that it is dangerous to mix chaotic state or iteration number of the chaotic system with ciphertext. In this paper, a new chaotic cryptosystem is proposed. Instead of simply mixing the chaotic signal of the proposed chaotic cryptosystem with the ciphertext, a noise-like variable is utilized to govern the encryption and decryption processes. This adds statistical sense to the new cryptosystem. Numerical simulations show that the new cryptosystem is practical whenever efficiency, ciphertext length or security is concerned
Bidirectional communication using delay coupled chaotic directly ...
Indian Academy of Sciences (India)
Corresponding author. ... 30 September 2009. Abstract. Chaotic synchronization of two directly modulated semiconductor lasers with ... For InGaAsP lasers used in optical communication systems, the nonlinear gain re- duction is very strong and its ...
Yanagisawa, Hirofumi; Schnepp, Sascha; Hafner, Christian; Hengsberger, Matthias; Kim, Dong Eon; Kling, Matthias F.; Landsman, Alexandra; Gallmann, Lukas; Osterwalder, Jürg
2016-01-01
Illuminating a nano-sized metallic tip with ultrashort laser pulses leads to the emission of electrons due to multiphoton excitations. As optical fields become stronger, tunnelling emission directly from the Fermi level becomes prevalent. This can generate coherent electron waves in vacuum leading to a variety of attosecond phenomena. Working at high emission currents where multi-electron effects are significant, we were able to characterize the transition from one regime to the other. Specifically, we found that the onset of laser-driven tunnelling emission is heralded by the appearance of a peculiar delayed emission channel. In this channel, the electrons emitted via laser-driven tunnelling emission are driven back into the metal, and some of the electrons reappear in the vacuum with some delay time after undergoing inelastic scattering and cascading processes inside the metal. Our understanding of these processes gives insights on attosecond tunnelling emission from solids and should prove useful in designing new types of pulsed electron sources. PMID:27786287
Zhang, Yu-Yu; Chen, Xiang-You
2017-01-01
A novel, unexplored nonperturbative deep-strong coupling (npDSC) achieved in superconducting circuits has been studied in the anisotropic Rabi model by the generalized squeezing rotating-wave approximation (GSRWA). Energy levels are evaluated analytically from the reformulated Hamiltonian and agree well with numerical ones under a wide range of coupling strength. Such improvement ascribes to deformation effects in the displaced-squeezed state presented by the squeezed momentum variance, which...
Inversion of Qubit Energy Levels in Qubit-Oscillator Circuits in the Deep-Strong-Coupling Regime
Yoshihara, F.; Fuse, T.; Ao, Z.; Ashhab, S.; Kakuyanagi, K.; Saito, S.; Aoki, T.; Koshino, K.; Semba, K.
2018-05-01
We report on experimentally measured light shifts of superconducting flux qubits deep-strongly coupled to L C oscillators, where the coupling constants are comparable to the qubit and oscillator resonance frequencies. By using two-tone spectroscopy, the energies of the six lowest levels of each circuit are determined. We find huge Lamb shifts that exceed 90% of the bare qubit frequencies and inversions of the qubits' ground and excited states when there are a finite number of photons in the oscillator. Our experimental results agree with theoretical predictions based on the quantum Rabi model.
International Nuclear Information System (INIS)
Saiki, Yoshitaka; Yamada, Michio; Chian, Abraham C.-L.; Miranda, Rodrigo A.; Rempel, Erico L.
2015-01-01
The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originate from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs
Energy Technology Data Exchange (ETDEWEB)
Saiki, Yoshitaka, E-mail: yoshi.saiki@r.hit-u.ac.jp [Graduate School of Commerce and Management, Hitotsubashi University, Tokyo 186-8601 (Japan); Yamada, Michio [Research Institute for Mathematical Sciences (RIMS), Kyoto University, Kyoto 606-8502 (Japan); Chian, Abraham C.-L. [Paris Observatory, LESIA, CNRS, 92195 Meudon (France); National Institute for Space Research (INPE), P.O. Box 515, São José dos Campos, São Paulo 12227-010 (Brazil); Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), São José dos Campos, São Paulo 12228-900 (Brazil); School of Mathematical Sciences, University of Adelaide, Adelaide SA 5005 (Australia); Department of Biomedical Engineering, George Washington University, Washington, DC 20052 (United States); Miranda, Rodrigo A. [Faculty UnB-Gama, and Plasma Physics Laboratory, Institute of Physics, University of Brasília (UnB), Brasília DF 70910-900 (Brazil); Rempel, Erico L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), São José dos Campos, São Paulo 12228-900 (Brazil)
2015-10-15
The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originate from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs.
International Nuclear Information System (INIS)
Cook, A.
1990-09-01
An elementary account of the origin of chaotic behaviour in classical dynamics is given with examples from geophysics, and in conclusion some thoughts about what can be predicted of chaotic behaviour and what sorts of arguments can be used to guide human behaviour in chaotic conditions are presented. 4 refs
International Nuclear Information System (INIS)
Lanty, Gaetan
2011-01-01
The research work which is reported in this manuscript focuses on 2D perovskites and their use to obtain micro-cavities working in the strong coupling regime. Perovskite structure forms a multi-quantum wells in which the excitonic states have a high oscillator strength and a large binding energy (a few 100 MeV) due to quantum and dielectric confinement effects. A first axis of this work was to collect information on the excitonic properties of these materials. On a particular perovskite (PEPI), we performed photoluminescence and pump-probe measurements, which seem to suggest the existence, under high excitation density, a process of Auger recombination of excitons. A second research axis was to put in cavity thin layers of some perovskites. With PEPI and PEPC perovskites, we have shown that the realization of micro-cavities with a quality factor of the order of ten is sufficient to obtain at room temperature, the strong coupling regime in absorption and emission with Rabi splitting up to 220 MeV. A bottleneck effect has been clearly demonstrated for the PEPI microcavity. We have also shown that perovskites could be associated with inorganic semiconductors in 'hybrid' micro-cavities. According Agranovich et al., these micro-cavities could present polariton lasing with lower quality factors. To this end, the ZnO/MFMPB association seems particularly promising. (author)
Hash function based on piecewise nonlinear chaotic map
International Nuclear Information System (INIS)
Akhavan, A.; Samsudin, A.; Akhshani, A.
2009-01-01
Chaos-based cryptography appeared recently in the early 1990s as an original application of nonlinear dynamics in the chaotic regime. In this paper, an algorithm for one-way hash function construction based on piecewise nonlinear chaotic map with a variant probability parameter is proposed. Also the proposed algorithm is an attempt to present a new chaotic hash function based on multithreaded programming. In this chaotic scheme, the message is connected to the chaotic map using probability parameter and other parameters of chaotic map such as control parameter and initial condition, so that the generated hash value is highly sensitive to the message. Simulation results indicate that the proposed algorithm presented several interesting features, such as high flexibility, good statistical properties, high key sensitivity and message sensitivity. These properties make the scheme a suitable choice for practical applications.
Salvesen, Greg; Simon, Jacob B.; Armitage, Philip J.; Begelman, Mitchell C.
2016-03-01
Strongly magnetized accretion discs around black holes have attractive features that may explain enigmatic aspects of X-ray binary behaviour. The structure and evolution of these discs are governed by a dynamo-like mechanism, which channels part of the accretion power liberated by the magnetorotational instability (MRI) into an ordered toroidal magnetic field. To study dynamo activity, we performed three-dimensional, stratified, isothermal, ideal magnetohydrodynamic shearing box simulations. The strength of the self-sustained toroidal magnetic field depends on the net vertical magnetic flux, which we vary across almost the entire range over which the MRI is linearly unstable. We quantify disc structure and dynamo properties as a function of the initial ratio of mid-plane gas pressure to vertical magnetic field pressure, β _0^mid = p_gas / p_B. For 10^5 ≥ β _0^mid ≥ 10 the effective α-viscosity parameter scales as a power law. Dynamo activity persists up to and including β _0^mid = 10^2, at which point the entire vertical column of the disc is magnetic pressure dominated. Still stronger fields result in a highly inhomogeneous disc structure, with large density fluctuations. We show that the turbulent steady state βmid in our simulations is well matched by the analytic model of Begelman et al. describing the creation and buoyant escape of toroidal field, while the vertical structure of the disc can be broadly reproduced using this model. Finally, we discuss the implications of our results for observed properties of X-ray binaries.
Directory of Open Access Journals (Sweden)
A. W. Wernik
1996-01-01
Full Text Available Four data sets of density fluctuations measured in-situ by the Dynamics Explorer (DE 2 were analyzed in an attempt to study chaotic nature of the high-latitude turbulence and, in this way to complement the conventional spectral analysis. It has been found that the probability distribution function of density differences is far from Gaussian and similar to that observed in the intermittent fluid or MBD turbulence. This indicates that ionospheric density fluctuations are not stochastic but coherent to some extent. Wayland's and surrogate data tests for determinism in a time series of density data allowed us to differentiate between regions of intense shear and moderate shear. We observe that in the region of strong field aligned currents (FAC and intense shear, or along the convection in the collisional regime, ionospheric turbulence behaves like a random noise with non-Gaussian statistics implying that the underlying physical process is nondeterministic. On the other hand, when FACs are weak, and shear is moderate or observations made in the inertial regime the turbulence is chaotic. The attractor dimension is lowest (1.9 for 'old' convected irregularities. The dimension 3.2 is found for turbulence in the inertial regime and considerably smaller (2.4 in the collisional regime. It is suggested that a high dimension in the inertial regime may be caused by a complicated velocity structure in the shear instability region.
Design of chaotic analog noise generators with logistic map and MOS QT circuits
International Nuclear Information System (INIS)
Vazquez-Medina, R.; Diaz-Mendez, A.; Rio-Correa, J.L. del; Lopez-Hernandez, J.
2009-01-01
In this paper a method to design chaotic analog noise generators using MOS transistors is presented. Two aspects are considered, the determination of operation regime of the MOS circuit and the statistical distribution of its output signal. The operation regime is related with the transconductance linear (TL: translinear) principle. For MOS transistors this principle was originally formulated in weak inversion regime; but, strong inversion regimen is used because in 1991, Seevinck and Wiegerink made the generalization for this principle. The statistical distribution of the output signal on the circuit, which should be a uniform distribution, is related with the parameter value that rules the transfer function of the circuit, the initial condition (seed) in the circuit and its operation as chaotic generator. To show these concepts, the MOS Quadratic Translinear circuit proposed by Wiegerink in 1993 was selected and it is related with the logistic map and its properties. This circuit will operate as noise generator if it works in strong inversion regime using current-mode approach when the parameter that rules the transfer function is higher than the onset chaos value (3.5699456...) for the logistic map.
Chaotic bubbling and nonstagnant foams.
Tufaile, Alberto; Sartorelli, José Carlos; Jeandet, Philippe; Liger-Belair, Gerard
2007-06-01
We present an experimental investigation of the agglomeration of bubbles obtained from a nozzle working in different bubbling regimes. This experiment consists of a continuous production of bubbles from a nozzle at the bottom of a liquid column, and these bubbles create a two-dimensional (2D) foam (or a bubble raft) at the top of this column. The bubbles can assemble in various dynamically stable arrangement, forming different kinds of foams in a liquid mixture of water and glycerol, with the effect that the bubble formation regimes influence the foam obtained from this agglomeration of bubbles. The average number of bubbles in the foam is related to the bubble formation frequency and the bubble mean lifetime. The periodic bubbling can generate regular or irregular foam, while a chaotic bubbling only generates irregular foam.
Stages of chaotic synchronization.
Tang, D. Y.; Dykstra, R.; Hamilton, M. W.; Heckenberg, N. R.
1998-09-01
In an experimental investigation of the response of a chaotic system to a chaotic driving force, we have observed synchronization of chaos of the response system in the forms of generalized synchronization, phase synchronization, and lag synchronization to the driving signal. In this paper we compare the features of these forms of synchronized chaos and study their relations and physical origins. We found that different forms of chaotic synchronization could be interpreted as different stages of nonlinear interaction between the coupled chaotic systems. (c) 1998 American Institute of Physics.
Chaos desynchronization in strongly coupled systems
International Nuclear Information System (INIS)
Wu Ye; Liu Weiqing; Xiao, Jinghua; Zhan Meng
2007-01-01
The dynamics of chaos desynchronization in strongly coupled oscillator systems is studied. We find a new bifurcation from synchronous chaotic state, chaotic short wave bifurcation, i.e. a chaotic desynchronization attractor is new born in the systems due to chaos desynchronization. In comparison with the usual periodic short wave bifurcation, very rich but distinct phenomena are observed
Chaotic interactions of self-replicating RNA.
Forst, C V
1996-03-01
A general system of high-order differential equations describing complex dynamics of replicating biomolecules is given. Symmetry relations and coordinate transformations of general replication systems leading to topologically equivalent systems are derived. Three chaotic attractors observed in Lotka-Volterra equations of dimension n = 3 are shown to represent three cross-sections of one and the same chaotic regime. Also a fractal torus in a generalized three-dimensional Lotka-Volterra Model has been linked to one of the chaotic attractors. The strange attractors are studied in the equivalent four-dimensional catalytic replicator network. The fractal torus has been examined in adapted Lotka-Volterra equations. Analytic expressions are derived for the Lyapunov exponents of the flow in the replicator system. Lyapunov spectra for different pathways into chaos has been calculated. In the generalized Lotka-Volterra system a second inner rest point--coexisting with (quasi)-periodic orbits--can be observed; with an abundance of different bifurcations. Pathways from chaotic tori, via quasi-periodic tori, via limit cycles, via multi-periodic orbits--emerging out of periodic doubling bifurcations--to "simple" chaotic attractors can be found.
Tunable power law in the desynchronization events of coupled chaotic electronic circuits
International Nuclear Information System (INIS)
Oliveira, Gilson F. de; Lorenzo, Orlando di; Chevrollier, Martine; Passerat de Silans, Thierry; Oriá, Marcos; Souza Cavalcante, Hugo L. D. de
2014-01-01
We study the statistics of the amplitude of the synchronization error in chaotic electronic circuits coupled through linear feedback. Depending on the coupling strength, our system exhibits three qualitatively different regimes of synchronization: weak coupling yields independent oscillations; moderate to strong coupling produces a regime of intermittent synchronization known as attractor bubbling; and stronger coupling produces complete synchronization. In the regime of moderate coupling, the probability distribution for the sizes of desynchronization events follows a power law, with an exponent that can be adjusted by changing the coupling strength. Such power-law distributions are interesting, as they appear in many complex systems. However, most of the systems with such a behavior have a fixed value for the exponent of the power law, while here we present an example of a system where the exponent of the power law is easily tuned in real time
Synchronization of chaotic systems
International Nuclear Information System (INIS)
Pecora, Louis M.; Carroll, Thomas L.
2015-01-01
We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators
Suzuki, Hideyuki; Imura, Jun-ichi; Horio, Yoshihiko; Aihara, Kazuyuki
2013-01-01
The chaotic Boltzmann machine proposed in this paper is a chaotic pseudo-billiard system that works as a Boltzmann machine. Chaotic Boltzmann machines are shown numerically to have computing abilities comparable to conventional (stochastic) Boltzmann machines. Since no randomness is required, efficient hardware implementation is expected. Moreover, the ferromagnetic phase transition of the Ising model is shown to be characterised by the largest Lyapunov exponent of the proposed system. In general, a method to relate probabilistic models to nonlinear dynamics by derandomising Gibbs sampling is presented. PMID:23558425
Random nanolasing in the Anderson localized regime
DEFF Research Database (Denmark)
Liu, Jin; Garcia, P. D.; Ek, Sara
2014-01-01
The development of nanoscale optical devices for classical and quantum photonics is affected by unavoidable fabrication imperfections that often impose performance limitations. However, disorder may also enable new functionalities, for example in random lasers, where lasing relies on random...... multiple scattering. The applicability of random lasers has been limited due to multidirectional emission, lack of tunability, and strong mode competition with chaotic fluctuations due to a weak mode confinement. The regime of Anderson localization of light has been proposed for obtaining stable multimode...... random lasing, and initial work concerned macroscopic one-dimensional layered media. Here, we demonstrate on-chip random nanolasers where the cavity feedback is provided by the intrinsic disorder. The strong confinement achieved by Anderson localization reduces the spatial overlap between lasing modes...
International Nuclear Information System (INIS)
Munmuangsaen, Buncha; Srisuchinwong, Banlue
2011-01-01
Highlights: → Five new elementary chaotic snap flows and a generalization of an existing chaotic snap flow have been presented. → Three of all are conservative systems whilst three others are dissipative systems. → Four cases need only a single control parameter and a single nonlinearity. → A cubic case in a jerk representation requires only two terms and a single nonlinearity. - Abstract: Hyperjerk systems with 4th-order derivative of the form x .... =f(x ... ,x .. ,x . ,x) have been referred to as snap systems. Five new elementary chaotic snap flows and a generalization of an existing flow are presented through an extensive numerical search. Four of these flows demonstrate elegant simplicity of a single control parameter based on a single nonlinearity of a quadratic, a piecewise-linear or an exponential type. Two others demonstrate elegant simplicity of all unity-in-magnitude parameters based on either a single cubic nonlinearity or three cubic nonlinearities. The chaotic snap flow with a single cubic nonlinearity requires only two terms and can be transformed to its equivalent dynamical form of only five terms which have a single nonlinearity. An advantage is that such a chaotic flow offers only five terms even though the (four) dimension is high. Three of the chaotic snap flows are characterized as conservative systems whilst three others are dissipative systems. Basic dynamical properties are described.
Generalized Models from Beta(p, 2) Densities with Strong Allee Effect: Dynamical Approach
Aleixo, Sandra M.; Rocha, J. Leonel
2012-01-01
A dynamical approach to study the behaviour of generalized populational growth models from Beta(p, 2) densities, with strong Allee effect, is presented. The dynamical analysis of the respective unimodal maps is performed using symbolic dynamics techniques. The complexity of the correspondent discrete dynamical systems is measured in terms of topological entropy. Different populational dynamics regimes are obtained when the intrinsic growth rates are modified: extinction, bistability, chaotic ...
Synchronization of identical chaotic systems through external chaotic driving
International Nuclear Information System (INIS)
Patidar, V.; Sud, K.K.
2005-11-01
In recent years, the study of synchronization of identical chaotic systems subjected to a common fluctuating random driving signal has drawn considerable interest. In this communication, we report that it is possible to achieve synchronization between two identical chaotic systems, which are not coupled directly but subjected to an external chaotic signal. The external chaotic signal may be obtained from any chaotic system identical or non-identical to both identical chaotic systems. Results of numerical simulations on well known Roessler and jerk dynamical systems have been presented. (author)
Composing chaotic music from the letter m
Sotiropoulos, Anastasios D.
Chaotic music is composed from a proposed iterative map depicting the letter m, relating the pitch, duration and loudness of successive steps. Each of the two curves of the letter m is based on the classical logistic map. Thus, the generating map is xn+1 = r xn(1/2 - xn) for xn between 0 and 1/2 defining the first curve, and xn+1 = r (xn - 1/2)(1 - xn) for xn between 1/2 and 1 representing the second curve. The parameter r which determines the height(s) of the letter m varies from 2 to 16, the latter value ensuring fully developed chaotic solutions for the whole letter m; r = 8 yielding full chaotic solutions only for its first curve. The m-model yields fixed points, bifurcation points and chaotic regions for each separate curve, as well as values of the parameter r greater than 8 which produce inter-fixed points, inter-bifurcation points and inter-chaotic regions from the interplay of the two curves. Based on this, music is composed from mapping the m- recurrence model solutions onto actual notes. The resulting musical score strongly depends on the sequence of notes chosen by the composer to define the musical range corresponding to the range of the chaotic mathematical solutions x from 0 to 1. Here, two musical ranges are used; one is the middle chromatic scale and the other is the seven- octaves range. At the composer's will and, for aesthetics, within the same composition, notes can be the outcome of different values of r and/or shifted in any octave. Compositions with endings of non-repeating note patterns result from values of r in the m-model that do not produce bifurcations. Scores of chaotic music composed from the m-model and the classical logistic model are presented.
Cascade Chaotic System With Applications.
Zhou, Yicong; Hua, Zhongyun; Pun, Chi-Man; Chen, C L Philip
2015-09-01
Chaotic maps are widely used in different applications. Motivated by the cascade structure in electronic circuits, this paper introduces a general chaotic framework called the cascade chaotic system (CCS). Using two 1-D chaotic maps as seed maps, CCS is able to generate a huge number of new chaotic maps. Examples and evaluations show the CCS's robustness. Compared with corresponding seed maps, newly generated chaotic maps are more unpredictable and have better chaotic performance, more parameters, and complex chaotic properties. To investigate applications of CCS, we introduce a pseudo-random number generator (PRNG) and a data encryption system using a chaotic map generated by CCS. Simulation and analysis demonstrate that the proposed PRNG has high quality of randomness and that the data encryption system is able to protect different types of data with a high-security level.
Design of the Chaotic Signal Generator Based on LABVIEW
Directory of Open Access Journals (Sweden)
Jian-Guo Zhang
2014-01-01
Full Text Available We introduces a new method that can achieve the generation of Colpitts chaotic signal The system is based on virtual instrument platform and combined with MATLAB calculation to achieve the generation of Colpitts chaotic signal and making it analysis with autocorrelation and power spectrum at the same time. Signal channel output of chaotic signal was realized through USB-6009 acquisition module extending DA5405 high-speed DAC (Digital-to-Analog Converter chip. The system can adjust parameters based on customers’ requirements to achieve different frequency chaotic signal generation. Compared with the traditional autonomy Colpitts chaotic signal generator, this generator is simple and clear in structure, simple to operate, strong stability, easy to achieve etc.
International Nuclear Information System (INIS)
Kawai, Y.
1991-08-01
It has recently been recognized that the research on various aspects of chaotic dynamics grows rapidly as one of some areas in nonlinear science. On the other hands, the plasma has long been called a treasure-house of nonlinear phenomena, so it is easy to imagine that the plasma is abundant in chaotic phenomena. In fact, the research on plasma chaos is going on, such as the research on the stochastic magnetic field and the chaotic orbit in the toroidal helical system, as well as the research in other experiments. To review the present status of the research on plasma chaos and to make clear the basic common physics, a working group was organized in 1990 as a collaboration research of National Institute for Fusion Science. This is the report on its activity in 1990, with a stress on experimental data obtained in basic plasma experiments and RFP, and on the relaxed theories and computer simulations. (author)
Cryptography with chaotic mixing
International Nuclear Information System (INIS)
Oliveira, Luiz P.L. de; Sobottka, Marcelo
2008-01-01
We propose a cryptosystem based on one-dimensional chaotic maps of the form H p (x)=r p -1 0G0r p (x) defined in the interval [0, 10 p ) for a positive integer parameter p, where G(x)=10x(mod10) and r p (x)= p √(x), which is a topological conjugacy between G and the shift map σ on the space Σ of the sequences with 10 symbols. There are three advantages in comparison with the recently proposed cryptosystem based on chaotic logistic maps F μ (x)=μx(1-x) with 3 p is always chaotic for all parameters p, (b) the knowledge of an ergodic measure allows assignments of the alphabetic symbols to equiprobable sites of H p 's domain and (c) for each p, the security of the cryptosystem is manageable against brute force attacks
Hypogenetic chaotic jerk flows
International Nuclear Information System (INIS)
Li, Chunbiao; Sprott, Julien Clinton; Xing, Hongyan
2016-01-01
Removing the amplitude or polarity information in the feedback loop of a jerk structure shows that special nonlinearities with partial information in the variable can also lead to chaos. Some striking properties are found for this kind of hypogenetic chaotic jerk flow, including multistability of symmetric coexisting attractors from an asymmetric structure, hidden attractors with respect to equilibria but with global attraction, easy amplitude control, and phase reversal which is convenient for chaos applications. - Highlights: • Hypogenetic chaotic jerk flows with incomplete feedback of amplitude or polarity are obtained. • Multistability of symmetric coexisting attractors from an asymmetric structure is found. • Some jerk systems have hidden attractors with respect to equilibria but have global attraction. • These chaotic jerk flows have the properties of amplitude control and phase reversal.
Initial conditions for chaotic inflation
International Nuclear Information System (INIS)
Brandenberger, R.; Kung, J.; Feldman, H.
1991-01-01
In contrast to many other inflationary Universe models, chaotic inflation does not depend on fine tuning initial conditions. Within the context of linear perturbation theory, it is shown that chaotic inflation is stable towards both metric and matter perturbations. Neglecting gravitational perturbations, it is shown that chaotic inflation is an attractor in initial condition space. (orig.)
Chaotic advection near a three-vortex collapse
International Nuclear Information System (INIS)
Leoncini, X.; Kuznetsov, L.; Zaslavsky, G. M.
2001-01-01
Dynamical and statistical properties of tracer advection are studied in a family of flows produced by three point-vortices of different signs. Tracer dynamics is analyzed by numerical construction of Poincare sections, and is found to be strongly chaotic: advection pattern in the region around the center of vorticity is dominated by a well developed stochastic sea, which grows as the vortex system's initial conditions are set closer to those leading to the collapse of the vortices; at the same time, the islands of regular motion around vortices, known as vortex cores, shrink. An estimation of the core's radii from the minimum distance of vortex approach to each other is obtained. Tracer transport was found to be anomalous: for all of the three numerically investigated cases, the variance of the tracer distribution grows faster than a linear function of time, corresponding to a superdiffusive regime. The transport exponent varies with time decades, implying the presence of multi-fractal transport features. Yet, its value is never too far from 3/2, indicating some kind of universality. Statistics of Poincare recurrences is non-Poissonian: distributions have long power-law tails. The anomalous properties of tracer statistics are the result of the complex structure of the advection phase space, in particular, of strong stickiness on the boundaries between the regions of chaotic and regular motion. The role of the different phase space structures involved in this phenomenon is analyzed. Based on this analysis, a kinetic description is constructed, which takes into account different time and space scalings by using a fractional equation
Chaotic hydrodynamics of fluidized beds
Energy Technology Data Exchange (ETDEWEB)
Van der Stappen, M.L.M. [Unit Process and Systems Engineering, Advanced Manufacturing Technology Group, Unilever Research Laboratorium, Vlaardingen (Netherlands)
1996-12-31
The major goals of this thesis are: (1) to develop and evaluate an analysis method based on techniques from non-linear chaos theory to characterize the nonlinear hydrodynamics of gas-solids fluidized beds quantitatively; and (2) to determine the dependence of the chaotic invariants on the operating conditions and investigate how the chaos analysis method can be profitably applied to improve scale-up and design of gas-solids fluidized bed reactors. Chaos theory is introduced in chapter 2 with emphasis on analysis techniques for (experimental) time series, known from literature at the start of this work (1990-1991). In chapter 3, the testing of existing and newly developed techniques on both model and fluidized bed data is described. This leads to the development of the chaos analysis method to analyze measured pressure fluctuations time series of a fluidized bed. Following, in chapter 4, this method is tested and all choices for the parameters are evaluated. The influence of the experimental parameters and external disturbances on the measurements and analysis results is discussed and quantified. The result is a chaos measurement and analysis protocol, which is further used in this work. In chapter 5, the applications to fluidized beds are discussed. It is shown that the entropy is a good measure for the characterization of the dynamical behavior of gas-solids bubbling/slugging fluidized beds. Entropy is applied to characterize the influence of the operating conditions, to assess regime transitions and to analyze dimensionless similar beds of different scale. Quantitative design correlations that relate entropy to the operating parameters (including the bed diameter) are described. Finally, it is discussed how the results of this work might be used in scaling up the chaotic dynamics of fluidized beds. The overall conclusions and outlook from this work are presented in chapter 6. 182 refs.
International Nuclear Information System (INIS)
Linde, A.D.
1986-05-01
It is shown that the universe evolution in the chaotic inflation scenario has no end and may have no beginning. According to this scenario, the universe consists of exponentially large number of different mini-universes inside which all possible metastable vacuum states and all possible types of compactification are realized. (author)
International Nuclear Information System (INIS)
Schaefer, Mirko
2011-01-01
The main topic of this thesis is the investigation of dynamical properties of coupled Tchebycheff map networks. The results give insights into the chaotic string model and its network generalization from a dynamical point of view. As a first approach, discrete symmetry transformations of the model are studied. These transformations are formulated in a general way in order to be also applicable to similar dynamics on bipartite network structures. The dynamics is studied numerically via Lyapunov measures, spatial correlations, and ergodic properties. It is shown that the zeros of the interaction energy are distinguished only with respect to this specific observable, but not by a more general dynamical principle. The original chaotic string model is defined on a one-dimensional lattice (ring-network) as the underlying network topology. This thesis studies a modification of the model based on the introduction of tunable disorder. The effects of inhomogeneous coupling weights as well as small-world perturbations of the ring-network structure on the interaction energy are discussed. Synchronization properties of the chaotic string model and its network generalization are studied in later chapters of this thesis. The analysis is based on the master stability formalism, which relates the stability of the synchronized state to the spectral properties of the network. Apart from complete synchronization, where the dynamics at all nodes of the network coincide, also two-cluster synchronization on bipartite networks is studied. For both types of synchronization it is shown that depending on the type of coupling the synchronized dynamics can display chaotic as well as periodic or quasi-periodic behaviour. The semi-analytical calculations reveal that the respective synchronized states are often stable for a wide range of coupling values even for the ring-network, although the respective basins of attraction may inhabit only a small fraction of the phase space. To provide
Characteristics of level-spacing statistics in chaotic graphene billiards.
Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2011-03-01
A fundamental result in nonrelativistic quantum nonlinear dynamics is that the spectral statistics of quantum systems that possess no geometric symmetry, but whose classical dynamics are chaotic, are described by those of the Gaussian orthogonal ensemble (GOE) or the Gaussian unitary ensemble (GUE), in the presence or absence of time-reversal symmetry, respectively. For massless spin-half particles such as neutrinos in relativistic quantum mechanics in a chaotic billiard, the seminal work of Berry and Mondragon established the GUE nature of the level-spacing statistics, due to the combination of the chirality of Dirac particles and the confinement, which breaks the time-reversal symmetry. A question is whether the GOE or the GUE statistics can be observed in experimentally accessible, relativistic quantum systems. We demonstrate, using graphene confinements in which the quasiparticle motions are governed by the Dirac equation in the low-energy regime, that the level-spacing statistics are persistently those of GOE random matrices. We present extensive numerical evidence obtained from the tight-binding approach and a physical explanation for the GOE statistics. We also find that the presence of a weak magnetic field switches the statistics to those of GUE. For a strong magnetic field, Landau levels become influential, causing the level-spacing distribution to deviate markedly from the random-matrix predictions. Issues addressed also include the effects of a number of realistic factors on level-spacing statistics such as next nearest-neighbor interactions, different lattice orientations, enhanced hopping energy for atoms on the boundary, and staggered potential due to graphene-substrate interactions.
The chaotic dynamical aperture
International Nuclear Information System (INIS)
Lee, S.Y.; Tepikian, S.
1985-01-01
Nonlinear magnetic forces become more important for particles in the modern large accelerators. These nonlinear elements are introduced either intentionally to control beam dynamics or by uncontrollable random errors. Equations of motion in the nonlinear Hamiltonian are usually non-integrable. Because of the nonlinear part of the Hamiltonian, the tune diagram of accelerators is a jungle. Nonlinear magnet multipoles are important in keeping the accelerator operation point in the safe quarter of the hostile jungle of resonant tunes. Indeed, all the modern accelerator design have taken advantages of nonlinear mechanics. On the other hand, the effect of the uncontrollable random multipoles should be evaluated carefully. A powerful method of studying the effect of these nonlinear multipoles is using a particle tracking calculation, where a group of test particles are tracing through these magnetic multipoles in the accelerator hundreds to millions of turns in order to test the dynamical aperture of the machine. These methods are extremely useful in the design of a large accelerator such as SSC, LEP, HERA and RHIC. These calculations unfortunately take tremendous amount of computing time. In this paper, we try to apply the existing method in the nonlinear dynamics to study the possible alternative solution. When the Hamiltonian motion becomes chaotic, the tune of the machine becomes undefined. The aperture related to the chaotic orbit can be identified as chaotic dynamical aperture. We review the method of determining chaotic orbit and apply the method to nonlinear problems in accelerator physics. We then discuss the scaling properties and effect of random sextupoles
Energy Technology Data Exchange (ETDEWEB)
Blacher, S; Perdang, J [Institut d' Astrophysique, B-4200 Cointe-Ougree (Belgium)
1981-09-01
A numerical experiment on Hamiltonian oscillations demonstrates the existence of chaotic motions which satisfy the property of phase coherence. It is observed that the low-frequency end of the power spectrum of such motions is remarkably similar in structure to the low-frequency SCLERA spectra. Since the smallness of the observed solar amplitudes is not a sufficient mathematical ground for inefficiency of non-linear effects the possibility of chaos among solar oscillations cannot be discarded a priori.
Digital chaotic sequence generator based on coupled chaotic systems
International Nuclear Information System (INIS)
Shu-Bo, Liu; Jing, Sun; Jin-Shuo, Liu; Zheng-Quan, Xu
2009-01-01
Chaotic systems perform well as a new rich source of cryptography and pseudo-random coding. Unfortunately their digital dynamical properties would degrade due to the finite computing precision. Proposed in this paper is a modified digital chaotic sequence generator based on chaotic logistic systems with a coupling structure where one chaotic subsystem generates perturbation signals to disturb the control parameter of the other one. The numerical simulations show that the length of chaotic orbits, the output distribution of chaotic system, and the security of chaotic sequences have been greatly improved. Moreover the chaotic sequence period can be extended at least by one order of magnitude longer than that of the uncoupled logistic system and the difficulty in decrypting increases 2 128 *2 128 times indicating that the dynamical degradation of digital chaos is effectively improved. A field programmable gate array (FPGA) implementation of an algorithm is given and the corresponding experiment shows that the output speed of the generated chaotic sequences can reach 571.4 Mbps indicating that the designed generator can be applied to the real-time video image encryption. (general)
Dynamic control of chaotic resonators
Di Falco, A.; Bruck, R.; Liu, C.; Muskens, O.; Fratalocchi, Andrea
2016-01-01
We report on the all-optical control of chaotic optical resonators based on silicon on insulator (SOI) platform. We show that simple non-chaotic cavities can be tuned to exhibit chaotic behavior via intense optical pump- ing, inducing a local change of refractive index. To this extent we have fabricated a number of devices and demonstrated experimentally and theoretically that chaos can be triggered on demand on an optical chip. © 2016 SPIE.
Dynamic control of chaotic resonators
Di Falco, A.
2016-02-16
We report on the all-optical control of chaotic optical resonators based on silicon on insulator (SOI) platform. We show that simple non-chaotic cavities can be tuned to exhibit chaotic behavior via intense optical pump- ing, inducing a local change of refractive index. To this extent we have fabricated a number of devices and demonstrated experimentally and theoretically that chaos can be triggered on demand on an optical chip. © 2016 SPIE.
Using Chaotic System in Encryption
Findik, Oğuz; Kahramanli, Şirzat
In this paper chaotic systems and RSA encryption algorithm are combined in order to develop an encryption algorithm which accomplishes the modern standards. E.Lorenz's weather forecast' equations which are used to simulate non-linear systems are utilized to create chaotic map. This equation can be used to generate random numbers. In order to achieve up-to-date standards and use online and offline status, a new encryption technique that combines chaotic systems and RSA encryption algorithm has been developed. The combination of RSA algorithm and chaotic systems makes encryption system.
Application of chaotic ant swarm optimization in electric load forecasting
International Nuclear Information System (INIS)
Hong, W.-C.
2010-01-01
Support vector regression (SVR) had revealed strong potential in accurate electric load forecasting, particularly by employing effective evolutionary algorithms to determine suitable values of its three parameters. Based on previous research results, however, these employed evolutionary algorithms themselves have several drawbacks, such as converging prematurely, reaching slowly the global optimal solution, and trapping into a local optimum. This investigation presents an SVR-based electric load forecasting model that applied a novel algorithm, namely chaotic ant swarm optimization (CAS), to improve the forecasting performance by searching its suitable parameters combination. The proposed CAS combines with the chaotic behavior of single ant and self-organization behavior of ant colony in the foraging process to overcome premature local optimum. The empirical results indicate that the SVR model with CAS (SVRCAS) results in better forecasting performance than the other alternative methods, namely SVRCPSO (SVR with chaotic PSO), SVRCGA (SVR with chaotic GA), regression model, and ANN model.
Estimating parameters of chaotic systems synchronized by external driving signal
International Nuclear Information System (INIS)
Wu Xiaogang; Wang Zuxi
2007-01-01
Noise-induced synchronization (NIS) has evoked great research interests recently. Two uncoupled identical chaotic systems can achieve complete synchronization (CS) by feeding a common noise with appropriate intensity. Actually, NIS belongs to the category of external feedback control (EFC). The significance of applying EFC in secure communication lies in fact that the trajectory of chaotic systems is disturbed so strongly by external driving signal that phase space reconstruction attack fails. In this paper, however, we propose an approach that can accurately estimate the parameters of the chaotic systems synchronized by external driving signal through chaotic transmitted signal, driving signal and their derivatives. Numerical simulation indicates that this approach can estimate system parameters and external coupling strength under two driving modes in a very rapid manner, which implies that EFC is not superior to other methods in secure communication
A simple chaotic delay differential equation
International Nuclear Information System (INIS)
Sprott, J.C.
2007-01-01
The simplest chaotic delay differential equation with a sinusoidal nonlinearity is described, including the route to chaos, Lyapunov exponent spectrum, and chaotic diffusion. It is prototypical of many other high-dimensional chaotic systems
Quantifying chaotic dynamics from integrate-and-fire processes
Energy Technology Data Exchange (ETDEWEB)
Pavlov, A. N. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Saratov State Technical University, Politehnicheskaya Str. 77, 410054 Saratov (Russian Federation); Pavlova, O. N. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Mohammad, Y. K. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Tikrit University Salahudin, Tikrit Qadisiyah, University Str. P.O. Box 42, Tikrit (Iraq); Kurths, J. [Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473 Potsdam (Germany); Institute of Physics, Humboldt University Berlin, 12489 Berlin (Germany)
2015-01-15
Characterizing chaotic dynamics from integrate-and-fire (IF) interspike intervals (ISIs) is relatively easy performed at high firing rates. When the firing rate is low, a correct estimation of Lyapunov exponents (LEs) describing dynamical features of complex oscillations reflected in the IF ISI sequences becomes more complicated. In this work we discuss peculiarities and limitations of quantifying chaotic dynamics from IF point processes. We consider main factors leading to underestimated LEs and demonstrate a way of improving numerical determining of LEs from IF ISI sequences. We show that estimations of the two largest LEs can be performed using around 400 mean periods of chaotic oscillations in the regime of phase-coherent chaos. Application to real data is discussed.
Bearing Health Assessment Based on Chaotic Characteristics
Directory of Open Access Journals (Sweden)
Chen Lu
2013-01-01
Full Text Available Vibration signals extracted from rotating parts of machinery carry a lot of useful information about the condition of operating machine. Due to the strong non-linear, complex and non-stationary characteristics of vibration signals from working bearings, an accurate and reliable health assessment method for bearing is necessary. This paper proposes to utilize the selected chaotic characteristics of vibration signal for health assessment of a bearing by using self-organizing map (SOM. Both Grassberger-Procaccia algorithm and Takens' theory are employed to calculate the characteristic vector which includes three chaotic characteristics, such as correlation dimension, largest Lyapunov exponent and Kolmogorov entropy. After that, SOM is used to map the three corresponding characteristics into a confidence value (CV which represents the health state of the bearing. Finally, a case study based on vibration datasets of a group of testing bearings was conducted to demonstrate that the proposed method can reliably assess the health state of bearing.
Predicting chaotic time series
International Nuclear Information System (INIS)
Farmer, J.D.; Sidorowich, J.J.
1987-01-01
We present a forecasting technique for chaotic data. After embedding a time series in a state space using delay coordinates, we ''learn'' the induced nonlinear mapping using local approximation. This allows us to make short-term predictions of the future behavior of a time series, using information based only on past values. We present an error estimate for this technique, and demonstrate its effectiveness by applying it to several examples, including data from the Mackey-Glass delay differential equation, Rayleigh-Benard convection, and Taylor-Couette flow
Stochastic and Chaotic Relaxation Oscillations
Grasman, J.; Roerdink, J.B.T.M.
1988-01-01
For relaxation oscillators stochastic and chaotic dynamics are investigated. The effect of random perturbations upon the period is computed. For an extended system with additional state variables chaotic behavior can be expected. As an example, the Van der Pol oscillator is changed into a
Aydiner, Ekrem
2018-01-15
In this study, we consider nonlinear interactions between components such as dark energy, dark matter, matter and radiation in the framework of the Friedman-Robertson-Walker space-time and propose a simple interaction model based on the time evolution of the densities of these components. By using this model we show that these interactions can be given by Lotka-Volterra type equations. We numerically solve these coupling equations and show that interaction dynamics between dark energy-dark matter-matter or dark energy-dark matter-matter-radiation has a strange attractor for 0 > w de >-1, w dm ≥ 0, w m ≥ 0 and w r ≥ 0 values. These strange attractors with the positive Lyapunov exponent clearly show that chaotic dynamics appears in the time evolution of the densities. These results provide that the time evolution of the universe is chaotic. The present model may have potential to solve some of the cosmological problems such as the singularity, cosmic coincidence, big crunch, big rip, horizon, oscillation, the emergence of the galaxies, matter distribution and large-scale organization of the universe. The model also connects between dynamics of the competing species in biological systems and dynamics of the time evolution of the universe and offers a new perspective and a new different scenario for the universe evolution.
Lu, Jia; Zhang, Xiaoxing; Xiong, Hao
The chaotic van der Pol oscillator is a powerful tool for detecting defects in electric systems by using online partial discharge (PD) monitoring. This paper focuses on realizing weak PD signal detection in the strong periodic narrowband interference by using high sensitivity to the periodic narrowband interference signals and immunity to white noise and PD signals of chaotic systems. A new approach to removing the periodic narrowband interference by using a van der Pol chaotic oscillator is described by analyzing the motion characteristic of the chaotic oscillator on the basis of the van der Pol equation. Furthermore, the Floquet index for measuring the amplitude of periodic narrowband signals is redefined. The denoising signal processed by the chaotic van der Pol oscillators is further processed by wavelet analysis. Finally, the denoising results verify that the periodic narrowband and white noise interference can be removed efficiently by combining the theory of the chaotic van der Pol oscillator and wavelet analysis.
Directory of Open Access Journals (Sweden)
S. Vaidyanathan
2013-09-01
Full Text Available This research work describes the modelling of two novel 3-D chaotic systems, the first with a hyperbolic sinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (A and the second with a hyperbolic cosinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (B. In this work, a detailed qualitative analysis of the novel chaotic systems (A and (B has been presented, and the Lyapunov exponents and Kaplan-Yorke dimension of these chaotic systems have been obtained. It is found that the maximal Lyapunov exponent (MLE for the novel chaotic systems (A and (B has a large value, viz. for the system (A and for the system (B. Thus, both the novel chaotic systems (A and (B display strong chaotic behaviour. This research work also discusses the problem of finding adaptive controllers for the global chaos synchronization of identical chaotic systems (A, identical chaotic systems (B and nonidentical chaotic systems (A and (B with unknown system parameters. The adaptive controllers for achieving global chaos synchronization of the novel chaotic systems (A and (B have been derived using adaptive control theory and Lyapunov stability theory. MATLAB simulations have been shown to illustrate the novel chaotic systems (A and (B, and also the adaptive synchronization results derived for the novel chaotic systems (A and (B.
International Nuclear Information System (INIS)
Li Nian-Qiang; Pan Wei; Yan Lian-Shan; Luo Bin; Xu Ming-Feng; Tang Yi-Long
2012-01-01
Symbolic transfer entropy (STE) is employed to quantify the dominant direction of information flow between two chaotic-semiconductor-laser time series. The information flow in unidirectionally and bidirectionally coupled systems was analyzed systematically. Numerical results show that the dependence relationship can be revealed if there exists any coupling between two chaotic semiconductor lasers. More importantly, in both unsynchronized and good synchronization regimes, the STE can be used to quantify the direction of information flow between the lasers, although the former case leads to a better identification. The results thus establish STE as an effective tool for quantifying the direction of information flow between chaotic-laser-based systems
Explosion of limit cycles and chaotic waves in a simple nonlinear chemical system
DEFF Research Database (Denmark)
Brøns, Morten; Sturis, Jeppe
2001-01-01
A model of an autocatalytic chemical reaction was employed to study the explosion of limit cycles and chaotic waves in a nonlinear chemical system. The bifurcation point was determined using asymptotic analysis and perturbations. Scaling laws for amplitude and period were derived. A strong sensit...... sensitivity was introduced due to bifurcation to infinity resulting in chaotic dynamics on adding diffusion....
Air-clad fibers: pump absorption assisted by chaotic wave dynamics?
DEFF Research Database (Denmark)
Mortensen, Niels Asger
2007-01-01
Wave chaos is a concept which has already proved its practical usefulness in design of double-clad fibers for cladding-pumped fiber lasers and fiber amplifiers. In general, classically chaotic geometries will favor strong pump absorption and we address the extent of chaotic wave dynamics in typical...
Chaotic Fluid Mixing in Crystalline Sphere Arrays
Turuban, Regis; Lester, Daniel; Meheust, Yves; Le Borgne, Tanguy
2017-11-01
We study the Lagrangian dynamics of steady 3D Stokes flow over simple cubic (SC) and body-centered cubic (BCC) lattices of close-packed spheres, and uncover the mechanisms governing chaotic mixing. Due to the cusp-shaped sphere contacts, the topology of the skin friction field is fundamentally different to that of continuous (non-granular) media (e.g. open pore networks), with significant implications for fluid mixing. Weak symmetry breaking of the flow orientation with respect to the lattice symmetries imparts a transition from regular to strong chaotic mixing in the BCC lattice, whereas the SC lattice only exhibits weak mixing. Whilst the SC and BCC lattices share the same symmetry point group, these differences are explained in terms of their space groups, and we find that a glide symmetry of the BCC lattice generates chaotic mixing. These insights are used to develop accurate predictions of the Lyapunov exponent distribution over the parameter space of mean flow orientation, and point to a general theory of mixing and dispersion based upon the inherent symmetries of arbitrary crystalline structures. The authors acknowledge the support of ERC project ReactiveFronts (648377).
Chaotic spectra: How to extract dynamic information
International Nuclear Information System (INIS)
Taylor, H.S.; Gomez Llorente, J.M.; Zakrzewski, J.; Kulander, K.C.
1988-10-01
Nonlinear dynamics is applied to chaotic unassignable atomic and molecular spectra with the aim of extracting detailed information about regular dynamic motions that exist over short intervals of time. It is shown how this motion can be extracted from high resolution spectra by doing low resolution studies or by Fourier transforming limited regions of the spectrum. These motions mimic those of periodic orbits (PO) and are inserts into the dominant chaotic motion. Considering these inserts and the PO as a dynamically decoupled region of space, resonant scattering theory and stabilization methods enable us to compute ladders of resonant states which interact with the chaotic quasi-continuum computed in principle from basis sets placed off the PO. The interaction of the resonances with the quasicontinuum explains the low resolution spectra seen in such experiments. It also allows one to associate low resolution features with a particular PO. The motion on the PO thereby supplies the molecular movements whose quantization causes the low resolution spectra. Characteristic properties of the periodic orbit based resonances are discussed. The method is illustrated on the photoabsorption spectrum of the hydrogen atom in a strong magnetic field and on the photodissociation spectrum of H 3 + . Other molecular systems which are currently under investigation using this formalism are also mentioned. 53 refs., 10 figs., 2 tabs
Synchronization of mobile chaotic oscillator networks
Energy Technology Data Exchange (ETDEWEB)
Fujiwara, Naoya, E-mail: fujiwara@csis.u-tokyo.ac.jp [Center for Spatial Information Science, The University of Tokyo, 277-8568 Chiba (Japan); Kurths, Jürgen [Potsdam Institute for Climate Impact Research (PIK), 14473 Potsdam, Germany and Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen (United Kingdom); Díaz-Guilera, Albert [Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain and Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, Barcelona (Spain)
2016-09-15
We study synchronization of systems in which agents holding chaotic oscillators move in a two-dimensional plane and interact with nearby ones forming a time dependent network. Due to the uncertainty in observing other agents' states, we assume that the interaction contains a certain amount of noise that turns out to be relevant for chaotic dynamics. We find that a synchronization transition takes place by changing a control parameter. But this transition depends on the relative dynamic scale of motion and interaction. When the topology change is slow, we observe an intermittent switching between laminar and burst states close to the transition due to small noise. This novel type of synchronization transition and intermittency can happen even when complete synchronization is linearly stable in the absence of noise. We show that the linear stability of the synchronized state is not a sufficient condition for its stability due to strong fluctuations of the transverse Lyapunov exponent associated with a slow network topology change. Since this effect can be observed within the linearized dynamics, we can expect such an effect in the temporal networks with noisy chaotic oscillators, irrespective of the details of the oscillator dynamics. When the topology change is fast, a linearized approximation describes well the dynamics towards synchrony. These results imply that the fluctuations of the finite-time transverse Lyapunov exponent should also be taken into account to estimate synchronization of the mobile contact networks.
Synchronization of mobile chaotic oscillator networks
International Nuclear Information System (INIS)
Fujiwara, Naoya; Kurths, Jürgen; Díaz-Guilera, Albert
2016-01-01
We study synchronization of systems in which agents holding chaotic oscillators move in a two-dimensional plane and interact with nearby ones forming a time dependent network. Due to the uncertainty in observing other agents' states, we assume that the interaction contains a certain amount of noise that turns out to be relevant for chaotic dynamics. We find that a synchronization transition takes place by changing a control parameter. But this transition depends on the relative dynamic scale of motion and interaction. When the topology change is slow, we observe an intermittent switching between laminar and burst states close to the transition due to small noise. This novel type of synchronization transition and intermittency can happen even when complete synchronization is linearly stable in the absence of noise. We show that the linear stability of the synchronized state is not a sufficient condition for its stability due to strong fluctuations of the transverse Lyapunov exponent associated with a slow network topology change. Since this effect can be observed within the linearized dynamics, we can expect such an effect in the temporal networks with noisy chaotic oscillators, irrespective of the details of the oscillator dynamics. When the topology change is fast, a linearized approximation describes well the dynamics towards synchrony. These results imply that the fluctuations of the finite-time transverse Lyapunov exponent should also be taken into account to estimate synchronization of the mobile contact networks.
Chaotic Fluid Mixing in Crystalline Sphere Arrays
Turuban, R.; Lester, D. R.; Le Borgne, T.; Méheust, Y.
2017-12-01
We study the Lagrangian dynamics of steady 3D Stokes flow over simple cubic (SC) and body-centered cubic (BCC) lattices of close-packed spheres, and uncover the mechanisms governing chaotic mixing. Due to the cusp-shaped sphere contacts, the topology of the skin friction field is fundamentally different to that of continuous (non-granular) media (e.g. open pore networks), with significant implications for fluid mixing. Weak symmetry breaking of the flow orientation with respect to the lattice symmetries imparts a transition from regular to strong chaotic mixing in the BCC lattice, whereas the SC lattice only exhibits weak mixing. Whilst the SC and BCC lattices share the same symmetry point group, these differences are explained in terms of their space groups, and we find that a glide symmetry of the BCC lattice generates chaotic mixing. These insight are used to develop accurate predictions of the Lyapunov exponent distribution over the parameter space of mean flow orientation, and point to a general theory of mixing and dispersion based upon the inherent symmetries of arbitrary crystalline structures.
Synchronization of mobile chaotic oscillator networks.
Fujiwara, Naoya; Kurths, Jürgen; Díaz-Guilera, Albert
2016-09-01
We study synchronization of systems in which agents holding chaotic oscillators move in a two-dimensional plane and interact with nearby ones forming a time dependent network. Due to the uncertainty in observing other agents' states, we assume that the interaction contains a certain amount of noise that turns out to be relevant for chaotic dynamics. We find that a synchronization transition takes place by changing a control parameter. But this transition depends on the relative dynamic scale of motion and interaction. When the topology change is slow, we observe an intermittent switching between laminar and burst states close to the transition due to small noise. This novel type of synchronization transition and intermittency can happen even when complete synchronization is linearly stable in the absence of noise. We show that the linear stability of the synchronized state is not a sufficient condition for its stability due to strong fluctuations of the transverse Lyapunov exponent associated with a slow network topology change. Since this effect can be observed within the linearized dynamics, we can expect such an effect in the temporal networks with noisy chaotic oscillators, irrespective of the details of the oscillator dynamics. When the topology change is fast, a linearized approximation describes well the dynamics towards synchrony. These results imply that the fluctuations of the finite-time transverse Lyapunov exponent should also be taken into account to estimate synchronization of the mobile contact networks.
Semenova, N. I.; Strelkova, G. I.; Anishchenko, V. S.; Zakharova, A.
2017-06-01
We describe numerical results for the dynamics of networks of nonlocally coupled chaotic maps. Switchings in time between amplitude and phase chimera states have been first established and studied. It has been shown that in autonomous ensembles, a nonstationary regime of switchings has a finite lifetime and represents a transient process towards a stationary regime of phase chimera. The lifetime of the nonstationary switching regime can be increased to infinity by applying short-term noise perturbations.
Correlation control theory of chaotic laser systems
International Nuclear Information System (INIS)
Li Fuli.
1986-04-01
A novel control theory of chaotic systems is studied. The correlation functions are calculated and used as feedback signals of the chaotic lasers. Computer experiments have shown that in this way the chaotic systems can be controlled to have time-independent output when the external control parameters are in chaotic domain. (author)
International Nuclear Information System (INIS)
Mitchel, G.; Shriner, J.
2005-01-01
Although the predictions of Random Matrix Theory (RMT) were available by the early 1960s, data of sufficiently high quality to adequately test the theory were only obtained a decade later by Rainwater. It was another decade later that Bohigas, Haq and Pandey combined the best available nuclear resonance data - the Columbia neutron resonances in heavy nuclei and the TUNL proton resonances in lighter nuclei - to form the Nuclear Data Ensemble. They obtained excellent agreement for the level statistics with the RMT predictions. The expected Porter-Thomas (PT) distribution was considered very early. However, since the widths (amplitudes squared) are measured, the predicted Gaussian distribution for the amplitudes was only qualitatively confirmed. A much more sensitive test was performed by measuring two widths and the relative phase between the two amplitudes. By comparison of the width and amplitude correlations, the Gaussian distribution was confirmed at the 1% level. Following the Bohigas conjecture - that quantum analogs of classically chaotic systems obey RMT - there was an explosion of activity utilizing level statistics in many different quantum systems. In nuclei the focus was verifying the range of applicability of RMT. Of particular interest was the effect of collectivity and of excitation energy on statistical properties. The effect of symmetry breaking on level statistics was examined and early predictions by Dyson were confirmed. The effect of symmetry breaking on the width distribution was also measured for the first time. Although heuristic arguments predicted no change from the PT distribution, experimentally there was a large deviation from the PT prediction. Later theoretical efforts were consistent with this result. The stringent conditions placed on the experiments - for eigenvalue tests the data need to be essentially perfect (few or no missing levels or mis assigned quantum numbers) - has limited the amount of suitable experimental data. The
Chaotic advection in the ocean
Energy Technology Data Exchange (ETDEWEB)
Koshel' , Konstantin V; Prants, Sergei V [V.I. Il' ichev Pacific Oceanological Institute, Far-Eastern Division of the Russian Academy of Sciences, Vladivostok (Russian Federation)
2006-11-30
The problem of chaotic advection of passive scalars in the ocean and its topological, dynamical, and fractal properties are considered from the standpoint of the theory of dynamical systems. Analytic and numerical results on Lagrangian transport and mixing in kinematic and dynamic chaotic advection models are described for meandering jet currents, topographical eddies in a barotropic ocean, and a two-layer baroclinic ocean. Laboratory experiments on hydrodynamic flows in rotating tanks as an imitation of geophysical chaotic advection are described. Perspectives of a dynamical system approach in physical oceanography are discussed. (reviews of topical problems)
Modeling of Coupled Chaotic Oscillators
International Nuclear Information System (INIS)
Lai, Y.; Grebogi, C.
1999-01-01
Chaotic dynamics may impose severe limits to deterministic modeling by dynamical equations of natural systems. We give theoretical argument that severe modeling difficulties may occur for high-dimensional chaotic systems in the sense that no model is able to produce reasonably long solutions that are realized by nature. We make these ideas concrete by investigating systems of coupled chaotic oscillators. They arise in many situations of physical and biological interests, and they also arise from discretization of nonlinear partial differential equations. copyright 1999 The American Physical Society
Reconfigurable chaotic logic gates based on novel chaotic circuit
International Nuclear Information System (INIS)
Behnia, S.; Pazhotan, Z.; Ezzati, N.; Akhshani, A.
2014-01-01
Highlights: • A novel method for implementing logic gates based on chaotic maps is introduced. • The logic gates can be implemented without any changes in the threshold voltage. • The chaos-based logic gates may serve as basic components of future computing devices. - Abstract: The logical operations are one of the key issues in today’s computer architecture. Nowadays, there is a great interest in developing alternative ways to get the logic operations by chaos computing. In this paper, a novel implementation method of reconfigurable logic gates based on one-parameter families of chaotic maps is introduced. The special behavior of these chaotic maps can be utilized to provide same threshold voltage for all logic gates. However, there is a wide interval for choosing a control parameter for all reconfigurable logic gates. Furthermore, an experimental implementation of this nonlinear system is presented to demonstrate the robustness of computing capability of chaotic circuits
Amplification through chaotic synchronization in spatially extended beam-plasma systems
Moskalenko, Olga I.; Frolov, Nikita S.; Koronovskii, Alexey A.; Hramov, Alexander E.
2017-12-01
In this paper, we have studied the relationship between chaotic synchronization and microwave signal amplification in coupled beam-plasma systems. We have considered a 1D particle-in-cell numerical model of unidirectionally coupled beam-plasma oscillatory media being in the regime of electron pattern formation. We have shown the significant gain of microwave oscillation power in coupled beam-plasma media being in the different regimes of generation. The discovered effect has a close connection with the chaotic synchronization phenomenon, so we have observed that amplification appears after the onset of the complete time scale synchronization regime in the analyzed coupled spatially extended systems. We have also provided the numerical study of physical processes in the chain of beam-plasma systems leading to the chaotic synchronization and the amplification of microwave oscillations power, respectively.
Nuclear friction and chaotic motion
International Nuclear Information System (INIS)
Srokowski, T.; Szczurek, A.; Drozdz, S.
1990-01-01
The concept of nuclear friction is considered from the point of view of regular versus chaotic motion in an atomic nucleus. Using a realistic nuclear Hamiltonian it is explicitly shown that the frictional description of the gross features of nuclear collisions is adequate if the system behaves chaotically. Because of the core in the Hamiltonian, the three-body nuclear system already reveals a structure of the phase space rich enough for this concept to be applicable
Chaotic diagonal recurrent neural network
International Nuclear Information System (INIS)
Wang Xing-Yuan; Zhang Yi
2012-01-01
We propose a novel neural network based on a diagonal recurrent neural network and chaos, and its structure and learning algorithm are designed. The multilayer feedforward neural network, diagonal recurrent neural network, and chaotic diagonal recurrent neural network are used to approach the cubic symmetry map. The simulation results show that the approximation capability of the chaotic diagonal recurrent neural network is better than the other two neural networks. (interdisciplinary physics and related areas of science and technology)
Hash function based on chaotic map lattices.
Wang, Shihong; Hu, Gang
2007-06-01
A new hash function system, based on coupled chaotic map dynamics, is suggested. By combining floating point computation of chaos and some simple algebraic operations, the system reaches very high bit confusion and diffusion rates, and this enables the system to have desired statistical properties and strong collision resistance. The chaos-based hash function has its advantages for high security and fast performance, and it serves as one of the most highly competitive candidates for practical applications of hash function for software realization and secure information communications in computer networks.
The chaotic regime of D-term inflation
Buchmüller, W.; Domcke, V.; Schmitz, K.
2014-01-01
We consider D-term inflation for small couplings of the inflaton to matter fields. Standard hybrid inflation then ends at a critical value of the inflaton field that exceeds the Planck mass. During the subsequent waterfall transition the inflaton continues its slow-roll motion, whereas the waterfall field rapidly grows by quantum fluctuations. Beyond the decoherence time, the waterfall field becomes classical and approaches a time-dependent minimum, which is determined by the value of the inf...
Efficient chaotic based satellite power supply subsystem
International Nuclear Information System (INIS)
Ramos Turci, Luiz Felipe; Macau, Elbert E.N.; Yoneyama, Takashi
2009-01-01
In this work, we investigate the use of the Dynamical System Theory to increase the efficiency of the satellite power supply subsystems. The core of a satellite power subsystem relies on its DC/DC converter. This is a very nonlinear system that presents a multitude of phenomena ranging from bifurcations, quasi-periodicity, chaos, coexistence of attractors, among others. The traditional power subsystem design techniques try to avoid these nonlinear phenomena so that it is possible to use linear system theory in small regions about the equilibrium points. Here, we show that more efficiency can be drawn from a power supply subsystem if the DC/DC converter operates in regions of high nonlinearity. In special, if it operates in a chaotic regime, is has an intrinsic sensitivity that can be exploited to efficiently drive the power subsystem over high ranges of power requests by using control of chaos techniques.
Efficient chaotic based satellite power supply subsystem
Energy Technology Data Exchange (ETDEWEB)
Ramos Turci, Luiz Felipe [Technological Institute of Aeronautics (ITA), Sao Jose dos Campos, SP (Brazil)], E-mail: felipeturci@yahoo.com.br; Macau, Elbert E.N. [National Institute of Space Research (Inpe), Sao Jose dos Campos, SP (Brazil)], E-mail: elbert@lac.inpe.br; Yoneyama, Takashi [Technological Institute of Aeronautics (ITA), Sao Jose dos Campos, SP (Brazil)], E-mail: takashi@ita.br
2009-10-15
In this work, we investigate the use of the Dynamical System Theory to increase the efficiency of the satellite power supply subsystems. The core of a satellite power subsystem relies on its DC/DC converter. This is a very nonlinear system that presents a multitude of phenomena ranging from bifurcations, quasi-periodicity, chaos, coexistence of attractors, among others. The traditional power subsystem design techniques try to avoid these nonlinear phenomena so that it is possible to use linear system theory in small regions about the equilibrium points. Here, we show that more efficiency can be drawn from a power supply subsystem if the DC/DC converter operates in regions of high nonlinearity. In special, if it operates in a chaotic regime, is has an intrinsic sensitivity that can be exploited to efficiently drive the power subsystem over high ranges of power requests by using control of chaos techniques.
Strong memory in time series of human magnetoencephalograms can identify photosensitive epilepsy
International Nuclear Information System (INIS)
Yulmetyev, R. M.; Yulmetyeva, D. G.; Haenggi, P.; Shimojo, S.; Bhattacharya, J.
2007-01-01
To discuss the salient role of statistical memory effects in human brain functioning, we have analyzed a set of stochastic memory quantifiers that reflects the dynamical characteristics of neuromagnetic responses of magnetoencephalographic signals to a flickering stimulus of different color combinations from a group of control subjects, and compared them with those for a patient with photosensitive epilepsy. We have discovered that the emergence of strong memory and the accompanying transition to a regular and robust regime of chaotic behavior of signals in separate areas for a patient most likely identifies the regions where the protective mechanism against the occurrence of photosensitive epilepsy is located
Raby chaotic vacuum oscillations in resonator quantum electrodynamics
International Nuclear Information System (INIS)
Kon'kov, L.E.; Prants, S.V.
1997-01-01
It is shown in numerical experiments with two-level atoms, moving through a single-mode high-quality resonator, that a new type of spontaneous radiation - the Raby chaotic vacuum oscillation - originates in the mode of strong atom-field bonds
Dimension of chaotic attractors
Energy Technology Data Exchange (ETDEWEB)
Farmer, J.D.; Ott, E.; Yorke, J.A.
1982-09-01
Dimension is perhaps the most basic property of an attractor. In this paper we discuss a variety of different definitions of dimension, compute their values for a typical example, and review previous work on the dimension of chaotic attractors. The relevant definitions of dimension are of two general types, those that depend only on metric properties, and those that depend on probabilistic properties (that is, they depend on the frequency with which a typical trajectory visits different regions of the attractor). Both our example and the previous work that we review support the conclusion that all of the probabilistic dimensions take on the same value, which we call the dimension of the natural measure, and all of the metric dimensions take on a common value, which we call the fractal dimension. Furthermore, the dimension of the natural measure is typically equal to the Lyapunov dimension, which is defined in terms of Lyapunov numbers, and thus is usually far easier to calculate than any other definition. Because it is computable and more physically relevant, we feel that the dimension of the natural measure is more important than the fractal dimension.
Jamming and chaotic dynamics in different granular systems
Maghsoodi, Homayoon; Luijten, Erik
Although common in nature and industry, the jamming transition has long eluded a concrete, mechanistic explanation. Recently, Banigan et al. (Nat. Phys. 9, 288-292, 2013) proposed a method for characterizing this transition in a granular system in terms of the system's chaotic properties, as quantified by the largest Lyapunov exponent. They demonstrated that in a two-dimensional shear cell the jamming transition coincides with the bulk density at which the system's largest Lyapunov exponent changes sign, indicating a transition between chaotic and non-chaotic regimes. To examine the applicability of this observation to realistic granular systems, we study a model that includes frictional forces within an expanded phase space. Furthermore, we test the generality of the relation between chaos and jamming by investigating the relationship between jamming and the chaotic properties of several other granular systems, notably sheared systems (Howell, D., Behringer R. P., Veje C., Phys. Rev. Lett. 82, 5241-5244, 1999) and systems with a free boundary. Finally, we quantify correlations between the largest Lyapunov vector and collective rearrangements of the system to demonstrate the predictive capabilities enabled by adopting this perspective of jamming.
International Nuclear Information System (INIS)
Kh'yuitt, G.
1980-01-01
An introduction into the problem of two-phase flows is presented. Flow regimes arizing in two-phase flows are described, and classification of these regimes is given. Structures of vertical and horizontal two-phase flows and a method of their identification using regime maps are considered. The limits of this method application are discussed. The flooding phenomena and phenomena of direction change (flow reversal) of the flow and interrelation of these phenomena as well as transitions from slug regime to churn one and from churn one to annular one in vertical flows are described. Problems of phase transitions and equilibrium are discussed. Flow regimes in tubes where evaporating liquid is running, are described [ru
Studies in Chaotic adiabatic dynamics
International Nuclear Information System (INIS)
Jarzynski, C.
1994-01-01
Chaotic adiabatic dynamics refers to the study of systems exhibiting chaotic evolution under slowly time-dependent equations of motion. In this dissertation the author restricts his attention to Hamiltonian chaotic adiabatic systems. The results presented are organized around a central theme, namely, that the energies of such systems evolve diffusively. He begins with a general analysis, in which he motivates and derives a Fokker-Planck equation governing this process of energy diffusion. He applies this equation to study the open-quotes goodnessclose quotes of an adiabatic invariant associated with chaotic motion. This formalism is then applied to two specific examples. The first is that of a gas of noninteracting point particles inside a hard container that deforms slowly with time. Both the two- and three-dimensional cases are considered. The results are discussed in the context of the Wall Formula for one-body dissipation in nuclear physics, and it is shown that such a gas approaches, asymptotically with time, an exponential velocity distribution. The second example involves the Fermi mechanism for the acceleration of cosmic rays. Explicit evolution equations are obtained for the distribution of cosmic ray energies within this model, and the steady-state energy distribution that arises when this equation is modified to account for the injection and removal of cosmic rays is discussed. Finally, the author re-examines the multiple-time-scale approach as applied to the study of phase space evolution under a chaotic adiabatic Hamiltonian. This leads to a more rigorous derivation of the above-mentioned Fokker-Planck equation, and also to a new term which has relevance to the problem of chaotic adiabatic reaction forces (the forces acting on slow, heavy degrees of freedom due to their coupling to light, fast chaotic degrees)
Discrete and mesoscopic regimes of finite-size wave turbulence
International Nuclear Information System (INIS)
L'vov, V. S.; Nazarenko, S.
2010-01-01
Bounding volume results in discreteness of eigenmodes in wave systems. This leads to a depletion or complete loss of wave resonances (three-wave, four-wave, etc.), which has a strong effect on wave turbulence (WT) i.e., on the statistical behavior of broadband sets of weakly nonlinear waves. This paper describes three different regimes of WT realizable for different levels of the wave excitations: discrete, mesoscopic and kinetic WT. Discrete WT comprises chaotic dynamics of interacting wave 'clusters' consisting of discrete (often finite) number of connected resonant wave triads (or quarters). Kinetic WT refers to the infinite-box theory, described by well-known wave-kinetic equations. Mesoscopic WT is a regime in which either the discrete and the kinetic evolutions alternate or when none of these two types is purely realized. We argue that in mesoscopic systems the wave spectrum experiences a sandpile behavior. Importantly, the mesoscopic regime is realized for a broad range of wave amplitudes which typically spans over several orders on magnitude, and not just for a particular intermediate level.
Chaotic scattering and quantum dynamics
International Nuclear Information System (INIS)
Doron, Eyal.
1992-11-01
The main concern of this thesis is the application of the semiclassical approximation to quantum chaotic scattering systems. We deal with two separate, although interconnected, subjects. The first subject dealt with is the semiclassical characterization of the fluctuations of the S matrix. A particular important parameter is the magnetic field B, and we show how the correlation length and line shape of S matrix elements under a change of B may be derived. An effect which is present in many physical wave systems is absorption of energy flux. We show how absorption affects both the reflectivity and the scattering phase and time delay of a scattering system. In the second part of the thesis, we show how the formalism and results obtained from chaotic scattering can be applied to the investigation of closed chaotic systems, and in particular to chaotic billiards. The semiclassical expansion for billiards is presented. In the last part of the thesis we deal with the statistics of S matrices of chaotic scattering systems. The main message of this work is that scattering matrix, and its classical counterpart the Poincare Scattering Map can be used to yield a powerful formulation of the quantum mechanical dynamics of bounded systems. (author)
International Nuclear Information System (INIS)
Liles, D.R.
1982-01-01
Internal boundaries in multiphase flow greatly complicate fluid-dynamic and heat-transfer descriptions. Different flow regimes or topological configurations can have radically dissimilar interfacial and wall mass, momentum, and energy exchanges. To model the flow dynamics properly requires estimates of these rates. In this paper the common flow regimes for gas-liquid systems are defined and the techniques used to estimate the extent of a particular regime are described. Also, the current computer-code procedures are delineated and introduce a potentially better method is introduced
Observer based on sliding mode variable structure for synchronization of chaotic systems
International Nuclear Information System (INIS)
Yin Xunhe; Shan Xiuming; Ren Yong
2003-01-01
In the paper an approach, based on the state observer of sliding mode variable structure, is used for synchronizing chaotic systems. It does not require either the computation of the Lyapunov exponents, or the initial conditions belonging to the same basin of attraction as the existed approaches based on the state observer for synchronizing chaotic systems. The approach is more robust against noise and parameter mismatch than the existed approaches based on the state observer for synchronizing chaotic systems, because the former uses variable structure control, which is strong robust with respect to noise and parameter mismatch in the error dynamics, the later uses an appropriate choice of the feedback gain. Two well-known chaotic systems, a chaotic Roessler system and a hyperchaotic Roessler system are considered as illustrative examples to demonstrate the effectiveness of the used approach by numerical simulations
Designing key-dependent chaotic S-box with larger key space
International Nuclear Information System (INIS)
Yin Ruming; Yuan Jian; Wang Jian; Shan Xiuming; Wang Xiqin
2009-01-01
The construction of cryptographically strong substitution boxes (S-boxes) is an important concern in designing secure cryptosystems. The key-dependent S-boxes designed using chaotic maps have received increasing attention in recent years. However, the key space of such S-boxes does not seem to be sufficiently large due to the limited parameter range of discretized chaotic maps. In this paper, we propose a new key-dependent S-box based on the iteration of continuous chaotic maps. We explore the continuous-valued state space of chaotic systems, and devise the discrete mapping between the input and the output of the S-box. A key-dependent S-box is constructed with the logistic map in this paper. We show that its key space could be much larger than the current key-dependent chaotic S-boxes.
On synchronization of three chaotic systems
International Nuclear Information System (INIS)
Yan Jianping; Li Changpin
2005-01-01
In this paper, a simple but efficient method is applied to the synchronization of three chaotic systems, i.e., the chaotic Lorenz, Chua, and Chen systems. Numerical simulations show this method works very well
Intermittent chaotic chimeras for coupled rotators
DEFF Research Database (Denmark)
Olmi, Simona; Martens, Erik Andreas; Thutupalli, Shashi
2015-01-01
Two symmetrically coupled populations of N oscillators with inertia m display chaotic solutions with broken symmetry similar to experimental observations with mechanical pendulums. In particular, we report evidence of intermittent chaotic chimeras, where one population is synchronized and the other...
On the Design of Chaotic Oscillators
DEFF Research Database (Denmark)
Lindberg, Erik; Tamasevicius, A; Cenys, A.
1998-01-01
A discussion of the chaotic oscillator concept from a design methodology pointof view. The attributes of some chaoticoscillators are discussed and a systematicdesign method based on eigenvalue investigation is proposed. The method isillustrated with a chaotic Wien-bridgeoscillator design....
Chaotic saddles in nonlinear modulational interactions in a plasma
International Nuclear Information System (INIS)
Miranda, Rodrigo A.; Rempel, Erico L.; Chian, Abraham C.-L.
2012-01-01
A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.
Chaotic saddles in nonlinear modulational interactions in a plasma
Energy Technology Data Exchange (ETDEWEB)
Miranda, Rodrigo A. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); University of Brasilia (UnB), Gama Campus, and Plasma Physics Laboratory, Institute of Physics, Brasilia, DF 70910-900 (Brazil); Rempel, Erico L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); Chian, Abraham C.-L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); Observatoire de Paris, LESIA, CNRS, 92195 Meudon (France)
2012-11-15
A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.
A new chaotic secure communication scheme
International Nuclear Information System (INIS)
Hua Changchun; Yang Bo; Ouyang Gaoxiang; Guan Xinping
2005-01-01
A new chaotic secure communication scheme is constructed. Unified chaotic system is used to encrypt the emitted signal. Different from the existing chaotic secure communication methods, the useful information is embodied in the parameter of chaotic systems in this Letter. The receiver is designed which can succeed in recovering the former signal. Finally computer simulations are done to verify the proposed methods, and the results show that the obtained theoretic results are feasible and efficient
Chaotic structure of oil prices
Bildirici, Melike; Sonustun, Fulya Ozaksoy
2018-01-01
The fluctuations in oil prices are very complicated and therefore, it is unable to predict its effects on economies. For modelling complex system of oil prices, linear economic models are not sufficient and efficient tools. Thus, in recent years, economists attached great attention to non-linear structure of oil prices. For analyzing this relationship, GARCH types of models were used in some papers. Distinctively from the other papers, in this study, we aimed to analyze chaotic pattern of oil prices. Thus, it was used the Lyapunov Exponents and Hennon Map to determine chaotic behavior of oil prices for the selected time period.
Chaotic signals in digital communications
Eisencraft, Marcio; Suyama, Ricardo
2013-01-01
Chaotic Signals in Digital Communications combines fundamental background knowledge with state-of-the-art methods for using chaotic signals and systems in digital communications. The book builds a bridge between theoretical works and practical implementation to help researchers attain consistent performance in realistic environments. It shows the possible shortcomings of the chaos-based communication systems proposed in the literature, particularly when they are subjected to non-ideal conditions. It also presents a toolbox of techniques for researchers working to actually implement such system
Lectures on chaotic dynamical systems
Afraimovich, Valentin
2002-01-01
This book is devoted to chaotic nonlinear dynamics. It presents a consistent, up-to-date introduction to the field of strange attractors, hyperbolic repellers, and nonlocal bifurcations. The authors keep the highest possible level of "physical" intuition while staying mathematically rigorous. In addition, they explain a variety of important nonstandard algorithms and problems involving the computation of chaotic dynamics. The book will help readers who are not familiar with nonlinear dynamics to understand and appreciate sophisticated modern dynamical systems and chaos. Intended for courses in either mathematics, physics, or engineering, prerequisites are calculus, differential equations, and functional analysis.
Chaotic fluid mixing by alternating microparticle topologies to enhance biochemical reactions
Gao, Y.; Reenen, van A.; Hulsen, M.A.; Jong, de A.M.; Prins, M.W.J.; Toonder, den J.M.J.
2014-01-01
We report experimental results on chaotic mass transport induced by alternating topological changes of magnetic particle chains actuated by a rotating magnetic field. Results on the induced fluid flows, through particle tracing experiments and mixing experiments, are obtained for (1) the regime of
Examining Chaotic Convection with Super-Parameterization Ensembles
Jones, Todd R.
This study investigates a variety of features present in a new configuration of the Community Atmosphere Model (CAM) variant, SP-CAM 2.0. The new configuration (multiple-parameterization-CAM, MP-CAM) changes the manner in which the super-parameterization (SP) concept represents physical tendency feedbacks to the large-scale by using the mean of 10 independent two-dimensional cloud-permitting model (CPM) curtains in each global model column instead of the conventional single CPM curtain. The climates of the SP and MP configurations are examined to investigate any significant differences caused by the application of convective physical tendencies that are more deterministic in nature, paying particular attention to extreme precipitation events and large-scale weather systems, such as the Madden-Julian Oscillation (MJO). A number of small but significant changes in the mean state climate are uncovered, and it is found that the new formulation degrades MJO performance. Despite these deficiencies, the ensemble of possible realizations of convective states in the MP configuration allows for analysis of uncertainty in the small-scale solution, lending to examination of those weather regimes and physical mechanisms associated with strong, chaotic convection. Methods of quantifying precipitation predictability are explored, and use of the most reliable of these leads to the conclusion that poor precipitation predictability is most directly related to the proximity of the global climate model column state to atmospheric critical points. Secondarily, the predictability is tied to the availability of potential convective energy, the presence of mesoscale convective organization on the CPM grid, and the directive power of the large-scale.
Barkai, E.
2002-01-01
We demonstrate aging behavior in a simple non-linear system. Our model is a chaotic map which generates deterministically sub-diffusion. Asymptotic behaviors of the diffusion process are described using aging continuous time random walks, introduced previously to model diffusion in glasses.
Chaotic dynamics from interspike intervals
DEFF Research Database (Denmark)
Pavlov, A N; Sosnovtseva, Olga; Mosekilde, Erik
2001-01-01
Considering two different mathematical models describing chaotic spiking phenomena, namely, an integrate-and-fire and a threshold-crossing model, we discuss the problem of extracting dynamics from interspike intervals (ISIs) and show that the possibilities of computing the largest Lyapunov expone...
Applications of Chaotic Dynamics in Robotics
Directory of Open Access Journals (Sweden)
Xizhe Zang
2016-03-01
Full Text Available This article presents a summary of applications of chaos and fractals in robotics. Firstly, basic concepts of deterministic chaos and fractals are discussed. Then, fundamental tools of chaos theory used for identifying and quantifying chaotic dynamics will be shared. Principal applications of chaos and fractal structures in robotics research, such as chaotic mobile robots, chaotic behaviour exhibited by mobile robots interacting with the environment, chaotic optimization algorithms, chaotic dynamics in bipedal locomotion and fractal mechanisms in modular robots will be presented. A brief survey is reported and an analysis of the reviewed publications is also presented.
Dynamic Parameter-Control Chaotic System.
Hua, Zhongyun; Zhou, Yicong
2016-12-01
This paper proposes a general framework of 1-D chaotic maps called the dynamic parameter-control chaotic system (DPCCS). It has a simple but effective structure that uses the outputs of a chaotic map (control map) to dynamically control the parameter of another chaotic map (seed map). Using any existing 1-D chaotic map as the control/seed map (or both), DPCCS is able to produce a huge number of new chaotic maps. Evaluations and comparisons show that chaotic maps generated by DPCCS are very sensitive to their initial states, and have wider chaotic ranges, better unpredictability and more complex chaotic behaviors than their seed maps. Using a chaotic map of DPCCS as an example, we provide a field-programmable gate array design of this chaotic map to show the simplicity of DPCCS in hardware implementation, and introduce a new pseudo-random number generator (PRNG) to investigate the applications of DPCCS. Analysis and testing results demonstrate the excellent randomness of the proposed PRNG.
Visibility graphlet approach to chaotic time series
Energy Technology Data Exchange (ETDEWEB)
Mutua, Stephen [Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China); Computer Science Department, Masinde Muliro University of Science and Technology, P.O. Box 190-50100, Kakamega (Kenya); Gu, Changgui, E-mail: gu-changgui@163.com, E-mail: hjyang@ustc.edu.cn; Yang, Huijie, E-mail: gu-changgui@163.com, E-mail: hjyang@ustc.edu.cn [Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China)
2016-05-15
Many novel methods have been proposed for mapping time series into complex networks. Although some dynamical behaviors can be effectively captured by existing approaches, the preservation and tracking of the temporal behaviors of a chaotic system remains an open problem. In this work, we extended the visibility graphlet approach to investigate both discrete and continuous chaotic time series. We applied visibility graphlets to capture the reconstructed local states, so that each is treated as a node and tracked downstream to create a temporal chain link. Our empirical findings show that the approach accurately captures the dynamical properties of chaotic systems. Networks constructed from periodic dynamic phases all converge to regular networks and to unique network structures for each model in the chaotic zones. Furthermore, our results show that the characterization of chaotic and non-chaotic zones in the Lorenz system corresponds to the maximal Lyapunov exponent, thus providing a simple and straightforward way to analyze chaotic systems.
Advances and applications in chaotic systems
Volos, Christos
2016-01-01
This book reports on the latest advances and applications of chaotic systems. It consists of 25 contributed chapters by experts who are specialized in the various topics addressed in this book. The chapters cover a broad range of topics of chaotic systems such as chaos, hyperchaos, jerk systems, hyperjerk systems, conservative and dissipative systems, circulant chaotic systems, multi-scroll chaotic systems, finance chaotic system, highly chaotic systems, chaos control, chaos synchronization, circuit realization and applications of chaos theory in secure communications, mobile robot, memristors, cellular neural networks, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in chaos theory. This book will serve as a reference book for graduate students and researchers with a basic knowledge of chaos theory and control systems. The resulting design procedures on the chaotic systems are emphasized using MATLAB software.
International Nuclear Information System (INIS)
Pilat, Joseph F.; Budlong-Sylvester, K.W.
2004-01-01
Following the 1998 nuclear tests in South Asia and later reinforced by revelations about North Korean and Iraqi nuclear activities, there has been growing concern about increasing proliferation dangers. At the same time, the prospects of radiological/nuclear terrorism are seen to be rising - since 9/11, concern over a proliferation/terrorism nexus has never been higher. In the face of this growing danger, there are urgent calls for stronger measures to strengthen the current international nuclear nonproliferation regime, including recommendations to place civilian processing of weapon-useable material under multinational control. As well, there are calls for entirely new tools, including military options. As proliferation and terrorism concerns grow, the regime is under pressure and there is a temptation to consider fundamental changes to the regime. In this context, this paper will address the following: Do we need to change the regime centered on the Treaty on the Nonproliferation of Nuclear Weapons (NPT) and the International Atomic Energy Agency (IAEA)? What improvements could ensure it will be the foundation for the proliferation resistance and physical protection needed if nuclear power grows? What will make it a viable centerpiece of future nonproliferation and counterterrorism approaches?
The ferro-resonance, a phenomenon sometimes chaotic
Energy Technology Data Exchange (ETDEWEB)
Grison, P; Kieny, J C; Riouai, M [Electricite de France (EDF), 92 - Clamart (France)
1996-04-01
The ferro-resonance is a resonance phenomenon involving the saturation of the magnetic core in transformers; in particular, it is generated by the energization of that equipment during a power system restoration. It exhibits classical periodic regimes, but also more complex ones, as harmonic, pseudo-periodic, even chaotic, which have been measured on site or during laboratory tests. The mathematical analysis of this phenomenon belongs to the theory of bifurcations; the use of a program solving non linear systems may lead to a better understanding of the observed overvoltages. (authors). 14 figs., 2 photos.
A novel algorithm for image encryption based on mixture of chaotic maps
International Nuclear Information System (INIS)
Behnia, S.; Akhshani, A.; Mahmodi, H.; Akhavan, A.
2008-01-01
Chaos-based encryption appeared recently in the early 1990s as an original application of nonlinear dynamics in the chaotic regime. In this paper, an implementation of digital image encryption scheme based on the mixture of chaotic systems is reported. The chaotic cryptography technique used in this paper is a symmetric key cryptography. In this algorithm, a typical coupled map was mixed with a one-dimensional chaotic map and used for high degree security image encryption while its speed is acceptable. The proposed algorithm is described in detail, along with its security analysis and implementation. The experimental results based on mixture of chaotic maps approves the effectiveness of the proposed method and the implementation of the algorithm. This mixture application of chaotic maps shows advantages of large key space and high-level security. The ciphertext generated by this method is the same size as the plaintext and is suitable for practical use in the secure transmission of confidential information over the Internet
International Nuclear Information System (INIS)
Hu Manfeng; Xu Zhenyuan; Zhang Rong; Hu Aihua
2007-01-01
Based on the active control idea and the invariance principle of differential equations, a general scheme of adaptive full state hybrid projective synchronization (FSHPS) and parameters identification of a class of chaotic (hyper-chaotic) systems with linearly dependent uncertain parameters is proposed in this Letter. With this effective scheme parameters identification and FSHPS of chaotic and hyper-chaotic systems can be realized simultaneously. Numerical simulations on the chaotic Chen system and the hyper-chaotic Chen system are presented to verify the effectiveness of the proposed scheme
Directory of Open Access Journals (Sweden)
Danilo Icaza Ortiz
2013-01-01
Full Text Available This paper is a review of the competition regime works of various authors, published under the auspices of the University of the Hemispheres and the Corporation for Studies and Publications. Analyzes the structure, the general concepts, case law taken for development. Includes comments on the usefulness of this work for the study of competition law and the contribution to the lawyers who want to practice in this branch of economic law.
Illusion optics in chaotic light
International Nuclear Information System (INIS)
Zhang Suheng; Gan Shu; Xiong Jun; Zhang Xiangdong; Wang Kaige
2010-01-01
The time-reversal process provides the possibility to counteract the time evolution of a physical system. Recent research has shown that such a process can occur in the first-order field correlation of chaotic light and result in the spatial interference and phase-reversal diffraction in an unbalanced interferometer. Here we report experimental investigations on the invisibility cloak and illusion phenomena in chaotic light. In an unbalanced interferometer illuminated by thermal light, we have observed the cloak effect and the optical transformation of one object into another object. The experimental results can be understood by the phase-reversal diffraction, and they demonstrate the theoretical proposal of similar effects in complementary media.
Chaotic attractors with separated scrolls
International Nuclear Information System (INIS)
Bouallegue, Kais
2015-01-01
This paper proposes a new behavior of chaotic attractors with separated scrolls while combining Julia's process with Chua's attractor and Lorenz's attractor. The main motivation of this work is the ability to generate a set of separated scrolls with different behaviors, which in turn allows us to choose one or many scrolls combined with modulation (amplitude and frequency) for secure communication or synchronization. This set seems a new class of hyperchaos because each element of this set looks like a simple chaotic attractor with one positive Lyapunov exponent, so the cardinal of this set is greater than one. This new approach could be used to generate more general higher-dimensional hyperchaotic attractor for more potential application. Numerical simulations are given to show the effectiveness of the proposed theoretical results
Chaotic evolution of arms races
Tomochi, Masaki; Kono, Mitsuo
1998-12-01
A new set of model equations is proposed to describe the evolution of the arms race, by extending Richardson's model with special emphases that (1) power dependent defensive reaction or historical enmity could be a motive force to promote armaments, (2) a deterrent would suppress the growth of armaments, and (3) the defense reaction of one nation against the other nation depends nonlinearly on the difference in armaments between two. The set of equations is numerically solved to exhibit stationary, periodic, and chaotic behavior depending on the combinations of parameters involved. The chaotic evolution is realized when the economic situation of each country involved in the arms race is quite different, which is often observed in the real world.
Anomalous diffusion in chaotic scattering
International Nuclear Information System (INIS)
Srokowski, T.; Ploszajczak, M.
1994-01-01
The anomalous diffusion is found for peripheral collision of atomic nuclei described in the framework of the molecular dynamics. Similarly as for chaotic billiards, the long free paths are the source of the long-time correlations and the anomalous diffusion. Consequences of this finding for the energy dissipation in deep-inelastic collisions and the dynamics of fission in hot nuclei are discussed (authors). 30 refs., 2 figs
Analysis of the time structure of synchronization in multidimensional chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Makarenko, A. V., E-mail: avm.science@mail.ru [Constructive Cybernetics Research Group (Russian Federation)
2015-05-15
A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during synchronization of chaotic oscillations in the T-synchronization mode. A system of two identical logistic mappings with unidirectional coupling that operate in the developed chaos regime is analyzed. It is shown that the widely used approach, in which only synchronization patterns are subjected to analysis while desynchronization areas are considered as a background signal and removed from analysis, should be regarded as methodologically incomplete.
Analysis of the time structure of synchronization in multidimensional chaotic systems
International Nuclear Information System (INIS)
Makarenko, A. V.
2015-01-01
A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during synchronization of chaotic oscillations in the T-synchronization mode. A system of two identical logistic mappings with unidirectional coupling that operate in the developed chaos regime is analyzed. It is shown that the widely used approach, in which only synchronization patterns are subjected to analysis while desynchronization areas are considered as a background signal and removed from analysis, should be regarded as methodologically incomplete
CHAOTIC CAPTURE OF NEPTUNE TROJANS
International Nuclear Information System (INIS)
Nesvorny, David; Vokrouhlicky, David
2009-01-01
Neptune Trojans (NTs) are swarms of outer solar system objects that lead/trail planet Neptune during its revolutions around the Sun. Observations indicate that NTs form a thick cloud of objects with a population perhaps ∼10 times more numerous than that of Jupiter Trojans and orbital inclinations reaching ∼25 deg. The high inclinations of NTs are indicative of capture instead of in situ formation. Here we study a model in which NTs were captured by Neptune during planetary migration when secondary resonances associated with the mean-motion commensurabilities between Uranus and Neptune swept over Neptune's Lagrangian points. This process, known as chaotic capture, is similar to that previously proposed to explain the origin of Jupiter's Trojans. We show that chaotic capture of planetesimals from an ∼35 Earth-mass planetesimal disk can produce a population of NTs that is at least comparable in number to that inferred from current observations. The large orbital inclinations of NTs are a natural outcome of chaotic capture. To obtain the ∼4:1 ratio between high- and low-inclination populations suggested by observations, planetary migration into a dynamically excited planetesimal disk may be required. The required stirring could have been induced by Pluto-sized and larger objects that have formed in the disk.
Chaotic dynamics of respiratory sounds
International Nuclear Information System (INIS)
Ahlstrom, C.; Johansson, A.; Hult, P.; Ask, P.
2006-01-01
There is a growing interest in nonlinear analysis of respiratory sounds (RS), but little has been done to justify the use of nonlinear tools on such data. The aim of this paper is to investigate the stationarity, linearity and chaotic dynamics of recorded RS. Two independent data sets from 8 + 8 healthy subjects were recorded and investigated. The first set consisted of lung sounds (LS) recorded with an electronic stethoscope and the other of tracheal sounds (TS) recorded with a contact accelerometer. Recurrence plot analysis revealed that both LS and TS are quasistationary, with the parts corresponding to inspiratory and expiratory flow plateaus being stationary. Surrogate data tests could not provide statistically sufficient evidence regarding the nonlinearity of the data. The null hypothesis could not be rejected in 4 out of 32 LS cases and in 15 out of 32 TS cases. However, the Lyapunov spectra, the correlation dimension (D 2 ) and the Kaplan-Yorke dimension (D KY ) all indicate chaotic behavior. The Lyapunov analysis showed that the sum of the exponents was negative in all cases and that the largest exponent was found to be positive. The results are partly ambiguous, but provide some evidence of chaotic dynamics of RS, both concerning LS and TS. The results motivate continuous use of nonlinear tools for analysing RS data
Chaotic dynamics of respiratory sounds
Energy Technology Data Exchange (ETDEWEB)
Ahlstrom, C. [Department of Biomedical Engineering, Linkoepings Universitet, IMT/LIU, Universitetssjukhuset, S-58185 Linkoeping (Sweden) and Biomedical Engineering, Orebro University Hospital, S-70185 Orebro (Sweden)]. E-mail: christer@imt.liu.se; Johansson, A. [Department of Biomedical Engineering, Linkoepings Universitet, IMT/LIU, Universitetssjukhuset, S-58185 Linkoeping (Sweden); Hult, P. [Department of Biomedical Engineering, Linkoepings Universitet, IMT/LIU, Universitetssjukhuset, S-58185 Linkoeping (Sweden); Biomedical Engineering, Orebro University Hospital, S-70185 Orebro (Sweden); Ask, P. [Department of Biomedical Engineering, Linkoepings Universitet, IMT/LIU, Universitetssjukhuset, S-58185 Linkoeping (Sweden); Biomedical Engineering, Orebro University Hospital, S-70185 Orebro (Sweden)
2006-09-15
There is a growing interest in nonlinear analysis of respiratory sounds (RS), but little has been done to justify the use of nonlinear tools on such data. The aim of this paper is to investigate the stationarity, linearity and chaotic dynamics of recorded RS. Two independent data sets from 8 + 8 healthy subjects were recorded and investigated. The first set consisted of lung sounds (LS) recorded with an electronic stethoscope and the other of tracheal sounds (TS) recorded with a contact accelerometer. Recurrence plot analysis revealed that both LS and TS are quasistationary, with the parts corresponding to inspiratory and expiratory flow plateaus being stationary. Surrogate data tests could not provide statistically sufficient evidence regarding the nonlinearity of the data. The null hypothesis could not be rejected in 4 out of 32 LS cases and in 15 out of 32 TS cases. However, the Lyapunov spectra, the correlation dimension (D {sub 2}) and the Kaplan-Yorke dimension (D {sub KY}) all indicate chaotic behavior. The Lyapunov analysis showed that the sum of the exponents was negative in all cases and that the largest exponent was found to be positive. The results are partly ambiguous, but provide some evidence of chaotic dynamics of RS, both concerning LS and TS. The results motivate continuous use of nonlinear tools for analysing RS data.
Characterizing chaotic melodies in automatic music composition
Coca, Andrés E.; Tost, Gerard O.; Zhao, Liang
2010-09-01
In this paper, we initially present an algorithm for automatic composition of melodies using chaotic dynamical systems. Afterward, we characterize chaotic music in a comprehensive way as comprising three perspectives: musical discrimination, dynamical influence on musical features, and musical perception. With respect to the first perspective, the coherence between generated chaotic melodies (continuous as well as discrete chaotic melodies) and a set of classical reference melodies is characterized by statistical descriptors and melodic measures. The significant differences among the three types of melodies are determined by discriminant analysis. Regarding the second perspective, the influence of dynamical features of chaotic attractors, e.g., Lyapunov exponent, Hurst coefficient, and correlation dimension, on melodic features is determined by canonical correlation analysis. The last perspective is related to perception of originality, complexity, and degree of melodiousness (Euler's gradus suavitatis) of chaotic and classical melodies by nonparametric statistical tests.
Robust synchronization of chaotic systems via feedback
Energy Technology Data Exchange (ETDEWEB)
Femat, Ricardo [IPICYT, San Luis Potosi (Mexico). Dept. de Matematicas Aplicadas; Solis-Perales, Gualberto [Universidad de Guadalajara, Centro Univ. de Ciencias Exactas e Ingenierias (Mexico). Div. de Electronica y Computacion
2008-07-01
This volume includes the results derived during last ten years about both suppression and synchronization of chaotic -continuous time- systems. Along this time, the concept was to study how the intrinsic properties of dynamical systems can be exploited to suppress and to synchronize the chaotic behaviour and what synchronization phenomena can be found under feedback interconnection. A compilation of these findings is described in this book. This book shows a perspective on synchronization of chaotic systems. (orig.)
TOWARDS THRESHOLD FREQUENCY IN CHAOTIC COLPITTS OSCILLATOR
DEFF Research Database (Denmark)
Lindberg, Erik; Tamasevicius, Arunas; Mykolaitis, Gytis
2007-01-01
A novel version of chaotic Colpitts oscillator is described. Instead of a linear loss resistor, it includes an extra inductor and diode in the collector circuit of the transistor. The modified circuit in comparison with the common Colpitts oscillator may generate chaotic oscillations at the funda......A novel version of chaotic Colpitts oscillator is described. Instead of a linear loss resistor, it includes an extra inductor and diode in the collector circuit of the transistor. The modified circuit in comparison with the common Colpitts oscillator may generate chaotic oscillations...
Unstable periodic orbits and chaotic economic growth
International Nuclear Information System (INIS)
Ishiyama, K.; Saiki, Y.
2005-01-01
We numerically find many unstable periodic solutions embedded in a chaotic attractor in a macroeconomic growth cycle model of two countries with different fiscal policies, and we focus on a special type of the unstable periodic solutions. It is confirmed that chaotic behavior represented by the model is qualitatively and quantitatively related to the unstable periodic solutions. We point out that the structure of a chaotic solution is dissolved into a class of finite unstable periodic solutions picked out among a large number of periodic solutions. In this context it is essential for the unstable periodic solutions to be embedded in the chaotic attractor
Chaotic dynamics of flexible beams driven by external white noise
Awrejcewicz, J.; Krysko, A. V.; Papkova, I. V.; Zakharov, V. M.; Erofeev, N. P.; Krylova, E. Yu.; Mrozowski, J.; Krysko, V. A.
2016-10-01
Mathematical models of continuous structural members (beams, plates and shells) subjected to an external additive white noise are studied. The structural members are considered as systems with infinite number of degrees of freedom. We show that in mechanical structural systems external noise can not only lead to quantitative changes in the system dynamics (that is obvious), but also cause the qualitative, and sometimes surprising changes in the vibration regimes. Furthermore, we show that scenarios of the transition from regular to chaotic regimes quantified by Fast Fourier Transform (FFT) can lead to erroneous conclusions, and a support of the wavelet analysis is needed. We have detected and illustrated the modifications of classical three scenarios of transition from regular vibrations to deterministic chaos. The carried out numerical experiment shows that the white noise lowers the threshold for transition into spatio-temporal chaotic dynamics. A transition into chaos via the proposed modified scenarios developed in this work is sensitive to small noise and significantly reduces occurrence of periodic vibrations. Increase of noise intensity yields decrease of the duration of the laminar signal range, i.e., time between two successive turbulent bursts decreases. Scenario of transition into chaos of the studied mechanical structures essentially depends on the control parameters, and it can be different in different zones of the constructed charts (control parameter planes). Furthermore, we found an interesting phenomenon, when increase of the noise intensity yields surprisingly the vibrational characteristics with a lack of noisy effect (chaos is destroyed by noise and windows of periodicity appear).
Multifractal chaotic attractors in a system of delay-differential equations modeling road traffic.
Safonov, Leonid A.; Tomer, Elad; Strygin, Vadim V.; Ashkenazy, Yosef; Havlin, Shlomo
2002-12-01
We study a system of delay-differential equations modeling single-lane road traffic. The cars move in a closed circuit and the system's variables are each car's velocity and the distance to the car ahead. For low and high values of traffic density the system has a stable equilibrium solution, corresponding to the uniform flow. Gradually decreasing the density from high to intermediate values we observe a sequence of supercritical Hopf bifurcations forming multistable limit cycles, corresponding to flow regimes with periodically moving traffic jams. Using an asymptotic technique we find approximately small limit cycles born at Hopf bifurcations and numerically preform their global continuations with decreasing density. For sufficiently large delay the system passes to chaos following the Ruelle-Takens-Newhouse scenario (limit cycles-two-tori-three-tori-chaotic attractors). We find that chaotic and nonchaotic attractors coexist for the same parameter values and that chaotic attractors have a broad multifractal spectrum. (c) 2002 American Institute of Physics.
Transport, mixing and stretching in a chaotic Stokes flow: The two-roll mill
International Nuclear Information System (INIS)
Kaper, T.J.; Wiggins, S.
1989-01-01
We present the outline and preliminary results of an analytical and numerical study of transport, mixing, and stretching in a chaotic Stokes' flow in a two-roll mill apparatus. We use the theory of dynamical systems to describe the rich behavior and structure exhibited by these flows. The main features are the homoclinic tangle which functions as the backbone of the chaotic mixing region, the Smale horseshoe, and the island chains. We then use our detailed knowledge of these structures to develop a theory of transport and stretching of fluid in the chaotic regime. In particular, we show how a specific set of tools for adiabatic chaos- the adiabatic Melnikov function lobe area and flux computations and the adiabatic switching method is ideally suited to develop this theory of transport, mixing and stretching in time-dependent two-dimensional Stokes' flows. 19 refs., 8 figs
Chaotic Traversal (CHAT): Very Large Graphs Traversal Using Chaotic Dynamics
Changaival, Boonyarit; Rosalie, Martin; Danoy, Grégoire; Lavangnananda, Kittichai; Bouvry, Pascal
2017-12-01
Graph Traversal algorithms can find their applications in various fields such as routing problems, natural language processing or even database querying. The exploration can be considered as a first stepping stone into knowledge extraction from the graph which is now a popular topic. Classical solutions such as Breadth First Search (BFS) and Depth First Search (DFS) require huge amounts of memory for exploring very large graphs. In this research, we present a novel memoryless graph traversal algorithm, Chaotic Traversal (CHAT) which integrates chaotic dynamics to traverse large unknown graphs via the Lozi map and the Rössler system. To compare various dynamics effects on our algorithm, we present an original way to perform the exploration of a parameter space using a bifurcation diagram with respect to the topological structure of attractors. The resulting algorithm is an efficient and nonresource demanding algorithm, and is therefore very suitable for partial traversal of very large and/or unknown environment graphs. CHAT performance using Lozi map is proven superior than the, commonly known, Random Walk, in terms of number of nodes visited (coverage percentage) and computation time where the environment is unknown and memory usage is restricted.
Characterization of chaotic electroconvection near flat electrodes under oscillatory voltages
Kim, Jeonglae; Davidson, Scott; Mani, Ali
2017-11-01
Onset of hydrodynamic instability and chaotic electroconvection in aqueous systems are studied by directly solving the two-dimensional coupled Poisson-Nernst-Planck and Navier-Stokes equations. An aqueous binary electrolyte is bounded by two planar electrodes where time-harmonic voltage is applied at a constant oscillation frequency. The governing equations are solved using a fully-conservative second-order-accurate finite volume discretization and a second-order implicit Euler time advancement. At a sufficiently high amplitude of applied voltage, the system exhibits chaotic behaviors involving strong hydrodynamic mixing and enhanced electroconvection. The system responses are characterized as a function of oscillation frequency, voltage magnitude, and the ratio of diffusivities of two ion species. Our results indicate that electroconvection is most enhanced for frequencies on the order of inverse system RC time scale. We will discuss the dependence of this optimal frequency on the asymmetry of the diffusion coefficients of ionic species. Supported by the Stanford's Precourt Institute.
Gross-Pitaevski map as a chaotic dynamical system.
Guarneri, Italo
2017-03-01
The Gross-Pitaevski map is a discrete time, split-operator version of the Gross-Pitaevski dynamics in the circle, for which exponential instability has been recently reported. Here it is studied as a classical dynamical system in its own right. A systematic analysis of Lyapunov exponents exposes strongly chaotic behavior. Exponential growth of energy is then shown to be a direct consequence of rotational invariance and for stationary solutions the full spectrum of Lyapunov exponents is analytically computed. The present analysis includes the "resonant" case, when the free rotation period is commensurate to 2π, and the map has countably many constants of the motion. Except for lowest-order resonances, this case exhibits an integrable-chaotic transition.
Chaotic mixing by microswimmers moving on quasiperiodic orbits
Jalali, Mir Abbas; Khoshnood, Atefeh; Alam, Mohammad-Reza
2015-11-01
Life on the Earth is strongly dependent upon mixing across a vast range of scales. For example, mixing distributes nutrients for microorganisms in aquatic environments, and balances the spatial energy distribution in the oceans and the atmosphere. From industrial point of view, mixing is essential in many microfluidic processes and lab-on-a-chip operations, polymer engineering, pharmaceutics, food engineering, petroleum engineering, and biotechnology. Efficient mixing, typically characterized by chaotic advection, is hard to achieve in low Reynolds number conditions because of the linear nature of the Stokes equation that governs the motion. We report the first demonstration of chaotic mixing induced by a microswimmer that strokes on quasiperiodic orbits with multi-loop turning paths. Our findings can be utilized to understand the interactions of microorganisms with their environments, and to design autonomous robotic mixers that can sweep and mix an entire volume of complex-geometry containers.
Chaotic Patterns in Aeroelastic Signals
Directory of Open Access Journals (Sweden)
F. D. Marques
2009-01-01
patterns. With the reconstructed state spaces, qualitative analyses may be done, and the attractors evolutions with parametric variation are presented. Overall results reveal complex system dynamics associated with highly separated flow effects together with nonlinear coupling between aeroelastic modes. Bifurcations to the nonlinear aeroelastic system are observed for two investigations, that is, considering oscillations-induced aeroelastic evolutions with varying freestream speed, and aeroelastic evolutions at constant freestream speed and varying oscillations. Finally, Lyapunov exponent calculation is proceeded in order to infer on chaotic behavior. Poincaré mappings also suggest bifurcations and chaos, reinforced by the attainment of maximum positive Lyapunov exponents.
Chaotic bursting in semiconductor lasers
Ruschel, Stefan; Yanchuk, Serhiy
2017-11-01
We investigate the dynamic mechanisms for low frequency fluctuations in semiconductor lasers subjected to delayed optical feedback, using the Lang-Kobayashi model. This system of delay differential equations displays pronounced envelope dynamics, ranging from erratic, so called low frequency fluctuations to regular pulse packages, if the time scales of fast oscillations and envelope dynamics are well separated. We investigate the parameter regions where low frequency fluctuations occur and compute their Lyapunov spectra. Using the geometric singular perturbation theory, we study this intermittent chaotic behavior and characterize these solutions as bursting slow-fast oscillations.
Chaotic fluctuations in mathematical economics
Energy Technology Data Exchange (ETDEWEB)
Yoshida, Hiroyuki, E-mail: yoshida.hiroyuki@nihon-u.ac.jp [College of Economics, Nihon University, Chiyoda-ku, Tokyo 101-8360 (Japan)
2011-03-01
In this paper we examine a Cournot duopoly model, which expresses the strategic interaction between two firms. We formulate the dynamic adjustment process and investigate the dynamic properties of the stationary point. By introducing a memory mechanism characterized by distributed lag functions, we presuppose that each firm makes production decisions in a cautious manner. This implies that we have to deal with the system of integro-differential equations. By means of numerical simulations we show the occurrence of chaotic fluctuations in the case of fixed delays.
International Nuclear Information System (INIS)
Chien, T.-I.; Liao, T.-L.
2005-01-01
This paper presents a secure digital communication system based on chaotic modulation, cryptography, and chaotic synchronization techniques. The proposed system consists of a Chaotic Modulator (CM), a Chaotic Secure Transmitter (CST), a Chaotic Secure Receiver (CSR) and a Chaotic Demodulator (CDM). The CM module incorporates a chaotic system and a novel Chaotic Differential Peaks Keying (CDPK) modulation scheme to generate analog patterns corresponding to the input digital bits. The CST and CSR modules are designed such that a single scalar signal is transmitted in the public channel. Furthermore, by giving certain structural conditions of a particular class of chaotic system, the CST and the nonlinear observer-based CSR with an appropriate observer gain are constructed to synchronize with each other. These two slave systems are driven simultaneously by the transmitted signal and are designed to synchronize and generate appropriate cryptography keys for encryption and decryption purposes. In the CDM module, a nonlinear observer is designed to estimate the chaotic modulating system in the CM. A demodulation mechanism is then applied to decode the transmitted input digital bits. The effectiveness of the proposed scheme is demonstrated through the numerical simulation of an illustrative communication system. Synchronization between the chaotic circuits of the transmitter and receiver modules is guaranteed through the Lyapunov stability theorem. Finally, the security features of the proposed system in the event of attack by an intruder in either the time domain or the frequency domain are discussed
Theory and practice of chaotic cryptography
International Nuclear Information System (INIS)
Amigo, J.M.; Kocarev, L.; Szczepanski, J.
2007-01-01
In this Letter we address some basic questions about chaotic cryptography, not least the very definition of chaos in discrete systems. We propose a conceptual framework and illustrate it with different examples from private and public key cryptography. We elaborate also on possible limits of chaotic cryptography
Synchronization of Time-Continuous Chaotic Oscillators
DEFF Research Database (Denmark)
Yanchuk, S.; Maistrenko, Yuri; Mosekilde, Erik
2003-01-01
Considering a system of two coupled identical chaotic oscillators, the paper first establishes the conditions of transverse stability for the fully synchronized chaotic state. Periodic orbit threshold theory is applied to determine the bifurcations through which low-periodic orbits embedded...
Synthesizing chaotic maps with prescribed invariant densities
International Nuclear Information System (INIS)
Rogers, Alan; Shorten, Robert; Heffernan, Daniel M.
2004-01-01
The Inverse Frobenius-Perron Problem (IFPP) concerns the creation of discrete chaotic mappings with arbitrary invariant densities. In this Letter, we present a new and elegant solution to the IFPP, based on positive matrix theory. Our method allows chaotic maps with arbitrary piecewise-constant invariant densities, and with arbitrary mixing properties, to be synthesized
Repetitive learning control of continuous chaotic systems
International Nuclear Information System (INIS)
Chen Maoyin; Shang Yun; Zhou Donghua
2004-01-01
Combining a shift method and the repetitive learning strategy, a repetitive learning controller is proposed to stabilize unstable periodic orbits (UPOs) within chaotic attractors in the sense of least mean square. If nonlinear parts in chaotic systems satisfy Lipschitz condition, the proposed controller can be simplified into a simple proportional repetitive learning controller
A Hybrid Chaotic Quantum Evolutionary Algorithm
DEFF Research Database (Denmark)
Cai, Y.; Zhang, M.; Cai, H.
2010-01-01
A hybrid chaotic quantum evolutionary algorithm is proposed to reduce amount of computation, speed up convergence and restrain premature phenomena of quantum evolutionary algorithm. The proposed algorithm adopts the chaotic initialization method to generate initial population which will form a pe...... tests. The presented algorithm is applied to urban traffic signal timing optimization and the effect is satisfied....
Approximating chaotic saddles for delay differential equations.
Taylor, S Richard; Campbell, Sue Ann
2007-04-01
Chaotic saddles are unstable invariant sets in the phase space of dynamical systems that exhibit transient chaos. They play a key role in mediating transport processes involving scattering and chaotic transients. Here we present evidence (long chaotic transients and fractal basins of attraction) of transient chaos in a "logistic" delay differential equation. We adapt an existing method (stagger-and-step) to numerically construct the chaotic saddle for this system. This is the first such analysis of transient chaos in an infinite-dimensional dynamical system, and in delay differential equations in particular. Using Poincaré section techniques we illustrate approaches to visualizing the saddle set, and confirm that the saddle has the Cantor-like fractal structure consistent with a chaotic saddle generated by horseshoe-type dynamics.
Approximating chaotic saddles for delay differential equations
Taylor, S. Richard; Campbell, Sue Ann
2007-04-01
Chaotic saddles are unstable invariant sets in the phase space of dynamical systems that exhibit transient chaos. They play a key role in mediating transport processes involving scattering and chaotic transients. Here we present evidence (long chaotic transients and fractal basins of attraction) of transient chaos in a “logistic” delay differential equation. We adapt an existing method (stagger-and-step) to numerically construct the chaotic saddle for this system. This is the first such analysis of transient chaos in an infinite-dimensional dynamical system, and in delay differential equations in particular. Using Poincaré section techniques we illustrate approaches to visualizing the saddle set, and confirm that the saddle has the Cantor-like fractal structure consistent with a chaotic saddle generated by horseshoe-type dynamics.
Investigation of a chaotic thermostat
Morales, G. J.
2018-03-01
A numerical study is presented of a free particle interacting with a deterministic thermostat in which the usual friction force is supplemented with a fluctuating force that depends on the self-consistent damping coefficient associated with coupling to the heat bath. It is found that this addition results in a chaotic environment in which a particle self-heats from rest and moves in positive and negative directions, exhibiting a characteristic diffusive behavior. The frequency power spectrum of the dynamical quantities displays the exponential frequency dependence ubiquitous to chaotic dynamics. The velocity distribution function approximates a Maxwellian distribution, but it does show departures from perfect thermal equilibrium, while the distribution function for the damping coefficient shows a closer fit. The behavior for the classic Nosé-Hoover (NH) thermostat is compared to that of the enlarged Martyna-Klein-Tuckerman (MKT) model. Over a narrow amplitude range, the application of a constant external force results quantitatively in the Einstein relation for the NH thermostat, and for the MKT model it differs by a factor of 2.
Hybrid chaotic ant swarm optimization
International Nuclear Information System (INIS)
Li Yuying; Wen Qiaoyan; Li Lixiang; Peng Haipeng
2009-01-01
Chaotic ant swarm optimization (CASO) is a powerful chaos search algorithm that is used to find the global optimum solution in search space. However, the CASO algorithm has some disadvantages, such as lower solution precision and longer computational time, when solving complex optimization problems. To resolve these problems, an improved CASO, called hybrid chaotic swarm optimization (HCASO), is proposed in this paper. The new algorithm introduces preselection operator and discrete recombination operator into the CASO; meanwhile it replaces the best position found by own and its neighbors' ants with the best position found by preselection operator and discrete recombination operator in evolution equation. Through testing five benchmark functions with large dimensionality, the experimental results show the new method enhances the solution accuracy and stability greatly, as well as reduces the computational time and computer memory significantly when compared to the CASO. In addition, we observe the results can become better with swarm size increasing from the sensitivity study to swarm size. And we gain some relations between problem dimensions and swam size according to scalability study.
Chaotic Transport in Circumterrestrial Orbits
Rosengren, Aaron Jay
2018-04-01
The slow deformation of circumterrestrial orbits in the medium region, subject to lunisolar secular resonances, is well approximated by a Hamiltonian system with 2.5 degrees of freedom. This dynamical model is referred to in the astrophysical and celestial dynamics communities as the quadrupolar, secular, hierarchical three-body problem, and, in the non-autonomous case, gives rise to the classical Kozai-Lidov mechanism. In the time-dependent model, brought about in our case by the Moon's perturbed motion, the action variables of the system may experience chaotic variations and large drifts due to the possible overlap of nearby resonances. Using variational chaos indicators, we compute high-resolution portraits of the action space, revealing the existence of tori and structures filling chaotic regions. Our refined and elaborate calculations allow us to isolate precise initial conditions near specific areas of interest and to study their asymptotic behavior in time. We highlight in particular how the drift in phase space is mediated by the complement of the numerically detected KAM tori. Despite their reputed normality, Earth satellite orbits can possess an extraordinarily rich spectrum of dynamical behaviors, and, like the small body remnants of Solar system formation, they have all the complications that make them very interesting candidates for testing the modern tools of chaos theory.
Light Management in Optoelectronic Devices with Disordered and Chaotic Structures
Khan, Yasser
2012-07-01
With experimental realization, energy harvesting capabilities of chaotic microstructures were explored. Incident photons falling into chaotic trajectories resulted in energy buildup for certain frequencies. As a consequence, many fold enhancement in light trapping was observed. These ellipsoid like chaotic microstructures demonstrated 25% enhancement in light trapping at 450nm excitation and 15% enhancement at 550nm excitation. Optimization of these structures can drive novel chaos-assisted energy harvesting systems. In subsequent sections of the thesis, prospect of broadband light extraction from white light emitting diodes were investigated, which is an unchallenged but quintessential problem in solid-state lighting. Size dependent scattering allows microstructures to interact strongly with narrow-band light. If disorder is introduced in spread and sizes of microstructures, broadband light extraction is possible. A novel scheme with Voronoi tessellation to quantify disorder in physical systems was also introduced, and a link between voronoi disorder and state disorder of statistical mechanics was established. Overall, in this thesis some nascent concepts regarding disorder and chaos were investigated to efficiently manage electromagnetic waves in optoelectronic devices.
Evidence for bifurcation and universal chaotic behavior in nonlinear semiconducting devices
International Nuclear Information System (INIS)
Testa, J.; Perez, J.; Jeffries, C.
1982-01-01
Bifurcations, chaos, and extensive periodic windows in the chaotic regime are observed for a driven LRC circuit, the capacitive element being a nonlinear varactor diode. Measurements include power spectral analysis; real time amplitude data; phase portraits; and a bifurcation diagram, obtained by sampling methods. The effects of added external noise are studied. These data yield experimental determinations of several of the universal numbers predicted to characterize nonlinear systems having this route to chaos
On dynamics analysis of a new chaotic attractor
International Nuclear Information System (INIS)
Zhou Wuneng; Xu Yuhua; Lu Hongqian; Pan Lin
2008-01-01
In this Letter, a new chaotic system is discussed. Some basic dynamical properties, such as Lyapunov exponents, Poincare mapping, fractal dimension, bifurcation diagram, continuous spectrum and chaotic dynamical behaviors of the new chaotic system are studied, either numerically or analytically. The obtained results show clearly that the system discussed in this Letter is a new chaotic system and deserves a further detailed investigation
Regular transport dynamics produce chaotic travel times.
Villalobos, Jorge; Muñoz, Víctor; Rogan, José; Zarama, Roberto; Johnson, Neil F; Toledo, Benjamín; Valdivia, Juan Alejandro
2014-06-01
In the hope of making passenger travel times shorter and more reliable, many cities are introducing dedicated bus lanes (e.g., Bogota, London, Miami). Here we show that chaotic travel times are actually a natural consequence of individual bus function, and hence of public transport systems more generally, i.e., chaotic dynamics emerge even when the route is empty and straight, stops and lights are equidistant and regular, and loading times are negligible. More generally, our findings provide a novel example of chaotic dynamics emerging from a single object following Newton's laws of motion in a regularized one-dimensional system.
Chaotic inflation in models with flat directions
International Nuclear Information System (INIS)
Graziani, F.; Olive, K.
1989-01-01
We consider the chaotic inflationary scenario in models with flat directions. We find that unless the scalars along the flat directions have vacuum expectation values p or 10 14 M p 15 M p depending on the expectation values of the chaotic inflator, Ψ, one or two or more periods of inflation occur but with a resulting energy density perturbation δρ/ρ ≅ 10 -16 , far too small to be of any consequence for galaxy formation. Even with p only limited initial values of ≅ (3-200) M p result in inflation with reasonable density perturbations. Thus chaotic inflation in models with flat directions require rather special initial conditions. (orig.)
International Nuclear Information System (INIS)
Ahmadi, Mohamadreza; Mojallali, Hamed
2012-01-01
Highlights: ► A new meta-heuristic optimization algorithm. ► Integration of invasive weed optimization and chaotic search methods. ► A novel parameter identification scheme for chaotic systems. - Abstract: This paper introduces a novel hybrid optimization algorithm by taking advantage of the stochastic properties of chaotic search and the invasive weed optimization (IWO) method. In order to deal with the weaknesses associated with the conventional method, the proposed chaotic invasive weed optimization (CIWO) algorithm is presented which incorporates the capabilities of chaotic search methods. The functionality of the proposed optimization algorithm is investigated through several benchmark multi-dimensional functions. Furthermore, an identification technique for chaotic systems based on the CIWO algorithm is outlined and validated by several examples. The results established upon the proposed scheme are also supplemented which demonstrate superior performance with respect to other conventional methods.
International Nuclear Information System (INIS)
Goussev, Arseni; Waltner, Daniel; Richter, Klaus; Jalabert, Rodolfo A
2008-01-01
We address the sensitivity of quantum mechanical time evolution by considering the time decay of the Loschmidt echo (LE) (or fidelity) for local perturbations of the Hamiltonian. Within a semiclassical approach, we derive analytical expressions for the LE decay for chaotic systems for the whole range from weak to strong local perturbations and identify different decay regimes which complement those known for the case of global perturbations. For weak perturbations, a Fermi-golden-rule (FGR)-type behavior is recovered. For strong perturbations, the escape-rate regime is reached, where the LE decays exponentially with a rate independent of the perturbation strength. The transition between the FGR regime and the escape-rate regime is non-monotonic, i.e. the rate of the exponential time-decay of the LE oscillates as a function of the perturbation strength. We further perform extensive quantum mechanical calculations of the LE based on numerical wave packet evolution, which strongly support our semiclassical theory. Finally, we discuss in some detail possible experimental realizations for observing the predicted behavior of the LE
Chaotic radiation/turbulence interactions in flames
Energy Technology Data Exchange (ETDEWEB)
Menguec, M.P.; McDonough, J.M.
1998-11-01
In this paper, the authors present a review of their recent efforts to model chaotic radiation-turbulence interactions in flames. The main focus is to characterize soot volume fraction fluctuations in turbulent diffusion flames, as they strongly contribute to these interaction. The approach is based on the hypothesis that the fluctuations of properties in turbulent flames are deterministic in nature, rather than random. The authors first discuss the theoretical details and then they briefly outline the experiments conducted to measure the scattered light signals from fluctuating soot particles along the axis of an ethylene-air diffusion flame. They compare the power spectra and time series obtained from experiments against the ad-hoc and rigorous models derived using a series of logistic maps. These logistic maps can be used in simulation of the fluctuations in these type of flames, without extensive computational effort or sacrifice of physical detail. Availability of accurate models of these kinds allows investigation of radiation-turbulence interactions at a more fundamental level than it was previously possible.
Basko, D M
2014-02-01
We study the discrete nonlinear Schröinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved but, on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density ρ satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, D(ρ) = D(0)ρ(2). An explicit expression for D(0) is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed.
Characterization of chaotic dynamics in the human menstrual cycle
Derry, Gregory; Derry, Paula
2010-03-01
The human menstrual cycle exhibits much unexplained variability, which is typically dismissed as random variation. Given the many delayed nonlinear feedbacks in the reproductive endocrine system, however, the menstrual cycle might well be a nonlinear dynamical system in a chaotic trajectory, and that this instead accounts for the observed variability. Here, we test this hypothesis by performing a time series analysis on data for 7438 menstrual cycles from 38 women in the 20-40 year age range, using the database maintained by the Tremin Research Program on Women's Health. Using phase space reconstruction techniques with a maximum embedding dimension of 6, we find appropriate scaling behavior in the correlation sums for this data, indicating low dimensional deterministic dynamics. A correlation dimension of 2.6 is measured in this scaling regime, and this result is confirmed by recalculation using the Takens estimator. These results may be interpreted as offering an approximation to the fractal dimension of a strange attractor governing the chaotic dynamics of the menstrual cycle.
Controlling chaotic behavior in CO2 and other lasers
1993-06-01
Additional substantial experimental progress has been made, in the third month of the project, in setting up equipment and testing for producing chaotic behavior with a CO2 laser. The project goal is to synchronize and control chaos in CO2 and other lasers, and thereby increase the power in ensembles of coupled laser sources. Numerous investigations into the chaos regime have been made, a second CO2 laser has been brought on stream, and work is progressing in the fourth month toward coupling the two lasers and control of the first laser. It is also intended to submit at least two papers to the Second Experimental Chaos Conference which is supported by the Office of Naval Research. Abstracts to those two papers are attached. Last month's report discussed the experimental investigation of nonlinear dynamics of CO2 lasers which involved a new technique of inducing chaos. In this new technique, an acoustically modulated feedback of the laser light was used and led to chaotic dynamics at a very low modulation frequency of 375 Hz. Since then, new results have been obtained by an Electro-Optical Modulation (EOM) technique. In the new setup, the electro-optical modulator is placed in an external cavity outside the laser.
Bifurcation Control of Chaotic Dynamical Systems
National Research Council Canada - National Science Library
Wang, Hua O; Abed, Eyad H
1992-01-01
A nonlinear system which exhibits bifurcations, transient chaos, and fully developed chaos is considered, with the goal of illustrating the role of two ideas in the control of chaotic dynamical systems...
Prediction and Geometry of Chaotic Time Series
National Research Council Canada - National Science Library
Leonardi, Mary
1997-01-01
This thesis examines the topic of chaotic time series. An overview of chaos, dynamical systems, and traditional approaches to time series analysis is provided, followed by an examination of state space reconstruction...
Encryption in Chaotic Systems with Sinusoidal Excitations
Directory of Open Access Journals (Sweden)
G. Obregón-Pulido
2014-01-01
Full Text Available In this contribution an encryption method using a chaotic oscillator, excited by “n” sinusoidal signals, is presented. The chaotic oscillator is excited by a sum of “n” sinusoidal signals and a message. The objective is to encrypt such a message using the chaotic behavior and transmit it, and, as the chaotic system is perturbed by the sinusoidal signal, the transmission security could be increased due to the effect of such a perturbation. The procedure is based on the regulation theory and consider that the receiver knows the frequencies of the perturbing signal, with this considerations the algorithm estimates the excitation in such a way that the receiver can cancel out the perturbation and all the undesirable dynamics in order to produce only the message. In this way we consider that the security level is increased.
Chaotic Zones around Rotating Small Bodies
Energy Technology Data Exchange (ETDEWEB)
Lages, José; Shevchenko, Ivan I. [Institut UTINAM, Observatoire des Sciences de l’Univers THETA, CNRS, Université de Franche-Comté, Besançon F-25030 (France); Shepelyansky, Dima L., E-mail: jose.lages@utinam.cnrs.fr [Laboratoire de Physique Théorique du CNRS, IRSAMC, Université de Toulouse, UPS, Toulouse F-31062 (France)
2017-06-01
Small bodies of the solar system, like asteroids, trans-Neptunian objects, cometary nuclei, and planetary satellites, with diameters smaller than 1000 km usually have irregular shapes, often resembling dumb-bells or contact binaries. The spinning of such a gravitating dumb-bell creates around it a zone of chaotic orbits. We determine its extent analytically and numerically. We find that the chaotic zone swells significantly if the rotation rate is decreased; in particular, the zone swells more than twice if the rotation rate is decreased 10 times with respect to the “centrifugal breakup” threshold. We illustrate the properties of the chaotic orbital zones in examples of the global orbital dynamics about asteroid 243 Ida (which has a moon, Dactyl, orbiting near the edge of the chaotic zone) and asteroid 25143 Itokawa.
Nonlinear chaotic model for predicting storm surges
Directory of Open Access Journals (Sweden)
M. Siek
2010-09-01
Full Text Available This paper addresses the use of the methods of nonlinear dynamics and chaos theory for building a predictive chaotic model from time series. The chaotic model predictions are made by the adaptive local models based on the dynamical neighbors found in the reconstructed phase space of the observables. We implemented the univariate and multivariate chaotic models with direct and multi-steps prediction techniques and optimized these models using an exhaustive search method. The built models were tested for predicting storm surge dynamics for different stormy conditions in the North Sea, and are compared to neural network models. The results show that the chaotic models can generally provide reliable and accurate short-term storm surge predictions.
Indirect adaptive control of discrete chaotic systems
International Nuclear Information System (INIS)
Salarieh, Hassan; Shahrokhi, Mohammad
2007-01-01
In this paper an indirect adaptive control algorithm is proposed to stabilize the fixed points of discrete chaotic systems. It is assumed that the functionality of the chaotic dynamics is known but the system parameters are unknown. This assumption is usually applicable to many chaotic systems, such as the Henon map, logistic and many other nonlinear maps. Using the recursive-least squares technique, the system parameters are identified and based on the feedback linearization method an adaptive controller is designed for stabilizing the fixed points, or unstable periodic orbits of the chaotic maps. The stability of the proposed scheme has been shown and the effectiveness of the control algorithm has been demonstrated through computer simulations
Globally Coupled Chaotic Maps with Constant Force
International Nuclear Information System (INIS)
Li Jinghui
2008-01-01
We investigate the motion of the globally coupled maps (logistic map) with a constant force. It is shown that the constant force can cause multi-synchronization for the globally coupled chaotic maps studied by us.
Multiswitching compound antisynchronization of four chaotic systems
Indian Academy of Sciences (India)
Ayub Khan
2017-11-28
Nov 28, 2017 ... systems, electrical engineering, information process- ... model. The synchronization problem among three or more chaotic ...... we perform numerical simulations in MATLAB using ... In the simulation process we assume α1 =.
Experimental realization of a highly secure chaos communication under strong channel noise
International Nuclear Information System (INIS)
Ye Weiping; Dai Qionglin; Wang Shihong; Lu Huaping; Kuang Jinyu; Zhao Zhenfeng; Zhu Xiangqing; Tang Guoning; Huang Ronghuai; Hu Gang
2004-01-01
A one-way coupled spatiotemporally chaotic map lattice is used to construct cryptosystem. With the combinatorial applications of both chaotic computations and conventional algebraic operations, our system has optimal cryptographic properties much better than the separative applications of known chaotic and conventional methods. We have realized experiments to practice duplex voice secure communications in realistic Wired Public Switched Telephone Network by applying our chaotic system and the system of Advanced Encryption Standard (AES), respectively, for cryptography. Our system can work stably against strong channel noise when AES fails to work
Experimental realization of a highly secure chaos communication under strong channel noise
Ye, Weiping; Dai, Qionglin; Wang, Shihong; Lu, Huaping; Kuang, Jinyu; Zhao, Zhenfeng; Zhu, Xiangqing; Tang, Guoning; Huang, Ronghuai; Hu, Gang
2004-09-01
A one-way coupled spatiotemporally chaotic map lattice is used to construct cryptosystem. With the combinatorial applications of both chaotic computations and conventional algebraic operations, our system has optimal cryptographic properties much better than the separative applications of known chaotic and conventional methods. We have realized experiments to practice duplex voice secure communications in realistic Wired Public Switched Telephone Network by applying our chaotic system and the system of Advanced Encryption Standard (AES), respectively, for cryptography. Our system can work stably against strong channel noise when AES fails to work.
Chaotic dynamics in nanoscale NbO2 Mott memristors for analogue computing
Kumar, Suhas; Strachan, John Paul; Williams, R. Stanley
2017-08-01
At present, machine learning systems use simplified neuron models that lack the rich nonlinear phenomena observed in biological systems, which display spatio-temporal cooperative dynamics. There is evidence that neurons operate in a regime called the edge of chaos that may be central to complexity, learning efficiency, adaptability and analogue (non-Boolean) computation in brains. Neural networks have exhibited enhanced computational complexity when operated at the edge of chaos, and networks of chaotic elements have been proposed for solving combinatorial or global optimization problems. Thus, a source of controllable chaotic behaviour that can be incorporated into a neural-inspired circuit may be an essential component of future computational systems. Such chaotic elements have been simulated using elaborate transistor circuits that simulate known equations of chaos, but an experimental realization of chaotic dynamics from a single scalable electronic device has been lacking. Here we describe niobium dioxide (NbO2) Mott memristors each less than 100 nanometres across that exhibit both a nonlinear-transport-driven current-controlled negative differential resistance and a Mott-transition-driven temperature-controlled negative differential resistance. Mott materials have a temperature-dependent metal-insulator transition that acts as an electronic switch, which introduces a history-dependent resistance into the device. We incorporate these memristors into a relaxation oscillator and observe a tunable range of periodic and chaotic self-oscillations. We show that the nonlinear current transport coupled with thermal fluctuations at the nanoscale generates chaotic oscillations. Such memristors could be useful in certain types of neural-inspired computation by introducing a pseudo-random signal that prevents global synchronization and could also assist in finding a global minimum during a constrained search. We specifically demonstrate that incorporating such
Synchronizing a class of uncertain chaotic systems
International Nuclear Information System (INIS)
Chen Maoyin; Zhou Donghua; Shang Yun
2005-01-01
This Letter deals with the synchronization of a class of uncertain chaotic systems in the drive-response framework. A robust adaptive observer based response system is designed to synchronize a given chaotic system with unknown parameters and external disturbances. Lyapunov stability ensures the global synchronization between the drive and response systems even if Lipschitz constants on function matrices and bounds on uncertainties are unknown. Numerical simulation of Genesio-Tesi system verifies the effectiveness of this scheme
Anti-synchronization of chaotic oscillators
International Nuclear Information System (INIS)
Kim, Chil-Min; Rim, Sunghwan; Kye, Won-Ho; Ryu, Jung-Wan; Park, Young-Jai
2003-01-01
We have observed anti-synchronization phenomena in coupled identical chaotic oscillators. Anti-synchronization can be characterized by the vanishing of the sum of relevant variables. We have qualitatively analyzed its base mechanism by using the dynamics of the difference and the sum of the relevant variables in coupled chaotic oscillators. Near the threshold of the synchronization and anti-synchronization transition, we have obtained the novel characteristic relation
Design of Threshold Controller Based Chaotic Circuits
DEFF Research Database (Denmark)
Mohamed, I. Raja; Murali, K.; Sinha, Sudeshna
2010-01-01
We propose a very simple implementation of a second-order nonautonomous chaotic oscillator, using a threshold controller as the only source of nonlinearity. We demonstrate the efficacy and simplicity of our design through numerical and experimental results. Further, we show that this approach...... of using a threshold controller as a nonlinear element, can be extended to obtain autonomous and multiscroll chaotic attractor circuits as well....
Improvement on generalised synchronisation of chaotic systems
International Nuclear Information System (INIS)
Hui-Bin, Zhu; Fang, Qiu; Bao-Tong, Cui
2010-01-01
In this paper, the problem of generalised synchronisation of two different chaotic systems is investigated. Some less conservative conditions are derived using linear matrix inequality other than existing results. Furthermore, a simple adaptive control scheme is proposed to achieve the generalised synchronisation of chaotic systems. The proposed method is simple and easy to implement in practice and can be applied to secure communications. Numerical simulations are also given to demonstrate the effectiveness and feasibility of the theoretical analysis
Cryptographic pseudo-random sequence from the spatial chaotic map
International Nuclear Information System (INIS)
Sun Fuyan; Liu Shutang
2009-01-01
A scheme for pseudo-random binary sequence generation based on the spatial chaotic map is proposed. In order to face the challenge of using the proposed PRBS in cryptography, the proposed PRBS is subjected to statistical tests which are the well-known FIPS-140-1 in the area of cryptography, and correlation properties of the proposed sequences are investigated. The proposed PRBS successfully passes all these tests. Results of statistical testing of the sequences are found encouraging. The results of statistical tests suggest strong candidature for cryptographic applications.
Mixed synchronization in chaotic oscillators using scalar coupling
Energy Technology Data Exchange (ETDEWEB)
Bhowmick, Sourav K.; Hens, Chittaranjan [CSIR – Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032 (India); Ghosh, Dibakar, E-mail: drghosh_math@yahoo.co.in [Department of Mathematics, University of Kalyani, West Bengal 741235 (India); Dana, Syamal K. [CSIR – Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032 (India)
2012-07-23
We report experimental evidence of mixed synchronization in two unidirectionally coupled chaotic oscillators using a scalar coupling. In this synchronization regime, some of the state variables may be in complete synchronization while others may be in anti-synchronization state. We extended the theory by using an adaptive controller with an updating law based on Lyapunov function stability to include parameter fluctuation. Using the scheme, we implemented a cryptographic encoding for digital signal through parameter modulation. -- Highlights: ► We provided experimental evidence of the mixed synchronization scheme while other methods are mostly theoretical nature. ► We numerically studied adaptive mixed synchronization when the parameters are not completely known using scalar coupling. ► We proposed a secure communication system where three digital messages are transmitted using parameter modulation.
Generalized synchronization in discrete maps. New point of view on weak and strong synchronization
International Nuclear Information System (INIS)
Koronovskii, Alexey A.; Moskalenko, Olga I.; Shurygina, Svetlana A.; Hramov, Alexander E.
2013-01-01
In the present Letter we show that the concept of the generalized synchronization regime in discrete maps needs refining in the same way as it has been done for the flow systems Koronovskii et al. [Koronovskii AA, Moskalenko OI, Hramov AE. Nearest neighbors, phase tubes, and generalized synchronization. Phys Rev E 2011;84:037201]. We have shown that, in the general case, when the relationship between state vectors of the interacting chaotic maps are considered, the prehistory must be taken into account. We extend the phase tube approach to the systems with a discrete time coupled both unidirectionally and mutually and analyze the essence of the generalized synchronization by means of this technique. Obtained results show that the division of the generalized synchronization into the weak and the strong ones also must be reconsidered. Unidirectionally coupled logistic maps and Hénon maps coupled mutually are used as sample systems.
Improved chaotic maps-based password-authenticated key agreement using smart cards
Lin, Han-Yu
2015-02-01
Elaborating on the security of password-based authenticated key agreement, in this paper, the author cryptanalyzes a chaotic maps-based password-authenticated key agreement proposed by Guo and Chang recently. Specifically, their protocol could not achieve strong user anonymity due to a fixed parameter and a malicious adversary is able to derive the shared session key by manipulating the property of Chebyshev chaotic maps. Additionally, the author also presents an improved scheme to eliminate the above weaknesses and still maintain the efficiency.
Universality for the parameter-mismatching effect on weak synchronization in coupled chaotic systems
International Nuclear Information System (INIS)
Lim, Woochang; Kim, Sang-Yoon
2004-01-01
To examine the universality for the parameter-mismatching effect on weak chaotic synchronization, we study coupled multidimensional invertible systems such as the coupled Henon maps and coupled pendula. By generalizing the method proposed in coupled one-dimensional (1D) noninvertible maps, we introduce the parameter sensitivity exponent δ to measure the degree of the parameter sensitivity of a weakly stable synchronous chaotic attractor. In terms of the parameter sensitivity exponents, we characterize the effect of the parameter mismatch on the intermittent bursting and the basin riddling occurring in the regime of weak synchronization. It is thus found that the scaling exponent μ for the average characteristic time (i.e., the average interburst time and the average chaotic transient lifetime) for both the bubbling and riddling cases is given by the reciprocal of the parameter sensitivity exponent, as in the simple system of coupled 1D maps. Hence, the reciprocal relation (i.e., μ = 1/δ) seems to be 'universal', in the sense that it holds in typical coupled chaotic systems of different nature
Anticipating synchronization in a chain of chaotic oscillators with switching parameters
Energy Technology Data Exchange (ETDEWEB)
Pyragienė, T., E-mail: tatjana.pyragiene@ftmc.lt; Pyragas, K.
2015-12-18
A new coupling scheme for anticipating synchronization of chaotic systems is proposed. The scheme consists of a master system and two in series coupled slave systems with periodically switching parameters. The scheme does not require the presence of any time-delay terms either in a master or in slave systems and provides long-term anticipation. The value of anticipation time as well as the conditions of synchronization are derived in an analytical form. Analytical results are tested by numerical experiments with the chaotic Rössler and Lorenz systems as well as the Hindmarsh–Rose neuron in a regime of chaotic bursting. Also a robustness of the scheme with respect to parameter mismatch and noise is demonstrated. - Highlights: • A new coupling scheme for anticipating chaotic synchronization is proposed. • The scheme consists of three coupled systems with periodically switching parameters. • Long-term anticipation is achieved without using time-delay terms. • The method is verified for the Rössler, Lorenz and Hindmarsh–Rose neuron systems.
Anticipating synchronization in a chain of chaotic oscillators with switching parameters
International Nuclear Information System (INIS)
Pyragienė, T.; Pyragas, K.
2015-01-01
A new coupling scheme for anticipating synchronization of chaotic systems is proposed. The scheme consists of a master system and two in series coupled slave systems with periodically switching parameters. The scheme does not require the presence of any time-delay terms either in a master or in slave systems and provides long-term anticipation. The value of anticipation time as well as the conditions of synchronization are derived in an analytical form. Analytical results are tested by numerical experiments with the chaotic Rössler and Lorenz systems as well as the Hindmarsh–Rose neuron in a regime of chaotic bursting. Also a robustness of the scheme with respect to parameter mismatch and noise is demonstrated. - Highlights: • A new coupling scheme for anticipating chaotic synchronization is proposed. • The scheme consists of three coupled systems with periodically switching parameters. • Long-term anticipation is achieved without using time-delay terms. • The method is verified for the Rössler, Lorenz and Hindmarsh–Rose neuron systems.
International Nuclear Information System (INIS)
Wang Xing-Yuan; Bao Xue-Mei
2013-01-01
In this paper, we propose a novel block cryptographic scheme based on a spatiotemporal chaotic system and a chaotic neural network (CNN). The employed CNN comprises a 4-neuron layer called a chaotic neuron layer (CNL), where the spatiotemporal chaotic system participates in generating its weight matrix and other parameters. The spatiotemporal chaotic system used in our scheme is the typical coupled map lattice (CML), which can be easily implemented in parallel by hardware. A 160-bit-long binary sequence is used to generate the initial conditions of the CML. The decryption process is symmetric relative to the encryption process. Theoretical analysis and experimental results prove that the block cryptosystem is secure and practical, and suitable for image encryption. (general)
International Nuclear Information System (INIS)
Frerichs, Heinke Gerd
2010-04-01
The development of nuclear fusion as an alternative energy source requires the research on magnetically confined, high temperature plasmas. In particular, the quantification of plasma flows in the domain near exposed material surfaces of the plasma container by computer simulations is of key importance, both for guiding interpretation of present fusion experiments and for aiding the ongoing design activities for large future devices such as ITER, W7-X or the DEMO reactor. There is a large number of computational issues related to the physics of hot, fully ionized and magnetized plasmas near surfaces of the vacuum chamber. This thesis is dedicated to one particular such challenge, namely the numerical quantification of self-consistent kinetic neutral gas and plasma fluid flows in very complex 3D (partially chaotic) magnetic fields, in the absence of any common symmetries for plasma and neutral gas dynamics. Such magnetic field configurations are e.g. generated by externally applied magnetic perturbations at the plasma edge, and are of great interest for the control of particle and energy exhausts. In the present thesis the 3D edge plasma and neutral particle transport code EMC3-EIRENE is applied to two distinct configurations of open chaotic magnetic system: at the TEXTOR and DIII-D tokamaks. Improvements of the edge transport model and extensions of the transport code are presented, which have allowed such simulations for the first time for 3D scenarios at DIII-D with ITER similar plasmas. A strong 3D effect of the chaotic magnetic field on the DIII-D edge plasma is found and analyzed in detail. It is found that a pronounced striation pattern of target particle and heat fluxes at DIII-D can only be obtained up to a certain upper limiting level of anomalous cross-field transport. Hence, in comparison to experimental data, these findings allow to narrow down the range of this model parameter. One particular interest at TEXTOR is the achievement of a regime with
Spatial chaotic behavior of vortices in type-II superconductors with different pinning strength
International Nuclear Information System (INIS)
Lin, H.-T.; Pan, M.; Cheng, C.H.; Cui, Y.J.; Zhao, Y.
2008-01-01
Spatial chaotic character in systems where defects are arranged in periodic arrays has been investigated by computer simulation. Due to the high nonlinearity of the vortex-defect interaction, arrangement of the vortices in a periodic pinning array can be chaotic (glassy), depending on the vortex-defect interaction state and vortex-vortex interaction. Two types of disordered vortex states in the system are observed. The type-I disorder arises from the intrinsically chaotic nature of the nonlinear system, existing when the pinning disorder is low and the pinning strength is weak. The type-II disordered state is related to the pinning disorder, which is dominating when both the pinning disorder and the pinning strength are strong
Spatial chaotic behavior of vortices in type-II superconductors with different pinning strength
Energy Technology Data Exchange (ETDEWEB)
Lin, H.-T. [Faculty of Information Management, Cheng Shui University, Taiwan (China); Pan, M. [Key Laboratory of Magnetic Levitation Technologies and Maglev Trains, Ministry of Education of China, Superconductivity R and D Center, Southwest Jiaotong University, Chengdu, Sichuan 610031 (China); Cheng, C.H. [Key Laboratory of Magnetic Levitation Technologies and Maglev Trains, Ministry of Education of China, Superconductivity R and D Center, Southwest Jiaotong University, Chengdu, Sichuan 610031 (China); School of Materials Science and Engineering, University of New South Wales, Sydney (Australia); Cui, Y.J. [Key Laboratory of Magnetic Levitation Technologies and Maglev Trains, Ministry of Education of China, Superconductivity R and D Center, Southwest Jiaotong University, Chengdu, Sichuan 610031 (China); Zhao, Y. [Key Laboratory of Magnetic Levitation Technologies and Maglev Trains, Ministry of Education of China, Superconductivity R and D Center, Southwest Jiaotong University, Chengdu, Sichuan 610031 (China); School of Materials Science and Engineering, University of New South Wales, Sydney (Australia)], E-mail: yzhao@swjtu.edu.cn
2008-09-15
Spatial chaotic character in systems where defects are arranged in periodic arrays has been investigated by computer simulation. Due to the high nonlinearity of the vortex-defect interaction, arrangement of the vortices in a periodic pinning array can be chaotic (glassy), depending on the vortex-defect interaction state and vortex-vortex interaction. Two types of disordered vortex states in the system are observed. The type-I disorder arises from the intrinsically chaotic nature of the nonlinear system, existing when the pinning disorder is low and the pinning strength is weak. The type-II disordered state is related to the pinning disorder, which is dominating when both the pinning disorder and the pinning strength are strong.
One-way hash function construction based on chaotic map network
International Nuclear Information System (INIS)
Yang Huaqian; Wong, K.-W.; Liao Xiaofeng; Wang Yong; Yang Degang
2009-01-01
A novel chaotic hash algorithm based on a network structure formed by 16 chaotic maps is proposed. The original message is first padded with zeros to make the length a multiple of four. Then it is divided into a number of blocks each contains 4 bytes. In the hashing process, the blocks are mixed together by the chaotic map network since the initial value and the control parameter of each tent map are dynamically determined by the output of its neighbors. To enhance the confusion and diffusion effect, the cipher block chaining (CBC) mode is adopted in the algorithm. Theoretic analyses and numerical simulations both show that the proposed hash algorithm possesses good statistical properties, strong collision resistance and high flexibility, as required by practical keyed hash functions.
Regular and chaotic behaviors of plasma oscillations modeled by a modified Duffing equation
International Nuclear Information System (INIS)
Enjieu Kadji, H.G.; Chabi Orou, J.B.; Woafo, P.; Abdus Salam International Centre for Theoretical Physics, Trieste
2005-07-01
The regular and chaotic behavior of plasma oscillations governed by a modified Duffing equation is studied. The plasma oscillations are described by a nonlinear differential equation of the form x + w 0 2 x + βx 2 + αx 3 = 0 which is similar to a Duffing equation. By focusing on the quadratic term, which is mainly the term modifying the Duffing equation, the harmonic balance method and the fourth order Runge-Kutta algorithm are used to derive regular and chaotic motions respectively. A strong chaotic behavior exhibited by the system in that event when the system is subjected to an external periodic forcing oscillation is reported as β varies. (author)
Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng
2015-01-01
The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior.
Image Encryption and Chaotic Cellular Neural Network
Peng, Jun; Zhang, Du
Machine learning has been playing an increasingly important role in information security and assurance. One of the areas of new applications is to design cryptographic systems by using chaotic neural network due to the fact that chaotic systems have several appealing features for information security applications. In this chapter, we describe a novel image encryption algorithm that is based on a chaotic cellular neural network. We start by giving an introduction to the concept of image encryption and its main technologies, and an overview of the chaotic cellular neural network. We then discuss the proposed image encryption algorithm in details, which is followed by a number of security analyses (key space analysis, sensitivity analysis, information entropy analysis and statistical analysis). The comparison with the most recently reported chaos-based image encryption algorithms indicates that the algorithm proposed in this chapter has a better security performance. Finally, we conclude the chapter with possible future work and application prospects of the chaotic cellular neural network in other information assurance and security areas.
Qualitative feature extractions of chaotic systems
International Nuclear Information System (INIS)
Vicha, T.; Dohnal, M.
2008-01-01
The theory of chaos offers useful tools for systems analysis. However, models of complex systems are based on a network of inconsistent, space and uncertain knowledge items. Traditional quantitative methods of chaos analysis are therefore not applicable. The paper by the same authors [Vicha T, Dohnal M. Qualitative identification of chaotic systems behaviours. Chaos, Solitons and Fractals, in press, [Log. No. 601019] ] presents qualitative interpretation of some chaos concepts. There are only three qualitative values positive/increasing, negative/decreasing and zero/constant. It means that any set of qualitative multidimensional descriptions of unsteady state behaviours is discrete and finite. A finite upper limit exists for the total number of qualitatively distinguishable scenarios. A set of 21 published chaotic models is solved qualitatively and 21 sets of all existing qualitative scenarios are presented. The intersection of all 21 scenario sets is empty. There is no such a behaviour which is common for all 21 models. The set of 21 qualitative models (e.g. Lorenz, Roessler) can be used to compare chaotic behaviours of an unknown qualitative model with them to evaluate if its chaotic behaviours is close to e.g. Lorenz chaotic model and how much
Pei, Yan
2015-01-01
We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed.
2015-01-01
We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed. PMID:25879067
Directory of Open Access Journals (Sweden)
Yan Pei
2015-01-01
Full Text Available We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC algorithm, interactive chaotic evolution (ICE that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed.
Study of chaotic oscillations in practical work on radio physics
International Nuclear Information System (INIS)
Ezdov, A.A.; Il'in, V.A.; Petrova, E.B.
1995-01-01
A description is given of a laboratory study of chaotic oscillations in deterministic dynamical systems. This work utilizes mathematical modeling and a computer experiment, as well as a direct study of the chaotic behavior of nonlinear electrical circuits
Generalized projective synchronization of a unified chaotic system
International Nuclear Information System (INIS)
Yan Jianping; Li Changpin
2005-01-01
In the present paper, a simple but efficient control technique of the generalized projective synchronization is applied to a unified chaotic system. Numerical simulations show that this method works very well, which can also be applied to other chaotic systems
The Hausdorff measure of chaotic sets of adjoint shift maps
Energy Technology Data Exchange (ETDEWEB)
Wang Huoyun [Department of Mathematics of Guangzhou University, Guangzhou 510006 (China)]. E-mail: wanghuoyun@sina.com; Song Wangan [Department of Computer, Huaibei Coal Industry Teacher College, Huaibei 235000 (China)
2006-11-15
In this paper, the size of chaotic sets of adjoint shift maps is estimated by Hausdorff measure. We prove that for any adjoint shift map there exists a finitely chaotic set with full Hausdorff measure.
A new chaotic algorithm for image encryption
International Nuclear Information System (INIS)
Gao Haojiang; Zhang Yisheng; Liang Shuyun; Li Dequn
2006-01-01
Recent researches of image encryption algorithms have been increasingly based on chaotic systems, but the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. This paper presents a new nonlinear chaotic algorithm (NCA) which uses power function and tangent function instead of linear function. Its structural parameters are obtained by experimental analysis. And an image encryption algorithm in a one-time-one-password system is designed. The experimental results demonstrate that the image encryption algorithm based on NCA shows advantages of large key space and high-level security, while maintaining acceptable efficiency. Compared with some general encryption algorithms such as DES, the encryption algorithm is more secure
Describing chaotic attractors: Regular and perpetual points
Dudkowski, Dawid; Prasad, Awadhesh; Kapitaniak, Tomasz
2018-03-01
We study the concepts of regular and perpetual points for describing the behavior of chaotic attractors in dynamical systems. The idea of these points, which have been recently introduced to theoretical investigations, is thoroughly discussed and extended into new types of models. We analyze the correlation between regular and perpetual points, as well as their relation with phase space, showing the potential usefulness of both types of points in the qualitative description of co-existing states. The ability of perpetual points in finding attractors is indicated, along with its potential cause. The location of chaotic trajectories and sets of considered points is investigated and the study on the stability of systems is shown. The statistical analysis of the observing desired states is performed. We focus on various types of dynamical systems, i.e., chaotic flows with self-excited and hidden attractors, forced mechanical models, and semiconductor superlattices, exhibiting the universality of appearance of the observed patterns and relations.
Chaotic behavior learning of Chua's circuit
International Nuclear Information System (INIS)
Sun Jian-Cheng
2012-01-01
Least-square support vector machines (LS-SVM) are applied for learning the chaotic behavior of Chua's circuit. The system is divided into three multiple-input single-output (MISO) structures and the LS-SVM are trained individually. Comparing with classical approaches, the proposed one reduces the structural complexity and the selection of parameters is avoided. Some parameters of the attractor are used to compare the chaotic behavior of the reconstructed and the original systems for model validation. Results show that the LS-SVM combined with the MISO can be trained to identify the underlying link among Chua's circuit state variables, and exhibit the chaotic attractors under the autonomous working mode
Semi-classical quantization of chaotic billiards
International Nuclear Information System (INIS)
Smilansky, U.
1992-02-01
The semi-classical quantization of chaotic billiards will be developed using scattering theory approach. This will be used to introduce and explain the inherent difficulties in the semi-classical quantization of chaos, and to show some of the modern tools which were developed recently to overcome these difficulties. To this end, we shall first obtain a semi-classical secular equation which is based on a finite number of classical periodic orbits. We shall use it to derive some spectral properties, and in particular to investigate the relationship between spectral statistics of quantum chaotic systems and the predictions of random-matrix theory. We shall finally discuss an important family of chaotic billiard, whose statistics does not follow any of the canonical ensembles, (GOE,GUE,...) but rather, corresponds to a new universality class. (author)
Blended particle filters for large-dimensional chaotic dynamical systems
Majda, Andrew J.; Qi, Di; Sapsis, Themistoklis P.
2014-01-01
A major challenge in contemporary data science is the development of statistically accurate particle filters to capture non-Gaussian features in large-dimensional chaotic dynamical systems. Blended particle filters that capture non-Gaussian features in an adaptively evolving low-dimensional subspace through particles interacting with evolving Gaussian statistics on the remaining portion of phase space are introduced here. These blended particle filters are constructed in this paper through a mathematical formalism involving conditional Gaussian mixtures combined with statistically nonlinear forecast models compatible with this structure developed recently with high skill for uncertainty quantification. Stringent test cases for filtering involving the 40-dimensional Lorenz 96 model with a 5-dimensional adaptive subspace for nonlinear blended filtering in various turbulent regimes with at least nine positive Lyapunov exponents are used here. These cases demonstrate the high skill of the blended particle filter algorithms in capturing both highly non-Gaussian dynamical features as well as crucial nonlinear statistics for accurate filtering in extreme filtering regimes with sparse infrequent high-quality observations. The formalism developed here is also useful for multiscale filtering of turbulent systems and a simple application is sketched below. PMID:24825886
Double-well chimeras in 2D lattice of chaotic bistable elements
Shepelev, I. A.; Bukh, A. V.; Vadivasova, T. E.; Anishchenko, V. S.; Zakharova, A.
2018-01-01
We investigate spatio-temporal dynamics of a 2D ensemble of nonlocally coupled chaotic cubic maps in a bistability regime. In particular, we perform a detailed study on the transition ;coherence - incoherence; for varying coupling strength for a fixed interaction radius. For the 2D ensemble we show the appearance of amplitude and phase chimera states previously reported for 1D ensembles of nonlocally coupled chaotic systems. Moreover, we uncover a novel type of chimera state, double-well chimera, which occurs due to the interplay of the bistability of the local dynamics and the 2D ensemble structure. Additionally, we find double-well chimera behavior for steady states which we call double-well chimera death. A distinguishing feature of chimera patterns observed in the lattice is that they mainly combine clusters of different chimera types: phase, amplitude and double-well chimeras.
Driving-induced multistability in coupled chaotic oscillators: Symmetries and riddled basins
Energy Technology Data Exchange (ETDEWEB)
Ujjwal, Sangeeta Rani; Ramaswamy, Ram [School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067 (India); Punetha, Nirmal; Prasad, Awadhesh [Department of Physics and Astrophysics, University of Delhi, Delhi 110007 (India); Agrawal, Manish [Department of Physics, Sri Aurobindo College, University of Delhi, New Delhi 110017 (India)
2016-06-15
We study the multistability that results when a chaotic response system that has an invariant symmetry is driven by another chaotic oscillator. We observe that there is a transition from a desynchronized state to a situation of multistability. In the case considered, there are three coexisting attractors, two of which are synchronized and one is desynchronized. For large coupling, the asynchronous attractor disappears, leaving the system bistable. We study the basins of attraction of the system in the regime of multistability. The three attractor basins are interwoven in a complex manner, with extensive riddling within a sizeable region of (but not the entire) phase space. A quantitative characterization of the riddling behavior is made via the so–called uncertainty exponent, as well as by evaluating the scaling behavior of tongue–like structures emanating from the synchronization manifold.
Chaotic Flows Correlation effects and coherent structures
Bakunin, Oleg G
2011-01-01
The book introduces readers to and summarizes the current ideas and theories about the basic mechanisms for transport in chaotic flows. Typically no single paradigmatic approach exists as this topic is relevant for fields as diverse as plasma physics, geophysical flows and various branches of engineering. Accordingly, the dispersion of matter in chaotic or turbulent flows is analyzed from different perspectives. Partly based on lecture courses given by the author, this book addresses both graduate students and researchers in search of a high-level but approachable and broad introduction to the topic.
Higgs vacuum stability and modified chaotic inflation
Energy Technology Data Exchange (ETDEWEB)
Saha, Abhijit Kumar, E-mail: abhijit.saha@iitg.ernet.in; Sil, Arunansu, E-mail: asil@iitg.ernet.in
2017-02-10
The issue of electroweak vacuum stability is studied in presence of a scalar field which participates in modifying the minimal chaotic inflation model. It is shown that the threshold effect on the Higgs quartic coupling originating from the Higgs–inflaton sector interaction can essentially make the electroweak vacuum stable up to the Planck scale. On the other hand we observe that the new physics parameters in this combined framework are enough to provide deviation from the minimal chaotic inflation predictions so as to keep it consistent with recent observation by Planck 2015.
Chaotic behavior of a quantum waveguide
Energy Technology Data Exchange (ETDEWEB)
Pérez-Aguilar, H., E-mail: hiperezag@yahoo.com [Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Av. Francisco J. Mújica S/N 58030, Morelia, Michoacán (Mexico); Mendoza-Suárez, A.; Tututi, E.S. [Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Av. Francisco J. Mújica S/N 58030, Morelia, Michoacán (Mexico); Herrera-González, I.F. [Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570 Puebla (Mexico)
2013-02-15
In this work we consider an infinite quantum waveguide composed of two periodic, hard walls, one-dimensional rippled surfaces. We find that, under certain conditions, the proposed system presents some traces of quantum chaos, when the corresponding classical limit has chaotic behavior. Thus, it is possible to obtain disordered probability densities in a system with smooth surfaces. When the system has chaotic behavior we show numerically that the correlation length of the autocorrelation function of the probability density goes to zero. To corroborate some properties obtained for infinite waveguide that are physically admissible, we study the corresponding finite version of this system.
Chaotic behavior of a quantum waveguide
International Nuclear Information System (INIS)
Pérez-Aguilar, H.; Mendoza-Suárez, A.; Tututi, E.S.; Herrera-González, I.F.
2013-01-01
In this work we consider an infinite quantum waveguide composed of two periodic, hard walls, one-dimensional rippled surfaces. We find that, under certain conditions, the proposed system presents some traces of quantum chaos, when the corresponding classical limit has chaotic behavior. Thus, it is possible to obtain disordered probability densities in a system with smooth surfaces. When the system has chaotic behavior we show numerically that the correlation length of the autocorrelation function of the probability density goes to zero. To corroborate some properties obtained for infinite waveguide that are physically admissible, we study the corresponding finite version of this system
Searching of Chaotic Elements in Hydrology
Directory of Open Access Journals (Sweden)
Sorin VLAD
2014-03-01
Full Text Available Chaos theory offers new means of understanding and prediction of phenomena otherwise considered random and unpredictable. The signatures of chaos can be isolated by performing nonlinear analysis of the time series available. The paper presents the results obtained by conducting a nonlinear analysis of the time series of daily Siret river flow (located in the North-Eastern part of Romania. The time series analysis is recorded starting with January 1999 to July 2009. The attractor is embedded in the reconstructed phase space then the chaotic dynamics is revealed computing the chaotic invariants - correlation dimension and the maximum Lyapunov Exponent.
The transition to chaotic phase synchronization
DEFF Research Database (Denmark)
Mosekilde, E.; Laugesen, J. L.; Zhusubaliyev, Zh. T.
2012-01-01
The transition to chaotic phase synchronization for a periodically driven spiral-type chaotic oscillator is known to involve a dense set of saddle-node bifurcations. By following the synchronization transition through the cascade of period-doubling bifurcations in a forced Ro¨ssler system...... to the torus doubling bifurcations that take place outside this domain. By examining a physiology-based model of the blood flow regulation to the individual functional unit (nephron) of the kidney we demonstrate how a similar bifurcation structure may arise in this system as a response to a periodically...
A time-delayed method for controlling chaotic maps
International Nuclear Information System (INIS)
Chen Maoyin; Zhou Donghua; Shang Yun
2005-01-01
Combining the repetitive learning strategy and the optimality principle, this Letter proposes a time-delayed method to control chaotic maps. This method can effectively stabilize unstable periodic orbits within chaotic attractors in the sense of least mean square. Numerical simulations of some chaotic maps verify the effectiveness of this method
Chaotic correlations in barrier billiards with arbitrary barriers
International Nuclear Information System (INIS)
Osbaldestin, A H; Adamson, L N C
2013-01-01
We study autocorrelation functions in symmetric barrier billiards for golden mean trajectories with arbitrary barriers. Renormalization analysis reveals the presence of a chaotic invariant set and thus that, for a typical barrier, there are chaotic correlations. The chaotic renormalization set is the analogue of the so-called orchid that arises in a generalized Harper equation. (paper)
Empirically characteristic analysis of chaotic PID controlling particle swarm optimization.
Yan, Danping; Lu, Yongzhong; Zhou, Min; Chen, Shiping; Levy, David
2017-01-01
Since chaos systems generally have the intrinsic properties of sensitivity to initial conditions, topological mixing and density of periodic orbits, they may tactfully use the chaotic ergodic orbits to achieve the global optimum or their better approximation to given cost functions with high probability. During the past decade, they have increasingly received much attention from academic community and industry society throughout the world. To improve the performance of particle swarm optimization (PSO), we herein propose a chaotic proportional integral derivative (PID) controlling PSO algorithm by the hybridization of chaotic logistic dynamics and hierarchical inertia weight. The hierarchical inertia weight coefficients are determined in accordance with the present fitness values of the local best positions so as to adaptively expand the particles' search space. Moreover, the chaotic logistic map is not only used in the substitution of the two random parameters affecting the convergence behavior, but also used in the chaotic local search for the global best position so as to easily avoid the particles' premature behaviors via the whole search space. Thereafter, the convergent analysis of chaotic PID controlling PSO is under deep investigation. Empirical simulation results demonstrate that compared with other several chaotic PSO algorithms like chaotic PSO with the logistic map, chaotic PSO with the tent map and chaotic catfish PSO with the logistic map, chaotic PID controlling PSO exhibits much better search efficiency and quality when solving the optimization problems. Additionally, the parameter estimation of a nonlinear dynamic system also further clarifies its superiority to chaotic catfish PSO, genetic algorithm (GA) and PSO.
Recognizing chaotic states in stadium billiard by calculating gyration radius
Directory of Open Access Journals (Sweden)
M. Barezi
2006-12-01
Full Text Available Nowadays study of chaotic quantum billiards because of their relation to Nano technology. In this paper distribution of zeros of wave function on the boundary of two circular and stadium billiards are investigated. By calculating gyration radius for these points chaotic and non-chaotic states are distinguished.
Mixing enhancement and transport reduction in chaotic advection
Benzekri , Tounsia; Chandre , Cristel; Leoncini , Xavier; Lima , Ricardo; Vittot , Michel
2005-01-01
We present a method for reducing chaotic transport in a model of chaotic advection due to time-periodic forcing of an oscillating vortex chain. We show that by a suitable modification of this forcing, the modified model combines two effects: enhancement of mixing within the rolls and suppression of chaotic transport along the channel.
Synchronization of two different chaotic systems via nonlinear ...
African Journals Online (AJOL)
ADOWIE PERE
ABSTRACT: This work reports the synchronization of a pair of four chaotic systems via nonlinear control technique. This method has been found to be easy to implement and effective especially on two different chaotic systems. We paired four chaotic systems out of which one is new and we have six possible pairs.
International Nuclear Information System (INIS)
Batistic, Benjamin; Robnik, Marko
2010-01-01
In this work we study the level spacing distribution in the classically mixed-type quantum systems (which are generic), exhibiting regular motion on invariant tori for some initial conditions and chaotic motion for the complementary initial conditions. In the asymptotic regime of the sufficiently deep semiclassical limit (sufficiently small effective Planck constant) the Berry and Robnik (1984 J. Phys. A: Math. Gen. 17 2413) picture applies, which is very well established. We present a new quasi-universal semiempirical theory of the level spacing distribution in a regime away from the Berry-Robnik regime (the near semiclassical limit), by describing both the dynamical localization effects of chaotic eigenstates, and the tunneling effects which couple regular and chaotic eigenstates. The theory works extremely well in the 2D mixed-type billiard system introduced by Robnik (1983 J. Phys. A: Math. Gen. 16 3971) and is also tested in other systems (mushroom billiard and Prosen billiard).
The variation of the density functions on chaotic spheres in chaotic space-like Minkowski space time
International Nuclear Information System (INIS)
El-Ahmady, A.E.
2007-01-01
In this article we introduce types of chaotic spheres in chaotic space-like Minkowski space time M n+1 . The variations of the density functions under the folding of these chaotic spheres are defined. The foldings restriction imposed on the density function are also discussed. The relations between the folding of geometry and pure chaotic manifolds are deduced. Some theorems concerning these relations are presented
Dispersion compensation in an open-loop all-optical chaotic communication system
International Nuclear Information System (INIS)
Liu Hui-Jie; Feng Jiu-Chao; Ren Bin
2012-01-01
The optical chaotic communication system using open-loop fiber transmission is studied under strong injection conditions. The optical chaotic communication system with open-loop configuration is studied using fiber transmission under strong injection conditions. The performances of fiber links composed of two types of fiber segments in different dispersion compensation maps are compared by testing the quality of the recovered message with different bit rates and encrypted by chaotic modulation (CM) or chaotic shift keying (CSK). The result indicates that the performance of the pre-compensation map is always worst. Two types of symmetrical maps are identical whatever the encryption method and bit-rate of message are. For the transmitting and the recovering of message of lower bit rate (1 Gb/s), the post-compensation map is the best scheme. However, for the message of higher bit rate (2.5 Gb/s), the parameters in communication system need to be modified properly in order to adapt to the high-speed application. Meanwhile, two types of symmetrical maps are the best scheme. In addition, the CM method is superior to the CSK method for high-speed applications. It is in accordance with the result in a back-to-back configuration system. (general)
Chaotic behaviour of photonic crystals resonators
Di Falco, A.; Liu, C.; Krauss, T. F.; Fratalocchi, Andrea
2015-01-01
We show here theoretically and experimentally how chaotic Photonic Crystal resonators can be used for en- ergy harvesting applications and the demonstration of fundamental theories, like the onset of superradiance in quantum systems. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Controlling chaotic systems via nonlinear feedback control
International Nuclear Information System (INIS)
Park, Ju H.
2005-01-01
In this article, a new method to control chaotic systems is proposed. Using Lyapunov method, we design a nonlinear feedback controller to make the controlled system be stabilized. A numerical example is given to illuminate the design procedure and advantage of the result derived
Economic dispatch using chaotic bat algorithm
International Nuclear Information System (INIS)
Adarsh, B.R.; Raghunathan, T.; Jayabarathi, T.; Yang, Xin-She
2016-01-01
This paper presents the application of a new metaheuristic optimization algorithm, the chaotic bat algorithm for solving the economic dispatch problem involving a number of equality and inequality constraints such as power balance, prohibited operating zones and ramp rate limits. Transmission losses and multiple fuel options are also considered for some problems. The chaotic bat algorithm, a variant of the basic bat algorithm, is obtained by incorporating chaotic sequences to enhance its performance. Five different example problems comprising 6, 13, 20, 40 and 160 generating units are solved to demonstrate the effectiveness of the algorithm. The algorithm requires little tuning by the user, and the results obtained show that it either outperforms or compares favorably with several existing techniques reported in literature. - Highlights: • The chaotic bat algorithm, a new metaheuristic optimization algorithm has been used. • The problem solved – the economic dispatch problem – is nonlinear, discontinuous. • It has number of equality and inequality constraints. • The algorithm has been demonstrated to be applicable on high dimensional problems.
Chaotic magnetic field line in toroidal plasmas
International Nuclear Information System (INIS)
Hatori, Tadatsugu; Abe, Yoshihiko; Urata, Kazuhiro; Irie, Haruyuki.
1989-05-01
This is an introductory review of chaotic magnetic field line in plasmas, together with some new results, with emphasis on the long-time tail and the fractional Brownian motion of the magnetic field line. The chaotic magnetic field line in toroidal plasmas is a typical chaotic phenomena in the Hamiltonian dynamical systems. The onset of stochasticity induced by a major magnetic perturbation is thought to cause a macroscopic rapid phenomena called the current disruption in the tokamak discharges. Numerical simulations on the basis of magnetohydrodynamics reveal in fact the disruptive phenomena. Some dynamical models which include the area-preserving mapping such as the standard mapping, and the two-wave Hamiltonian system can model the stochastic magnetic field. Theoretical results with use of the functional integral representation are given regarding the long-time tail on the basis of the radial twist mapping. It is shown that application of renormalization group technique to chaotic orbit in the two-wave Hamiltonian system proves decay of the velocity autocorrelation function with the power law. Some new numerical results are presented which supports these theoretical results. (author)
Analyzing and improving a chaotic encryption method
International Nuclear Information System (INIS)
Wu Xiaogang; Hu Hanping; Zhang Baoliang
2004-01-01
To resist the return map attack [Phys. Rev. Lett. 74 (1995) 1970] presented by Perez and Cerdeira, Shouliang Bu and Bing-Hong Wang proposed a simple method to improve the security of the chaotic encryption by modulating the chaotic carrier with an appropriately chosen scalar signal in [Chaos, Solitons and Fractals 19 (2004) 919]. They maintained that this modulating strategy not only preserved all appropriate information required for synchronizing chaotic systems but also destroyed the possibility of the phase space reconstruction of the sender dynamics such as a return map. However, a critical defect does exist in this scheme. This paper gives a zero-point autocorrelation method, which can recover the parameters of the scalar signal from the modulated signal. Consequently, the messages will be extracted from the demodulated chaotic carrier by using return map. Based on such a fact, an improved scheme is presented to obtain higher security, and the numerical simulation indicates the improvement of the synchronizing performance as well
Study of chaos in chaotic satellite systems
Indian Academy of Sciences (India)
Lyapunov exponents are estimated. From these studies, chaosin satellite system has been established. Solution of equations of motion of the satellite system are drawn in the form of three-dimensional, two-dimensional and time series phase portraits. Phase portraits and time series display the chaotic nature of the ...
Entanglement production in quantized chaotic systems
Indian Academy of Sciences (India)
Abstract. Quantum chaos is a subject whose major goal is to identify and to investigate different quantum signatures of classical chaos. Here we study entanglement production in coupled chaotic systems as a possible quantum indicator of classical chaos. We use coupled kicked tops as a model for our extensive numerical ...
Entanglement production in quantized chaotic systems
Indian Academy of Sciences (India)
Quantum chaos is a subject whose major goal is to identify and to investigate different quantum signatures of classical chaos. Here we study entanglement production in coupled chaotic systems as a possible quantum indicator of classical chaos. We use coupled kicked tops as a model for our extensive numerical studies.
Cryptanalysis of a chaotic secure communication system
International Nuclear Information System (INIS)
Alvarez, G.; Montoya, F.; Romera, M.; Pastor, G.
2003-01-01
Recently a chaotic encryption system has been proposed by P. Garcia et al. It represents an improvement over an algorithm previously presented by some of the same authors. In this Letter, several weaknesses of the new cryptosystem are pointed out and four successful cryptanalytic attacks are described
Chaotic digital communication by encoding initial conditions.
Xiaofeng, Gong; Xingang, Wang; Meng, Zhan; Lai, C H
2004-06-01
We investigate the possibility to improve the noise performance of a chaotic digital communication scheme by utilizing further dynamical information. We show that by encoding the initial information of the chaotic carrier according to the transmitting bits, extra redundance can be introduced into the segments of chaotic signals corresponding to the consecutive bits. Such redundant information can be exploited effectively at the receiver end to improve the noise performance of the system. Compared to other methods (e.g., differential chaos shift keying), straightforward application of the proposed modulation/demodulation scheme already provides significant performance gain in the low signal-to-noise ratio (SNR) region. Furthermore, maximum likelihood precleaning procedure based on the Viterbi algorithm can be applied before the demodulation step to overcome the performance degradation in the high SNR region. The study indicates that it is possible to improve the noise performance of the chaotic digital communication scheme if further dynamics information is added to the system. (c) 2004 American Institute of Physics
Quantum Statistical Operator and Classically Chaotic Hamiltonian ...
African Journals Online (AJOL)
Quantum Statistical Operator and Classically Chaotic Hamiltonian System. ... Journal of the Nigerian Association of Mathematical Physics ... In a Hamiltonian system von Neumann Statistical Operator is used to tease out the quantum consequence of (classical) chaos engendered by the nonlinear coupling of system to its ...
Chaotic behaviour of photonic crystals resonators
Di Falco, A.
2015-02-08
We show here theoretically and experimentally how chaotic Photonic Crystal resonators can be used for en- ergy harvesting applications and the demonstration of fundamental theories, like the onset of superradiance in quantum systems. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
CHAOTIC DUFFING TYPE OSCILLATOR WITH INERTIAL DAMPING
DEFF Research Database (Denmark)
Tamaševicius, Arunas; Mykolaitis, Gytis; Kirvaitis, Raimundas
2009-01-01
A novel Duffing-Holmes type autonomous chaotic oscillator is described. In comparison with the well-known non-autonomous Duffing-Holmes circuit it lacks the external periodic drive, but includes two extra linear feedback sub-circuits, namely a direct positive feedback loop, and an inertial negati...... feedback loop. SPICE simulation and hardware experimental results are presented....
Linking Chaotic Advection with Subsurface Biogeochemical Processes
Mays, D. C.; Freedman, V. L.; White, S. K.; Fang, Y.; Neupauer, R.
2017-12-01
This work investigates the extent to which groundwater flow kinematics drive subsurface biogeochemical processes. In terms of groundwater flow kinematics, we consider chaotic advection, whose essential ingredient is stretching and folding of plumes. Chaotic advection is appealing within the context of groundwater remediation because it has been shown to optimize plume spreading in the laminar flows characteristic of aquifers. In terms of subsurface biogeochemical processes, we consider an existing model for microbially-mediated reduction of relatively mobile uranium(VI) to relatively immobile uranium(IV) following injection of acetate into a floodplain aquifer beneath a former uranium mill in Rifle, Colorado. This model has been implemented in the reactive transport code eSTOMP, the massively parallel version of STOMP (Subsurface Transport Over Multiple Phases). This presentation will report preliminary numerical simulations in which the hydraulic boundary conditions in the eSTOMP model are manipulated to simulate chaotic advection resulting from engineered injection and extraction of water through a manifold of wells surrounding the plume of injected acetate. This approach provides an avenue to simulate the impact of chaotic advection within the existing framework of the eSTOMP code.
Comment on two papers of chaotic synchronization
International Nuclear Information System (INIS)
Li Lixiang; Peng Haipeng; Wang Xiangdong; Yang Yixian
2004-01-01
This Letter comments on two papers of chaotic synchronization, namely [Phys. Rev. Lett. 76 (1996) 1232] and [Phys. Lett. A 321 (2004) 50]. We find that some statements in the two papers are incorrect by numerical simulations. The consequence of the incorrectness is analyzed as well
Adaptive projective synchronization between different chaotic ...
Indian Academy of Sciences (India)
Numerical simulation results are performed to explain the effectiveness and feasibility of ... analysis of nonlinear dynamics have gained immense popularity during the last few ... applications of projective synchronization is in secure communication [31] due to ... of uncertain chaotic systems using adaptive control method.
Review Article: Hazards of Chaotic Importation, Certification ...
African Journals Online (AJOL)
Review Article: Hazards of Chaotic Importation, Certification, Distribution and Marketing of Medical Laboratory Consumables in Nigeria. BC Nlemadim. Abstract. No abstract. Journal of Medical Laboratory Science Vol.12(2) 2003: 25 - 27. Full Text: EMAIL FULL TEXT EMAIL FULL TEXT · DOWNLOAD FULL TEXT ...
New robust chaotic system with exponential quadratic term
International Nuclear Information System (INIS)
Bao Bocheng; Li Chunbiao; Liu Zhong; Xu Jianping
2008-01-01
This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic attractor with only two equilibria, and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent. Some basic dynamical properties and chaotic behaviour of novel attractor are studied. By numerical simulation, this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviours by a constant controller. (general)
Building Chaotic Model From Incomplete Time Series
Siek, Michael; Solomatine, Dimitri
2010-05-01
This paper presents a number of novel techniques for building a predictive chaotic model from incomplete time series. A predictive chaotic model is built by reconstructing the time-delayed phase space from observed time series and the prediction is made by a global model or adaptive local models based on the dynamical neighbors found in the reconstructed phase space. In general, the building of any data-driven models depends on the completeness and quality of the data itself. However, the completeness of the data availability can not always be guaranteed since the measurement or data transmission is intermittently not working properly due to some reasons. We propose two main solutions dealing with incomplete time series: using imputing and non-imputing methods. For imputing methods, we utilized the interpolation methods (weighted sum of linear interpolations, Bayesian principle component analysis and cubic spline interpolation) and predictive models (neural network, kernel machine, chaotic model) for estimating the missing values. After imputing the missing values, the phase space reconstruction and chaotic model prediction are executed as a standard procedure. For non-imputing methods, we reconstructed the time-delayed phase space from observed time series with missing values. This reconstruction results in non-continuous trajectories. However, the local model prediction can still be made from the other dynamical neighbors reconstructed from non-missing values. We implemented and tested these methods to construct a chaotic model for predicting storm surges at Hoek van Holland as the entrance of Rotterdam Port. The hourly surge time series is available for duration of 1990-1996. For measuring the performance of the proposed methods, a synthetic time series with missing values generated by a particular random variable to the original (complete) time series is utilized. There exist two main performance measures used in this work: (1) error measures between the actual
Applications of chaotic neurodynamics in pattern recognition
Baird, Bill; Freeman, Walter J.; Eeckman, Frank H.; Yao, Yong
1991-08-01
Network algorithms and architectures for pattern recognition derived from neural models of the olfactory system are reviewed. These span a range from highly abstract to physiologically detailed, and employ the kind of dynamical complexity observed in olfactory cortex, ranging from oscillation to chaos. A simple architecture and algorithm for analytically guaranteed associative memory storage of analog patterns, continuous sequences, and chaotic attractors in the same network is described. A matrix inversion determines network weights, given prototype patterns to be stored. There are N units of capacity in an N node network with 3N2 weights. It costs one unit per static attractor, two per Fourier component of each sequence, and three to four per chaotic attractor. There are no spurious attractors, and for sequences there is a Liapunov function in a special coordinate system which governs the approach of transient states to stored trajectories. Unsupervised or supervised incremental learning algorithms for pattern classification, such as competitive learning or bootstrap Widrow-Hoff can easily be implemented. The architecture can be ''folded'' into a recurrent network with higher order weights that can be used as a model of cortex that stores oscillatory and chaotic attractors by a Hebb rule. Network performance is demonstrated by application to the problem of real-time handwritten digit recognition. An effective system with on-line learning has been written by Eeckman and Baird for the Macintosh. It utilizes static, oscillatory, and/or chaotic attractors of two kinds--Lorenze attractors, or attractors resulting from chaotically interacting oscillatory modes. The successful application to an industrial pattern recognition problem of a network architecture of considerable physiological and dynamical complexity, developed by Freeman and Yao, is described. The data sets of the problem come in three classes of difficulty, and performance of the biological network is
Are Some Technologies Beyond Regulatory Regimes?
Energy Technology Data Exchange (ETDEWEB)
Jones, Wendell B. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Kusnezov, Dimitri [National Nuclear Security Administration (NNSA), Washington, DC (United States)
2017-08-01
Regulatory frameworks are a common tool in governance to incent and coerce behaviors supporting national or strategic stability. This includes domestic regulations and international agreements. Though regulation is always a challenge, the domain of fast evolving threats, like cyber, are proving much more difficult to control. Many discussions are underway searching for approaches that can provide national security in these domains. We use game theoretic learning models to explore the question of strategic stability with respect to the democratization of certain technologies (such as cyber). We suggest that such many-player games could inherently be chaotic with no corresponding (Nash) equilibria. In the absence of such equilibria, traditional approaches, as measures to achieve levels of overall security, may not be suitable approaches to support strategic stability in these domains. Altogether new paradigms may be needed for these issues. At the very least, regulatory regimes that fail to address the basic nature of the technology domains should not be pursued as a default solution, regardless of success in other domains. In addition, the very chaotic nature of these domains may hold the promise of novel approaches to regulation.
Optimized chaotic Brillouin dynamic grating with filtered optical feedback.
Zhang, Jianzhong; Li, Zhuping; Wu, Yuan; Zhang, Mingjiang; Liu, Yi; Li, Mengwen
2018-01-16
Chaotic Brillouin dynamic gratings (BDGs) have special advantages such as the creation of single, permanent and localized BDG. However, the periodic signals induced by conventional optical feedback (COF) in chaotic semiconductor lasers can lead to the generation of spurious BDGs, which will limit the application of chaotic BDGs. In this paper, filtered optical feedback (FOF) is proposed to eliminate spurious BDGs. By controlling the spectral width of the optical filter and its detuning from the laser frequency, semiconductor lasers with FOF operate in the suppression region of the time-delay signature, and chaotic outputs serving as pump waves are then utilized to generate the chaotic BDG in a polarization maintaining fiber. Through comparative analysis of the COF and FOF schemes, it has been demonstrated that spurious BDGs are effectively eliminated and that the reflection characterization of the chaotic BDG is improved. The influence of FOF on the reflection and gain spectra of the chaotic BDG is analyzed as well.
Stirring Strongly Coupled Plasma
Fadafan, Kazem Bitaghsir; Rajagopal, Krishna; Wiedemann, Urs Achim
2009-01-01
We determine the energy it takes to move a test quark along a circle of radius L with angular frequency w through the strongly coupled plasma of N=4 supersymmetric Yang-Mills (SYM) theory. We find that for most values of L and w the energy deposited by stirring the plasma in this way is governed either by the drag force acting on a test quark moving through the plasma in a straight line with speed v=Lw or by the energy radiated by a quark in circular motion in the absence of any plasma, whichever is larger. There is a continuous crossover from the drag-dominated regime to the radiation-dominated regime. In the crossover regime we find evidence for significant destructive interference between energy loss due to drag and that due to radiation as if in vacuum. The rotating quark thus serves as a model system in which the relative strength of, and interplay between, two different mechanisms of parton energy loss is accessible via a controlled classical gravity calculation. We close by speculating on the implicati...
DEFF Research Database (Denmark)
Katajainen, Jyrki
2008-01-01
In this project the goal is to develop the safe * family of containers for the CPH STL. The containers to be developed should be safer and more reliable than any of the existing implementations. A special focus should be put on strong exception safety since none of the existing prototypes available...
Chaotic behaviour of an electrical analogue to the mechanical double pendulum
Directory of Open Access Journals (Sweden)
M. P. Hanias
2008-02-01
Full Text Available In this paper the analogy between a mechanical double pendulum and an oscillating electrical system is presented. Instead of using analytic equations, we used the MultiSim circuit simulation environment in order to reproduce and interpret the response of the electrical oscillator. The electrical double pendulum presents a chaotic regime which is studied quantita-tively by means of state space reconstruction. For this purpose the optimal delay time is calculated and the minimum em-bedding dimension is found with the method of False Nearest Neighbors.
International Nuclear Information System (INIS)
Froissart, Marcel
1976-01-01
Strong interactions are introduced by their more obvious aspect: nuclear forces. In hadron family, the nucleon octet, OMEGA - decuplet, and quark triply are successively considered. Pion wave having been put at the origin of nuclear forces, low energy phenomena are described, the force being explained as an exchange of structure corresponding to a Regge trajectory in a variable rotating state instead of the exchange of a well defined particle. At high energies the concepts of pomeron, parton and stratons are introduced, pionization and fragmentation are briefly differentiated [fr
Analysis of high-quality modes in open chaotic microcavities
International Nuclear Information System (INIS)
Fang, W.; Yamilov, A.; Cao, H.
2005-01-01
We present a numerical study of the high-quality modes in two-dimensional dielectric stadium microcavities. Although the classical ray mechanics is fully chaotic in a stadium billiard, all of the high-quality modes show a 'strong scar' around unstable periodic orbits. When the deformation (ratio of the length of the straight segments over the diameter of the half circles) is small, the high-quality modes correspond to whispering-gallery-type trajectories and their quality factors decrease monotonically with increasing deformation. At large deformation, each high-quality mode is associated with multiple unstable periodic orbits. Its quality factor changes nonmonotonically with the deformation, and there exists an optimal deformation for each mode at which its quality factor reaches a local maximum. This unusual behavior is attributed to the interference of waves propagating along different constituent orbits that could minimize light leakage out of the cavity
Chaotic Dynamical Ferromagnetic Phase Induced by Nonequilibrium Quantum Fluctuations
Lerose, Alessio; Marino, Jamir; Žunkovič, Bojan; Gambassi, Andrea; Silva, Alessandro
2018-03-01
We investigate the robustness of a dynamical phase transition against quantum fluctuations by studying the impact of a ferromagnetic nearest-neighbor spin interaction in one spatial dimension on the nonequilibrium dynamical phase diagram of the fully connected quantum Ising model. In particular, we focus on the transient dynamics after a quantum quench and study the prethermal state via a combination of analytic time-dependent spin wave theory and numerical methods based on matrix product states. We find that, upon increasing the strength of the quantum fluctuations, the dynamical critical point fans out into a chaotic dynamical phase within which the asymptotic ordering is characterized by strong sensitivity to the parameters and initial conditions. We argue that such a phenomenon is general, as it arises from the impact of quantum fluctuations on the mean-field out of equilibrium dynamics of any system which exhibits a broken discrete symmetry.
Chaotic behavior of the lattice Yang-Mills on CUDA
Directory of Open Access Journals (Sweden)
Forster Richárd
2015-12-01
Full Text Available The Yang-Mills fields plays important role in the strong interaction, which describes the quark gluon plasma. The non-Abelian gauge theory provides the theoretical background understanding of this topic. The real time evolution of the classical fields is derived by the Hamiltonian for SU(2 gauge field tensor. The microcanonical equations of motion is solved on 3 dimensional lattice and chaotic dynamics was searched by the monodromy matrix. The entropy-energy relation was presented by Kolmogorov-Sinai entropy. We used block Hessenberg reduction to compute the eigenvalues of the current matrix. While the purely CPU based algorithm can handle effectively only a small amount of values, the GPUs provide enough performance to give more computing power to solve the problem.
Connection adaption for control of networked mobile chaotic agents.
Zhou, Jie; Zou, Yong; Guan, Shuguang; Liu, Zonghua; Xiao, Gaoxi; Boccaletti, S
2017-11-22
In this paper, we propose a strategy for the control of mobile chaotic oscillators by adaptively rewiring connections between nearby agents with local information. In contrast to the dominant adaptive control schemes where coupling strength is adjusted continuously according to the states of the oscillators, our method does not request adaption of coupling strength. As the resulting interaction structure generated by this proposed strategy is strongly related to unidirectional chains, by investigating synchronization property of unidirectional chains, we reveal that there exists a certain coupling range in which the agents could be controlled regardless of the length of the chain. This feature enables the adaptive strategy to control the mobile oscillators regardless of their moving speed. Compared with existing adaptive control strategies for networked mobile agents, our proposed strategy is simpler for implementation where the resulting interaction networks are kept unweighted at all time.
Weak and strong regime of a discharge in gases
International Nuclear Information System (INIS)
Podliasky, I.
1957-06-01
After having briefly recalled the content of a previous note in which he determined the electrodynamic action of the axial component of current density in a cylindrical tube of ionised gas submitted to an axial electric field, the author addresses the case of a column containing only electrons and in which Coulombian action prevails and, which, instead of being in contraction, will be in a status of axifugal expansion. He shows that the presence of a certain number of positive ions is absolutely necessary to provoke a pinch by partial compensation of Coulombian actions
Spin dynamics in the strong spin-orbit coupling regime
Czech Academy of Sciences Publication Activity Database
Liu, X.; Liu, X.-J.; Sinova, Jairo
2011-01-01
Roč. 84, č. 3 (2011), 035318/1-035318/9 ISSN 1098-0121 Institutional research plan: CEZ:AV0Z10100521 Keywords : semiconductor quntum- wells Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.691, year: 2011 http://link.aps.org/doi/10.1103/PhysRevB.84.035318
Tree-level correlations in the strong field regime
Gelis, François
2017-09-01
We consider the correlation function of an arbitrary number of local observables in quantum field theory, in situations where the field amplitude is large. Using a quasi-classical approximation (valid for a highly occupied initial mixed state, or for a coherent initial state if the classical dynamics has instabilities), we show that at tree level these correlations are dominated by fluctuations at the initial time. We obtain a general expression of the correlation functions in terms of the classical solution of the field equation of motion and its derivatives with respect to its initial conditions, that can be arranged graphically as the sum of labeled trees where the nodes are the individual observables, and the links are pairs of derivatives acting on them. For 3-point (and higher) correlation functions, there are additional tree-level terms beyond the quasi-classical approximation, generated by fluctuations in the bulk.
Scaling of chaos in strongly nonlinear lattices.
Mulansky, Mario
2014-06-01
Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic observations still remain mostly in the dark. In this work, we numerically analyze the probability of chaos in strongly nonlinear Hamiltonian systems and find different scaling properties depending on the nonlinear structure of the model. We argue that these different scaling laws of chaos have definite consequences for the macroscopic diffusive behavior, as chaos is the microscopic mechanism of diffusion. This is compared with previous results on chaotic diffusion [M. Mulansky and A. Pikovsky, New J. Phys. 15, 053015 (2013)], and a relation between microscopic chaos and macroscopic diffusion is established.
Implementation of chaotic secure communication systems based on OPA circuits
International Nuclear Information System (INIS)
Huang, C.-K.; Tsay, S.-C.; Wu, Y.-R.
2005-01-01
In this paper, we proposed a novel three-order autonomous circuit to construct a chaotic circuit with double scroll characteristic. The design idea is to use RLC elements and a nonlinear resistor. The one of salient features of the chaotic circuit is that the circuit with two flexible breakpoints of nonlinear element, and the advantage of the flexible breakpoint is that it increased complexity of the dynamical performance. Here, if we take a large and suitable breakpoint value, then the chaotic state can masking a large input signal in the circuit. Furthermore, we proposed a secure communication hyperchaotic system based on the proposed chaotic circuits, where the chaotic communication system is constituted by a chaotic transmitter and a chaotic receiver. To achieve the synchronization between the transmitter and the receiver, we are using a suitable Lyapunov function and Lyapunov theorem to design the feedback control gain. Thus, the transmitting message masked by chaotic state in the transmitter can be guaranteed to perfectly recover in the receiver. To achieve the systems performance, some basic components containing OPA, resistor and capacitor elements are used to implement the proposed communication scheme. From the viewpoints of circuit implementation, this proposed chaotic circuit is superior to the Chua chaotic circuits. Finally, the test results containing simulation and the circuit measurement are shown to demonstrate that the proposed method is correct and feasible
Chaotic coordinates for the Large Helical Device
Energy Technology Data Exchange (ETDEWEB)
Hudson, S. R., E-mail: shudson@pppl.gov [Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543 (United States); Suzuki, Y. [National Institute for Natural Sciences, National Institute for Fusion Sciences, 322-6 Oroshi, Toki, 509-5292 (Japan)
2014-10-15
The theory of quadratic-flux-minimizing (QFM) surfaces is reviewed, and numerical techniques that allow high-order QFM surfaces to be efficiently constructed for experimentally relevant, non-integrable magnetic fields are described. As a practical example, the chaotic edge of the magnetic field in the Large Helical Device (LHD) is examined. A precise technique for finding the boundary surface is implemented, the hierarchy of partial barriers associated with the near-critical cantori is constructed, and a coordinate system, which we call chaotic coordinates, that is based on a selection of QFM surfaces is constructed that simplifies the description of the magnetic field, so that flux surfaces become “straight” and islands become “square.”.
Communicating via robust synchronization of chaotic lasers
International Nuclear Information System (INIS)
Lopez-Gutierrez, R.M.; Posadas-Castillo, C.; Lopez-Mancilla, D.; Cruz-Hernandez, C.
2009-01-01
In this paper, the robust synchronization problem for coupled chaotic Nd:YAG lasers is addressed. We resort to complex systems theory to achieve chaos synchronization. Based on stability theory, it is shown that the state trajectories of the perturbed error synchronization are ultimately bounded, provided the unperturbed synchronization error system is exponentially stable, and some conditions on the bounds of the perturbation terms are satisfied. So that, encoding, transmission, and decoding in chaotic optical communications are presented. We analyze the transmission and recovery of encrypted information when parameter mismatches are considered. Computer simulations are provided to show the effectiveness of this robustness synchronization property, we present the encrypted transmission of image messages, and we show that, the transmitted image is faithfully recovered.
Communicating via robust synchronization of chaotic lasers
Energy Technology Data Exchange (ETDEWEB)
Lopez-Gutierrez, R.M. [Engineering Faculty, Baja California Autonomous University (UABC), Km. 103 Carret. Tij-Ens., 22860 Ensenada, B.C. (Mexico); Posadas-Castillo, C. [Engineering Faculty, Baja California Autonomous University (UABC), Km. 103 Carret. Tij-Ens., 22860 Ensenada, B.C. (Mexico); FIME, Autonomous University of Nuevo Leon (UANL), Pedro de Alba, S.N., Cd. Universitaria, San Nicolas de los Garza, NL (Mexico); Lopez-Mancilla, D. [Departamento de Ciencias Exactas y Tecnologicas, Centro Universitario de los Lagos, Universidad de Guadalajara (CULagos-UdeG), Enrique Diaz de Leon s/n, 47460 Lagos de Moreno, Jal. (Mexico); Cruz-Hernandez, C. [Electronics and Telecommunications Department, Scientific Research and Advanced Studies of Ensenada (CICESE), Km. 107 Carret. Tij-Ens., 22860 Ensenada, B.C. (Mexico)], E-mail: ccruz@cicese.mx
2009-10-15
In this paper, the robust synchronization problem for coupled chaotic Nd:YAG lasers is addressed. We resort to complex systems theory to achieve chaos synchronization. Based on stability theory, it is shown that the state trajectories of the perturbed error synchronization are ultimately bounded, provided the unperturbed synchronization error system is exponentially stable, and some conditions on the bounds of the perturbation terms are satisfied. So that, encoding, transmission, and decoding in chaotic optical communications are presented. We analyze the transmission and recovery of encrypted information when parameter mismatches are considered. Computer simulations are provided to show the effectiveness of this robustness synchronization property, we present the encrypted transmission of image messages, and we show that, the transmitted image is faithfully recovered.
Cryptanalysis of a spatiotemporal chaotic cryptosystem
International Nuclear Information System (INIS)
Rhouma, Rhouma; Belghith, Safya
2009-01-01
This paper proposes three different attacks on a recently proposed chaotic cryptosystem in [Li P, Li Z, Halang WA, Chen G. A stream cipher based on a spatiotemporal chaotic system. Chaos, Solitons and Fractals 2007;32:1867-76]. The cryptosystem under study displays weakness in the generation of the keystream. The encryption is made by generating a keystream mixed with blocks generated from the plaintext. The so obtained keystream remains unchanged for every encryption procedure. Moreover, its generation does neither depend on the plaintext nor on the ciphertext, that's to say, the keystream remains unchangeable for every plaintext with the same length. Guessing the keystream leads to guessing the key. This paper presents three possible attacks able to break the whole cryptosystem based on this drawback in generating the keystream.
Enhanced energy storage in chaotic optical resonators
Liu, Changxu; Di Falco, Andrea; Molinari, Diego P.; Khan, Yasser; Ooi, Boon S.; Krauss, Thomas F.; Fratalocchi, Andrea
2013-01-01
Chaos is a phenomenon that occurs in many aspects of contemporary science. In classical dynamics, chaos is defined as a hypersensitivity to initial conditions. The presence of chaos is often unwanted, as it introduces unpredictability, which makes it difficult to predict or explain experimental results. Conversely, we demonstrate here how chaos can be used to enhance the ability of an optical resonator to store energy. We combine analytic theory with ab initio simulations and experiments in photonic-crystal resonators to show that a chaotic resonator can store six times more energy than its classical counterpart of the same volume. We explain the observed increase by considering the equipartition of energy among all degrees of freedom of the chaotic resonator (that is, the cavity modes) and discover a convergence of their lifetimes towards a single value. A compelling illustration of the theory is provided by enhanced absorption in deformed polystyrene microspheres. © 2013 Macmillan Publishers Limited. All rights reserved.
Exact solutions to chaotic and stochastic systems
González, J. A.; Reyes, L. I.; Guerrero, L. E.
2001-03-01
We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems.
International Nuclear Information System (INIS)
Theiler, J.; Eubank, S.
1993-01-01
A common first step in time series signal analysis involves digitally filtering the data to remove linear correlations. The residual data is spectrally white (it is ''bleached''), but in principle retains the nonlinear structure of the original time series. It is well known that simple linear autocorrelation can give rise to spurious results in algorithms for estimating nonlinear invariants, such as fractal dimension and Lyapunov exponents. In theory, bleached data avoids these pitfalls. But in practice, bleaching obscures the underlying deterministic structure of a low-dimensional chaotic process. This appears to be a property of the chaos itself, since nonchaotic data are not similarly affected. The adverse effects of bleaching are demonstrated in a series of numerical experiments on known chaotic data. Some theoretical aspects are also discussed
Exact folded-band chaotic oscillator.
Corron, Ned J; Blakely, Jonathan N
2012-06-01
An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.
Enhanced energy storage in chaotic optical resonators
Liu, Changxu
2013-05-05
Chaos is a phenomenon that occurs in many aspects of contemporary science. In classical dynamics, chaos is defined as a hypersensitivity to initial conditions. The presence of chaos is often unwanted, as it introduces unpredictability, which makes it difficult to predict or explain experimental results. Conversely, we demonstrate here how chaos can be used to enhance the ability of an optical resonator to store energy. We combine analytic theory with ab initio simulations and experiments in photonic-crystal resonators to show that a chaotic resonator can store six times more energy than its classical counterpart of the same volume. We explain the observed increase by considering the equipartition of energy among all degrees of freedom of the chaotic resonator (that is, the cavity modes) and discover a convergence of their lifetimes towards a single value. A compelling illustration of the theory is provided by enhanced absorption in deformed polystyrene microspheres. © 2013 Macmillan Publishers Limited. All rights reserved.
Control of hyper-chaotic system
International Nuclear Information System (INIS)
Yin Xunhe; Feng Rupeng
2000-01-01
The approach based on the exact linearization via feedback is used for controlling Roessler hyper-chaos. A controller for hyper-chaos Roessler is designed by using the approach. The method is used to realize global stabilization and to control hyper-chaotic motion not only to any unstable equilibrium point but also to any desired periodic orbit. Simulation results presented here prove the feasibility of the method, and its robustness is analyzed numerically
Collectivity and chaoticity in nuclear dynamics
International Nuclear Information System (INIS)
Zelevinsky, V.G.
1992-01-01
Collective and chaotic features of nuclear dynamics are discussed using simple criteria of complexity of wave functions and their coherence with respect to specific operators. Various physical phenomena are considered in this connection: - coherent interaction of collective modes; - fragmentation and spreading widths; - mixing of compound states and dynamical enhancement; - mean field as a smooth component of complicated dynamics; - coupling through continuum and collectivization of widths; - structure of giant resonances; - statistical properties of unstable states as generalization of canonical random matrix ensembles. (orig.)
Extraction of dynamical equations from chaotic data
International Nuclear Information System (INIS)
Rowlands, G.; Sprott, J.C.
1991-02-01
A method is described for extracting from a chaotic time series a system of equations whose solution reproduces the general features of the original data even when these are contaminated with noise. The equations facilitate calculation of fractal dimension, Lyapunov exponents and short-term predictions. The method is applied to data derived from numerical solutions of the Logistic equation, the Henon equations, the Lorenz equations and the Roessler equations. 10 refs., 5 figs
Chaos control of Chen chaotic dynamical system
International Nuclear Information System (INIS)
Yassen, M.T.
2003-01-01
This paper is devoted to study the problem of controlling chaos in Chen chaotic dynamical system. Two different methods of control, feedback and nonfeedback methods are used to suppress chaos to unstable equilibria or unstable periodic orbits (UPO). The Lyapunov direct method and Routh-Hurwitz criteria are used to study the conditions of the asymptotic stability of the steady states of the controlled system. Numerical simulations are presented to show these results
Cryptanalysis of an ergodic chaotic cipher
International Nuclear Information System (INIS)
Alvarez, G.; Montoya, F.; Romera, M.; Pastor, G.
2003-01-01
In recent years, a growing number of cryptosystems based on chaos have been proposed, many of them fundamentally flawed by a lack of robustness and security. In this Letter, we offer our results after having studied the security and possible attacks on a very interesting cipher algorithm based on the logistic map's ergodicity property. This algorithm has become very popular recently, as it has been taken as the development basis of new chaotic cryptosystems
Chaotic inflation with metric and matter perturbations
International Nuclear Information System (INIS)
Feldman, H.A.; Brandenberger, R.H.
1989-01-01
A perturbative scheme to analyze the evolution of both metric and scalar field perturbations in an expanding universe is developed. The scheme is applied to study chaotic inflation with initial metric and scalar field perturbations present. It is shown that initial gravitational perturbations with wavelength smaller than the Hubble radius rapidly decay. The metric simultaneously picks up small perturbations determined by the matter inhomogeneities. Both are frozen in once the wavelength exceeds the Hubble radius. (orig.)
Spatial statistics of magnetic field in two-dimensional chaotic flow in the resistive growth stage
Energy Technology Data Exchange (ETDEWEB)
Kolokolov, I.V., E-mail: igor.kolokolov@gmail.com [Landau Institute for Theoretical Physics RAS, 119334, Kosygina 2, Moscow (Russian Federation); NRU Higher School of Economics, 101000, Myasnitskaya 20, Moscow (Russian Federation)
2017-03-18
The correlation tensors of magnetic field in a two-dimensional chaotic flow of conducting fluid are studied. It is shown that there is a stage of resistive evolution where the field correlators grow exponentially with time. The two- and four-point field correlation tensors are computed explicitly in this stage in the framework of Batchelor–Kraichnan–Kazantsev model. They demonstrate strong temporal intermittency of the field fluctuations and high level of non-Gaussianity in spatial field distribution.
Flow regime and deposition pattern of evaporating binary mixture droplet suspended with particles.
Zhong, Xin; Duan, Fei
2016-02-01
The flow regimes and the deposition pattern have been investigated by changing the ethanol concentration in a water-based binary mixture droplet suspended with alumina nanoparticles. To visualize the flow patterns, Particle Image Velocimetry (PIV) has been applied in the binary liquid droplet containing the fluorescent microspheres. Three distinct flow regimes have been revealed in the evaporation. In Regime I, the vortices and chaotic flows are found to carry the particles to the liquid-vapor interface and to promote the formation of particle aggregation. The aggregates move inwards in Regime II as induced by the Marangoni flow along the droplet free surface. Regime III is dominated by the drying of the left water and the capillary flow driving particles radially outward is observed. The relative weightings of Regimes I and II, which are enhanced with an increasing load of ethanol, determine the motion of the nanoparticles and the formation of the final drying pattern.
Characterizing the chaotic nature of ocean ventilation
MacGilchrist, Graeme A.; Marshall, David P.; Johnson, Helen L.; Lique, Camille; Thomas, Matthew
2017-09-01
Ventilation of the upper ocean plays an important role in climate variability on interannual to decadal timescales by influencing the exchange of heat and carbon dioxide between the atmosphere and ocean. The turbulent nature of ocean circulation, manifest in a vigorous mesoscale eddy field, means that pathways of ventilation, once thought to be quasi-laminar, are in fact highly chaotic. We characterize the chaotic nature of ventilation pathways according to a nondimensional "filamentation number," which estimates the reduction in filament width of a ventilated fluid parcel due to mesoscale strain. In the subtropical North Atlantic of an eddy-permitting ocean model, the filamentation number is large everywhere across three upper ocean density surfaces—implying highly chaotic ventilation pathways—and increases with depth. By mapping surface ocean properties onto these density surfaces, we directly resolve the highly filamented structure and confirm that the filamentation number captures its spatial variability. These results have implications for the spreading of atmospherically-derived tracers into the ocean interior.
Transient chaotic transport in dissipative drift motion
Energy Technology Data Exchange (ETDEWEB)
Oyarzabal, R.S. [Pós-Graduação em Ciências/Física, Universidade Estadual de Ponta Grossa, 84030-900, Ponta Grossa, PR (Brazil); Szezech, J.D. [Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, 84030-900, Ponta Grossa, PR (Brazil); Batista, A.M., E-mail: antoniomarcosbatista@gmail.com [Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, 84030-900, Ponta Grossa, PR (Brazil); Souza, S.L.T. de [Departamento de Física e Matemática, Universidade Federal de São João del Rei, 36420-000, Ouro Branco, MG (Brazil); Caldas, I.L. [Instituto de Física, Universidade de São Paulo, 05315-970, São Paulo, SP (Brazil); Viana, R.L. [Departamento de Física, Universidade Federal do Paraná, 81531-990, Curitiba, PR (Brazil); Sanjuán, M.A.F. [Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid (Spain)
2016-04-22
Highlights: • We consider a situation for which a chaotic transient is present in the dynamics of the two-wave model with damping. • The damping in plasma models can be a way for study a realistic behavior of confinement due the collisional effect. • The escape time as a function of the damping obey a power-law scaling. • We have made a qualitative transport analysis with a simple model that can be useful for more complete models. • We have shown that the pattern of the basin of attraction depends on the damping parameter. - Abstract: We investigate chaotic particle transport in magnetised plasmas with two electrostatic drift waves. Considering dissipation in the drift motion, we verify that the removed KAM surfaces originate periodic attractors with their corresponding basins of attraction. We show that the properties of the basins depend on the dissipation and the space-averaged escape time decays exponentially when the dissipation increases. We find positive finite time Lyapunov exponents in dissipative drift motion, consequently the trajectories exhibit transient chaotic transport. These features indicate how the transient plasma transport depends on the dissipation.
Banknote authentication using chaotic elements technology
Ambadiyil, Sajan; P. S., Krishnendu; Mahadevan Pillai, V. P.; Prabhu, Radhakrishna
2017-10-01
The counterfeit banknote is a growing threat to the society since the advancements in the field of computers, scanners and photocopiers, as they have made the duplication process for banknote much simpler. The fake note detection systems developed so far have many drawbacks such as high cost, poor accuracy, unavailability, lack of user-friendliness and lower effectiveness. One possible solution to this problem could be the use of a system uniquely linked to the banknote itself. In this paper, we present a unique identification and authentication process for the banknote using chaotic elements embedded in it. A chaotic element means that the physical elements are formed from a random process independent from human intervention. The chaotic elements used in this paper are the random distribution patterns of such security fibres set into the paper pulp. A unique ID is generated from the fibre pattern obtained from UV image of the note, which can be verified by any person who receives the banknote to decide whether the banknote is authentic or not. Performance analysis of the system is also studied in this paper.
Wave dynamics of regular and chaotic rays
International Nuclear Information System (INIS)
McDonald, S.W.
1983-09-01
In order to investigate general relationships between waves and rays in chaotic systems, I study the eigenfunctions and spectrum of a simple model, the two-dimensional Helmholtz equation in a stadium boundary, for which the rays are ergodic. Statistical measurements are performed so that the apparent randomness of the stadium modes can be quantitatively contrasted with the familiar regularities observed for the modes in a circular boundary (with integrable rays). The local spatial autocorrelation of the eigenfunctions is constructed in order to indirectly test theoretical predictions for the nature of the Wigner distribution corresponding to chaotic waves. A portion of the large-eigenvalue spectrum is computed and reported in an appendix; the probability distribution of successive level spacings is analyzed and compared with theoretical predictions. The two principal conclusions are: 1) waves associated with chaotic rays may exhibit randomly situated localized regions of high intensity; 2) the Wigner function for these waves may depart significantly from being uniformly distributed over the surface of constant frequency in the ray phase space
Chaotic exploration and learning of locomotion behaviors.
Shim, Yoonsik; Husbands, Phil
2012-08-01
We present a general and fully dynamic neural system, which exploits intrinsic chaotic dynamics, for the real-time goal-directed exploration and learning of the possible locomotion patterns of an articulated robot of an arbitrary morphology in an unknown environment. The controller is modeled as a network of neural oscillators that are initially coupled only through physical embodiment, and goal-directed exploration of coordinated motor patterns is achieved by chaotic search using adaptive bifurcation. The phase space of the indirectly coupled neural-body-environment system contains multiple transient or permanent self-organized dynamics, each of which is a candidate for a locomotion behavior. The adaptive bifurcation enables the system orbit to wander through various phase-coordinated states, using its intrinsic chaotic dynamics as a driving force, and stabilizes on to one of the states matching the given goal criteria. In order to improve the sustainability of useful transient patterns, sensory homeostasis has been introduced, which results in an increased diversity of motor outputs, thus achieving multiscale exploration. A rhythmic pattern discovered by this process is memorized and sustained by changing the wiring between initially disconnected oscillators using an adaptive synchronization method. Our results show that the novel neurorobotic system is able to create and learn multiple locomotion behaviors for a wide range of body configurations and physical environments and can readapt in realtime after sustaining damage.
A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps
International Nuclear Information System (INIS)
Behnia, S.; Akhshani, A.; Ahadpour, S.; Mahmodi, H.; Akhavan, A.
2007-01-01
In recent years, a growing number of discrete chaotic cryptographic algorithms have been proposed. However, most of them encounter some problems such as the lack of robustness and security. In this Letter, we introduce a new image encryption algorithm based on one-dimensional piecewise nonlinear chaotic maps. The system is a measurable dynamical system with an interesting property of being either ergodic or having stable period-one fixed point. They bifurcate from a stable single periodic state to chaotic one and vice versa without having usual period-doubling or period-n-tippling scenario. Also, we present the KS-entropy of this maps with respect to control parameter. This algorithm tries to improve the problem of failure of encryption such as small key space, encryption speed and level of security
Normal form and synchronization of strict-feedback chaotic systems
International Nuclear Information System (INIS)
Wang, Feng; Chen, Shihua; Yu Minghai; Wang Changping
2004-01-01
This study concerns the normal form and synchronization of strict-feedback chaotic systems. We prove that, any strict-feedback chaotic system can be rendered into a normal form with a invertible transform and then a design procedure to synchronize the normal form of a non-autonomous strict-feedback chaotic system is presented. This approach needs only a scalar driving signal to realize synchronization no matter how many dimensions the chaotic system contains. Furthermore, the Roessler chaotic system is taken as a concrete example to illustrate the procedure of designing without transforming a strict-feedback chaotic system into its normal form. Numerical simulations are also provided to show the effectiveness and feasibility of the developed methods
Video encryption using chaotic masks in joint transform correlator
Saini, Nirmala; Sinha, Aloka
2015-03-01
A real-time optical video encryption technique using a chaotic map has been reported. In the proposed technique, each frame of video is encrypted using two different chaotic random phase masks in the joint transform correlator architecture. The different chaotic random phase masks can be obtained either by using different iteration levels or by using different seed values of the chaotic map. The use of different chaotic random phase masks makes the decryption process very complex for an unauthorized person. Optical, as well as digital, methods can be used for video encryption but the decryption is possible only digitally. To further enhance the security of the system, the key parameters of the chaotic map are encoded using RSA (Rivest-Shamir-Adleman) public key encryption. Numerical simulations are carried out to validate the proposed technique.
Video encryption using chaotic masks in joint transform correlator
International Nuclear Information System (INIS)
Saini, Nirmala; Sinha, Aloka
2015-01-01
A real-time optical video encryption technique using a chaotic map has been reported. In the proposed technique, each frame of video is encrypted using two different chaotic random phase masks in the joint transform correlator architecture. The different chaotic random phase masks can be obtained either by using different iteration levels or by using different seed values of the chaotic map. The use of different chaotic random phase masks makes the decryption process very complex for an unauthorized person. Optical, as well as digital, methods can be used for video encryption but the decryption is possible only digitally. To further enhance the security of the system, the key parameters of the chaotic map are encoded using RSA (Rivest–Shamir–Adleman) public key encryption. Numerical simulations are carried out to validate the proposed technique. (paper)
Fractional order control and synchronization of chaotic systems
Vaidyanathan, Sundarapandian; Ouannas, Adel
2017-01-01
The book reports on the latest advances in and applications of fractional order control and synchronization of chaotic systems, explaining the concepts involved in a clear, matter-of-fact style. It consists of 30 original contributions written by eminent scientists and active researchers in the field that address theories, methods and applications in a number of research areas related to fractional order control and synchronization of chaotic systems, such as: fractional chaotic systems, hyperchaotic systems, complex systems, fractional order discrete chaotic systems, chaos control, chaos synchronization, jerk circuits, fractional chaotic systems with hidden attractors, neural network, fuzzy logic controllers, behavioral modeling, robust and adaptive control, sliding mode control, different types of synchronization, circuit realization of chaotic systems, etc. In addition to providing readers extensive information on chaos fundamentals, fractional calculus, fractional differential equations, fractional contro...
Anti-synchronization between different chaotic complex systems
International Nuclear Information System (INIS)
Liu Ping; Liu Shutang
2011-01-01
Many studies on the anti-synchronization of nonlinear real dynamic systems have been carried out, whereas the anti-synchronization of chaotic complex systems has not been studied extensively. In this work, the anti-synchronization between a new chaotic complex system and a complex Lorenz system and that between a new chaotic complex system and a complex Lue system were separately investigated by active control and nonlinear control methods, and explicit expressions were derived for the controllers that are used to achieve the anti-synchronization of chaotic complex systems. These expressions were tested numerically and excellent agreement was found. Concerning the new chaotic complex system, we discuss its dynamical properties including dissipation, chaotic behavior, fixed points, and their stability and invariance.
Research on dynamic characteristics of new chaotic-advection fins
International Nuclear Information System (INIS)
Kong Songtao; Dong Qiwu; Liu Minshan; Zhu Qing
2007-01-01
Analysis and the numerical simulation has confirmed that the flow is of the chaotic advection in the flow channel of the new fin. The chaotic advection results in stronger mixing under low Re, and thus enhances the heat transfer and anti-scaling ability. The new fin provides the beneficial exploration to the concept of chaotic advection which applies to the plate-fin heat exchanger. (authors)
A novel block cryptosystem based on iterating a chaotic map
International Nuclear Information System (INIS)
Xiang Tao; Liao Xiaofeng; Tang Guoping; Chen Yong; Wong, Kwok-wo
2006-01-01
A block cryptographic scheme based on iterating a chaotic map is proposed. With random binary sequences generated from the real-valued chaotic map, the plaintext block is permuted by a key-dependent shift approach and then encrypted by the classical chaotic masking technique. Simulation results show that performance and security of the proposed cryptographic scheme are better than those of existing algorithms. Advantages and security of our scheme are also discussed in detail
Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity
Jeevarekha, A.; Paul Asir, M.; Philominathan, P.
2016-06-01
This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.
On analytical justification of phase synchronization in different chaotic systems
International Nuclear Information System (INIS)
Erjaee, G.H.
2009-01-01
In analytical or numerical synchronizations studies of coupled chaotic systems the phase synchronizations have less considered in the leading literatures. This article is an attempt to find a sufficient analytical condition for stability of phase synchronization in some coupled chaotic systems. The method of nonlinear feedback function and the scheme of matrix measure have been used to justify this analytical stability, and tested numerically for the existence of the phase synchronization in some coupled chaotic systems.
Empirically characteristic analysis of chaotic PID controlling particle swarm optimization
Yan, Danping; Lu, Yongzhong; Zhou, Min; Chen, Shiping; Levy, David
2017-01-01
Since chaos systems generally have the intrinsic properties of sensitivity to initial conditions, topological mixing and density of periodic orbits, they may tactfully use the chaotic ergodic orbits to achieve the global optimum or their better approximation to given cost functions with high probability. During the past decade, they have increasingly received much attention from academic community and industry society throughout the world. To improve the performance of particle swarm optimization (PSO), we herein propose a chaotic proportional integral derivative (PID) controlling PSO algorithm by the hybridization of chaotic logistic dynamics and hierarchical inertia weight. The hierarchical inertia weight coefficients are determined in accordance with the present fitness values of the local best positions so as to adaptively expand the particles’ search space. Moreover, the chaotic logistic map is not only used in the substitution of the two random parameters affecting the convergence behavior, but also used in the chaotic local search for the global best position so as to easily avoid the particles’ premature behaviors via the whole search space. Thereafter, the convergent analysis of chaotic PID controlling PSO is under deep investigation. Empirical simulation results demonstrate that compared with other several chaotic PSO algorithms like chaotic PSO with the logistic map, chaotic PSO with the tent map and chaotic catfish PSO with the logistic map, chaotic PID controlling PSO exhibits much better search efficiency and quality when solving the optimization problems. Additionally, the parameter estimation of a nonlinear dynamic system also further clarifies its superiority to chaotic catfish PSO, genetic algorithm (GA) and PSO. PMID:28472050
Empirically characteristic analysis of chaotic PID controlling particle swarm optimization.
Directory of Open Access Journals (Sweden)
Danping Yan
Full Text Available Since chaos systems generally have the intrinsic properties of sensitivity to initial conditions, topological mixing and density of periodic orbits, they may tactfully use the chaotic ergodic orbits to achieve the global optimum or their better approximation to given cost functions with high probability. During the past decade, they have increasingly received much attention from academic community and industry society throughout the world. To improve the performance of particle swarm optimization (PSO, we herein propose a chaotic proportional integral derivative (PID controlling PSO algorithm by the hybridization of chaotic logistic dynamics and hierarchical inertia weight. The hierarchical inertia weight coefficients are determined in accordance with the present fitness values of the local best positions so as to adaptively expand the particles' search space. Moreover, the chaotic logistic map is not only used in the substitution of the two random parameters affecting the convergence behavior, but also used in the chaotic local search for the global best position so as to easily avoid the particles' premature behaviors via the whole search space. Thereafter, the convergent analysis of chaotic PID controlling PSO is under deep investigation. Empirical simulation results demonstrate that compared with other several chaotic PSO algorithms like chaotic PSO with the logistic map, chaotic PSO with the tent map and chaotic catfish PSO with the logistic map, chaotic PID controlling PSO exhibits much better search efficiency and quality when solving the optimization problems. Additionally, the parameter estimation of a nonlinear dynamic system also further clarifies its superiority to chaotic catfish PSO, genetic algorithm (GA and PSO.
A combination chaotic system and application in color image encryption
Parvaz, R.; Zarebnia, M.
2018-05-01
In this paper, by using Logistic, Sine and Tent systems we define a combination chaotic system. Some properties of the chaotic system are studied by using figures and numerical results. A color image encryption algorithm is introduced based on new chaotic system. Also this encryption algorithm can be used for gray scale or binary images. The experimental results of the encryption algorithm show that the encryption algorithm is secure and practical.
Chaos synchronization of a unified chaotic system via partial linearization
International Nuclear Information System (INIS)
Yu Yongguang; Li Hanxiong; Duan Jian
2009-01-01
A partial linearization method is proposed for realizing the chaos synchronization of an unified chaotic system. Through synchronizing partial state of the chaotic systems can result in the synchronization of their entire states, and the resulting controller is singularity free. The results can be easily extended to the synchronization of other similar chaotic systems. Simulation results are conducted to show the effectiveness of the method.
On robust control of uncertain chaotic systems: a sliding-mode synthesis via chaotic optimization
International Nuclear Information System (INIS)
Lu Zhao; Shieh Leangsan; Chen GuanRong
2003-01-01
This paper presents a novel Lyapunov-based control approach which utilizes a Lyapunov function of the nominal plant for robust tracking control of general multi-input uncertain nonlinear systems. The difficulty of constructing a control Lyapunov function is alleviated by means of predefining an optimal sliding mode. The conventional schemes for constructing sliding modes of nonlinear systems stipulate that the system of interest is canonical-transformable or feedback-linearizable. An innovative approach that exploits a chaotic optimizing algorithm is developed thereby obtaining the optimal sliding manifold for the control purpose. Simulations on the uncertain chaotic Chen's system illustrate the effectiveness of the proposed approach
A challenge to chaotic itinerancy from brain dynamics
Kay, Leslie M.
2003-09-01
Brain hermeneutics and chaotic itinerancy proposed by Tsuda are attractive characterizations of perceptual dynamics in the mammalian olfactory system. This theory proposes that perception occurs at the interface between itinerant neural representation and interaction with the environment. Quantifiable application of these dynamics has been hampered by the lack of definable history and action processes which characterize the changes induced by behavioral state, attention, and learning. Local field potentials measured from several brain areas were used to characterize dynamic activity patterns for their use as representations of history and action processes. The signals were recorded from olfactory areas (olfactory bulb, OB, and pyriform cortex) and hippocampal areas (entorhinal cortex and dentate gyrus, DG) in the brains of rats. During odor-guided behavior the system shows dynamics at three temporal scales. Short time-scale changes are system-wide and can occur in the space of a single sniff. They are predictable, associated with learned shifts in behavioral state and occur periodically on the scale of the intertrial interval. These changes occupy the theta (2-12 Hz), beta (15-30 Hz), and gamma (40-100 Hz) frequency bands within and between all areas. Medium time-scale changes occur relatively unpredictably, manifesting in these data as alterations in connection strength between the OB and DG. These changes are strongly correlated with performance in associated trial blocks (5-10 min) and may be due to fluctuations in attention, mood, or amount of reward received. Long time-scale changes are likely related to learning or decline due to aging or disease. These may be modeled as slow monotonic processes that occur within or across days or even weeks or years. The folding of different time scales is proposed as a mechanism for chaotic itinerancy, represented by dynamic processes instead of static connection strengths. Thus, the individual maintains continuity of
International Nuclear Information System (INIS)
Tomita, Kenji.
1974-11-01
The theories regarding the origin of galaxies and elements are reviewed in this paper, and the assumptions made for these theories are discussed. It has been assumed that the universe has always been isotropic and homogeneous from the beginning of cosmic expansion. At the stage of very high density that any local irregularities such as galaxies cannot exist, the admissible deviation in this case from the mean value is only the statistical or quantum fluctuation of matter density, spatial curvature or their growth. It should be considered that the chemical composition of matters at the earliest stage consisted of most fundamental particles. However, if the fluctuation of matter density is statistical, the present values are too small. As for the origin of elements, it depends strongly on the period when cosmic radiation appeared. The final mass ratios of elements are given from the present baryon mass density, and are in agreement with observed values. The assumption of hot universe seems good. However, the time-independent ratio of photon number to baryon number is hardly understood. It is reasonable to assume for the early universe an inhomogeneous model whose space-time curvature is of turbulent character, according to weak cosmological principle. The inhomogeneous models to be considered are weakly non-linear perturbation theory, anti-Newtonian approximation and post anti-Newtonian approximation. Smoothing-out process, the origin of cosmic microwave radiation, the origin of galaxies and the origin of chemical elements are discussed. (Kato, T.)
Sustainable urban regime adjustments
DEFF Research Database (Denmark)
Quitzau, Maj-Britt; Jensen, Jens Stissing; Elle, Morten
2013-01-01
The endogenous agency that urban governments increasingly portray by making conscious and planned efforts to adjust the regimes they operate within is currently not well captured in transition studies. There is a need to acknowledge the ambiguity of regime enactment at the urban scale. This direc...
Indian Academy of Sciences (India)
First page Back Continue Last page Overview Graphics. Flux scaling: Ultimate regime. With the Nusselt number and the mixing length scales, we get the Nusselt number and Reynolds number (w'd/ν) scalings: and or. and. scaling expected to occur at extremely high Ra Rayleigh-Benard convection. Get the ultimate regime ...
Chaotic wave trains in an oscillatory/excitable medium
International Nuclear Information System (INIS)
Rabinovitch, A.; Gutman, M.; Biton, Y.; Aviram, I.
2006-01-01
We study the chaotic dynamics of a heterogeneous reaction-diffusion medium composed of two uniform regions: one oscillatory, and the other excitable. It is shown that, by altering the diffusion coefficient, local chaotic oscillations can be induced at the interface between regions, which in turn, generate different chaotic sequences of pulses traveling in the excitable region. We analyze the properties of the local chaotic driver, as well as the diffusion-induced transitions. A procedure based on the abnormal frequency-locking phenomenon is proposed for controlling such sequences. Relevance of the obtained results to cardiac dynamics is briefly discussed
Adaptive Synchronization of Memristor-based Chaotic Neural Systems
Directory of Open Access Journals (Sweden)
Xiaofang Hu
2014-11-01
Full Text Available Chaotic neural networks consisting of a great number of chaotic neurons are able to reproduce the rich dynamics observed in biological nervous systems. In recent years, the memristor has attracted much interest in the efficient implementation of artificial synapses and neurons. This work addresses adaptive synchronization of a class of memristor-based neural chaotic systems using a novel adaptive backstepping approach. A systematic design procedure is presented. Simulation results have demonstrated the effectiveness of the proposed adaptive synchronization method and its potential in practical application of memristive chaotic oscillators in secure communication.
Complex economic dynamics: Chaotic saddle, crisis and intermittency
International Nuclear Information System (INIS)
Chian, Abraham C.-L.; Rempel, Erico L.; Rogers, Colin
2006-01-01
Complex economic dynamics is studied by a forced oscillator model of business cycles. The technique of numerical modeling is applied to characterize the fundamental properties of complex economic systems which exhibit multiscale and multistability behaviors, as well as coexistence of order and chaos. In particular, we focus on the dynamics and structure of unstable periodic orbits and chaotic saddles within a periodic window of the bifurcation diagram, at the onset of a saddle-node bifurcation and of an attractor merging crisis, and in the chaotic regions associated with type-I intermittency and crisis-induced intermittency, in non-linear economic cycles. Inside a periodic window, chaotic saddles are responsible for the transient motion preceding convergence to a periodic or a chaotic attractor. The links between chaotic saddles, crisis and intermittency in complex economic dynamics are discussed. We show that a chaotic attractor is composed of chaotic saddles and unstable periodic orbits located in the gap regions of chaotic saddles. Non-linear modeling of economic chaotic saddle, crisis and intermittency can improve our understanding of the dynamics of financial intermittency observed in stock market and foreign exchange market. Characterization of the complex dynamics of economic systems is a powerful tool for pattern recognition and forecasting of business and financial cycles, as well as for optimization of management strategy and decision technology
On periodic and chaotic regions in the Mandelbrot set
International Nuclear Information System (INIS)
Pastor, G.; Romera, M.; Alvarez, G.; Arroyo, D.; Montoya, F.
2007-01-01
We show here in a graphic and simple way the relation between the periodic and chaotic regions in the Mandelbrot set. Since the relation between the periodic and chaotic regions in a one-dimensional (1D) quadratic set is already well known, we shall base on it to extend the results to the Mandelbrot set. We shall see that in the same way as the hyperbolic components of the period-doubling cascade determines the chaotic bands structure in 1D quadratic sets, the periodic region determines the chaotic region in the Mandelbrot set
Verjus, Romuald; Guillou, Sylvain; Ezersky, Alexander; Angilella, Jean-Régis
2016-12-01
The sedimentation of a pair of rigid circular particles in a two-dimensional vertical channel containing a Newtonian fluid is investigated numerically, for terminal particle Reynolds numbers (ReT) ranging from 1 to 10, and for a confinement ratio equal to 4. While it is widely admitted that sufficiently inertial pairs should sediment by performing a regular DKT oscillation (Drafting-Kissing-Tumbling), the present analysis shows in contrast that a chaotic regime can also exist for such particles, leading to a much slower sedimentation velocity. It consists of a nearly horizontal pair, corresponding to a maximum effective blockage ratio, and performing a quasiperiodic transition to chaos while increasing the particle weight. For less inertial regimes, the classical oblique doublet structure and its complex behavior (multiple stable states and hysteresis, period-doubling cascade and chaotic attractor) are recovered, in agreement with previous work [Aidun, C. K. and Ding, E.-J., "Dynamics of particle sedimentation in a vertical channel: Period-doubling bifurcation and chaotic state," Phys. Fluids 15, 1612 (2003)]. As a consequence of these various behaviors, the link between the terminal Reynolds number and the non-dimensional driving force is complex: it contains several branches displaying hysteresis as well as various bifurcations. For the range of Reynolds number considered here, a global bifurcation diagram is given.
International Nuclear Information System (INIS)
Pando L, C.L.; Doedel, E.J.
2004-07-01
We investigate the onset of chaotic dynamics of the one-dimensional discrete nonlinear Schroedinger equation (DNLSE) with periodic boundary conditions in the presence of a single on-site defect. This model describes a ring of weakly- coupled Bose-Einstein condensates. We focus on the transition to global stochasticity in three different scenarios as the defect is changed. We make use of a suitable Poincare section and continuation methods. Numerical continuation enables us to find different families of stationary solutions, where certain bifurcations lead to global stochasticity. The global stochasticity is characterized by chaotic symbolic synchronization between the population inversions of certain pairs of condensates. We have seen that the Poincare cycles are useful to gain insight in the dynamics of this problem. Indeed, the return maps of the Poincare cycles have been used successfully to follow the motion along the stochastic layers of different resonances in the chaotic self-trapping regime. Moreover, the time series of the Poincare cycles suggests that in the global stochasticity regime the dynamics is, to some extent, Markovian, in spite of the fact that the condensates are phase locked with almost the same phase. This phase locking induces a peculiar local interference of the matter waves of the condensates. (author)
Coexisting chaotic attractors in a single neuron model with adapting feedback synapse
International Nuclear Information System (INIS)
Li Chunguang; Chen Guanrong
2005-01-01
In this paper, we consider the nonlinear dynamical behavior of a single neuron model with adapting feedback synapse, and show that chaotic behaviors exist in this model. In some parameter domain, we observe two coexisting chaotic attractors, switching from the coexisting chaotic attractors to a connected chaotic attractor, and then switching back to the two coexisting chaotic attractors. We confirm the chaoticity by simulations with phase plots, waveform plots, and power spectra
Symmetric encryption algorithms using chaotic and non-chaotic generators: A review.
Radwan, Ahmed G; AbdElHaleem, Sherif H; Abd-El-Hafiz, Salwa K
2016-03-01
This paper summarizes the symmetric image encryption results of 27 different algorithms, which include substitution-only, permutation-only or both phases. The cores of these algorithms are based on several discrete chaotic maps (Arnold's cat map and a combination of three generalized maps), one continuous chaotic system (Lorenz) and two non-chaotic generators (fractals and chess-based algorithms). Each algorithm has been analyzed by the correlation coefficients between pixels (horizontal, vertical and diagonal), differential attack measures, Mean Square Error (MSE), entropy, sensitivity analyses and the 15 standard tests of the National Institute of Standards and Technology (NIST) SP-800-22 statistical suite. The analyzed algorithms include a set of new image encryption algorithms based on non-chaotic generators, either using substitution only (using fractals) and permutation only (chess-based) or both. Moreover, two different permutation scenarios are presented where the permutation-phase has or does not have a relationship with the input image through an ON/OFF switch. Different encryption-key lengths and complexities are provided from short to long key to persist brute-force attacks. In addition, sensitivities of those different techniques to a one bit change in the input parameters of the substitution key as well as the permutation key are assessed. Finally, a comparative discussion of this work versus many recent research with respect to the used generators, type of encryption, and analyses is presented to highlight the strengths and added contribution of this paper.
Feature Selection via Chaotic Antlion Optimization.
Directory of Open Access Journals (Sweden)
Hossam M Zawbaa
Full Text Available Selecting a subset of relevant properties from a large set of features that describe a dataset is a challenging machine learning task. In biology, for instance, the advances in the available technologies enable the generation of a very large number of biomarkers that describe the data. Choosing the more informative markers along with performing a high-accuracy classification over the data can be a daunting task, particularly if the data are high dimensional. An often adopted approach is to formulate the feature selection problem as a biobjective optimization problem, with the aim of maximizing the performance of the data analysis model (the quality of the data training fitting while minimizing the number of features used.We propose an optimization approach for the feature selection problem that considers a "chaotic" version of the antlion optimizer method, a nature-inspired algorithm that mimics the hunting mechanism of antlions in nature. The balance between exploration of the search space and exploitation of the best solutions is a challenge in multi-objective optimization. The exploration/exploitation rate is controlled by the parameter I that limits the random walk range of the ants/prey. This variable is increased iteratively in a quasi-linear manner to decrease the exploration rate as the optimization progresses. The quasi-linear decrease in the variable I may lead to immature convergence in some cases and trapping in local minima in other cases. The chaotic system proposed here attempts to improve the tradeoff between exploration and exploitation. The methodology is evaluated using different chaotic maps on a number of feature selection datasets. To ensure generality, we used ten biological datasets, but we also used other types of data from various sources. The results are compared with the particle swarm optimizer and with genetic algorithm variants for feature selection using a set of quality metrics.
Complex dynamics of a new 3D Lorenz-type autonomous chaotic ...
Indian Academy of Sciences (India)
Newautonomous chaotic system; chaotic attractors; Lyapunov stability theory; ultimate ... College of Mathematics and Statistics, Chongqing Technology and Business ... College of Electronic and Information Engineering, Southwest University, ...
Chaos control for a class of chaotic systems using PI-type state observer approach
International Nuclear Information System (INIS)
Jiang Guoping; Zheng Weixing
2004-01-01
In this paper, by using the PI-type state observer design approach and the characteristic of ergodicity of chaos, a new method is presented for controlling chaos, including the stabilization of unstable equilibrium points and set-point tracking, for a class of chaotic systems. Based on the theory of nonlinear ordinary differential equations, a simple criterion is derived for designing the controller gains for stabilization and tracking, in which control parameters can be selected via the pole placement technique of linear control theory. More importantly, this control method has a simple controller structure, high robustness against system parametric variations, and strong rejection of external constant disturbances. The method is applied to the chaotic Lorenz system for demonstration
Chaotic behaviour induced by space charge
International Nuclear Information System (INIS)
Lagniel, J.M.
1994-01-01
In numerous non-linear dynamical systems studied in various disciplines (fluid dynamics, celestial mechanisms, chemistry, biology, economy, ecology...), chaotic motions are generated by the dynamics itself whereas no random force is present. This phenomenon, already studied in the particle accelerator field to understand the beam-beam effect, is also observed in numerical experiments on space-charge dominated beams. Stochasticity threshold and halo formation are discussed for a continuous focusing channel (1D beam) and for a FODO channel (2D beam) with the possibility to take into account the defocusing effects of RF gaps localized between the quadrupoles. (authors). 7 refs., 4 figs
Experimental pulse synchronisation of two chaotic circuits
Fortuna, L; Rizzo, A
2003-01-01
In this work a novel synchronisation scheme for chaotic systems is presented. Taking inspiration from the system decomposition approach, the master and slave are connected via a switch which allows to alternate the signal fed into the slave between the master signal and the slave signal itself. The switching frequency has been taken into account as a control parameter to characterise the synchronisation properties of the system. Experimental results, performed on real Chua's circuits, confirm the validity of the approach, emphasising the fact that synchronisation is achieved for switching frequencies greater than a certain threshold.
Mechanical analysis of Chen chaotic system
International Nuclear Information System (INIS)
Liang, Xiyin; Qi, Guoyuan
2017-01-01
The Chen chaotic system is transformed into Kolmogorov type system, which is decomposed into four types of torques: inertial torque, internal torque, dissipation and external torque. By the combinations of different torques, five cases are studied to discover key factors of chaos generation and the physical meaning. The conversion among Hamiltonian energy, kinetic energy and potential energy is investigated in these five cases. The relationship between the energies and the parameters is studied. It concludes that the combination of these four types of torques is necessary conditions to produce chaos, and any combination of three types of torques cannot produce chaos in Chen system.
Noise-Induced Riddling in Chaotic Systems
International Nuclear Information System (INIS)
Lai, Y.; Grebogi, C.
1996-01-01
Recent works have considered the situation of riddling where, when a chaotic attractor lying in an invariant subspace is transversely stable, the basin of the attractor can be riddled with holes that belong to the basin of another attractor. We show that riddling can be induced by arbitrarily small random noise even if the attractor is transversely unstable, and we obtain universal scaling laws for noise-induced riddling. Our results imply that the phenomenon of riddling can be more prevalent than expected before, as noise is practically inevitable in dynamical systems. copyright 1996 The American Physical Society
Unitarity and irreversibility in chaotic systems
International Nuclear Information System (INIS)
Hasegawa, H.H.; Saphir, W.C.
1992-01-01
We analyze the spectral properties of the Perron-Frobenius operator U, associated with some simple highly chaotic maps. We obtain a spectral decomposition of U in terms of generalized eigenfunctions of U and its adjoint. The corresponding eigenvalues are related to the decay rates of correlation functions and have magnitude less than one, so that physically measurable quantities manifestly approach equilibrium. To obtain decaying eigenstates of unitary and isometric operators it is necessary to extend the Hilbert-space formulation of dynamical systems. We describe and illustrate a method to obtain the decomposition explicitly
Chaotic behavior in the Henon mapping
Energy Technology Data Exchange (ETDEWEB)
Marotto, F R [Drexel Univ., Philadelphia, PA (USA). Dept. of Mathematics
1979-01-01
In a previous work Henon investigated a two-dimensional difference equation which was motivated by a hydrodynamical system of Lorenz. Numerically solving this equation indicated for certain parameter values the existence of a 'strange attractor', i.e., a region in the plane which attracts bounded solutions and in which solutions wander erratically. In the present work it is shown that this behavior is related to the mathematical concept of 'chaos'. Using general methods previously developed, it is proven analytically that for some parameter values the mapping has a transversal homoclinic orbit, which implies the existence of the chaotic behavior observed by Henon.
A dynamic modification to sneutrino chaotic inflation
International Nuclear Information System (INIS)
Saha, Abhijit Kumar; Sil, Arunansu
2015-01-01
We consider a right-handed scalar neutrino as the inflaton which carries a gravitational coupling with a supersymmetric QCD sector responsible for breaking supersymmetry dynamically. The framework suggests an inflaton potential which is a deformed version of the quadratic chaotic inflation leading to a flatter potential. We find that this deformation results a sizable tensor to scalar ratio which falls within the allowed region by PLANCK 2015. At the same time supersymmetry breaking at the end of inflation can naturally be induced in this set-up. The symmetries required to construct the framework allows the neutrino masses and mixing to be of right order.
On the quantization of classically chaotic system
International Nuclear Information System (INIS)
Godoy, N.F. de.
1988-01-01
Some propeties of a quantization in terms of observables of a classically chaotic system, which exhibits a strange are studied. It is shown in particular that convenient expected values of some observables have the correct classical limit and that in these cases the limits ℎ → O and t → ∞ (t=time) rigorously comute. This model was alternatively quantized by R.Graham in terms of Wigner function. The Graham's analysis is completed a few points, in particular, we find out a remarkable analogy with general results about the semi-classical limit of Wigner function. Finally the expected values obtained by both methods of quantization were compared. (author) [pt
Targeting engineering synchronization in chaotic systems
Bhowmick, Sourav K.; Ghosh, Dibakar
2016-07-01
A method of targeting engineering synchronization states in two identical and mismatch chaotic systems is explained in detail. The method is proposed using linear feedback controller coupling for engineering synchronization such as mixed synchronization, linear and nonlinear generalized synchronization and targeting fixed point. The general form of coupling design to target any desire synchronization state under unidirectional coupling with the help of Lyapunov function stability theory is derived analytically. A scaling factor is introduced in the coupling definition to smooth control without any loss of synchrony. Numerical results are done on two mismatch Lorenz systems and two identical Sprott oscillators.
Parametric number covariance in quantum chaotic spectra.
Vinayak; Kumar, Sandeep; Pandey, Akhilesh
2016-03-01
We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the covariance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kicked rotors for the time-reversal invariant and time-reversal noninvariant cases. A local version of the parametric number variance introduced earlier is also investigated.
Chaotic combustion in spark ignition engines
International Nuclear Information System (INIS)
Wendeker, Miroslaw; Czarnigowski, Jacek; Litak, Grzegorz; Szabelski, Kazimierz
2003-01-01
We analyse the combustion process in a spark ignition engine using the experimental data of an internal pressure during the combustion process and show that the system can be driven to chaotic behaviour. Our conclusion is based on the observation of unperiodicity in the time series, suitable stroboscopic maps and a complex structure of a reconstructed strange attractor. This analysis can explain that in some circumstances the level of noise in spark ignition engines increases considerably due to nonlinear dynamics of a combustion process
Experimental pulse synchronisation of two chaotic circuits
International Nuclear Information System (INIS)
Fortuna, L.; Frasca, M.; Rizzo, A.
2003-01-01
In this work a novel synchronisation scheme for chaotic systems is presented. Taking inspiration from the system decomposition approach, the master and slave are connected via a switch which allows to alternate the signal fed into the slave between the master signal and the slave signal itself. The switching frequency has been taken into account as a control parameter to characterise the synchronisation properties of the system. Experimental results, performed on real Chua's circuits, confirm the validity of the approach, emphasising the fact that synchronisation is achieved for switching frequencies greater than a certain threshold
Chaotic Dynamos Generated by a Turbulent Flow of Liquid Sodium
International Nuclear Information System (INIS)
Ravelet, F.; Monchaux, R.; Aumaitre, S.; Chiffaudel, A.; Daviaud, F.; Dubrulle, B.; Berhanu, M.; Fauve, S.; Mordant, N.; Petrelis, F.; Bourgoin, M.; Odier, Ph.; Plihon, N.; Pinton, J.-F.; Volk, R.
2008-01-01
We report the observation of several dynamical regimes of the magnetic field generated by a turbulent flow of liquid sodium (VKS experiment). Stationary dynamos, transitions to relaxation cycles or to intermittent bursts, and random field reversals occur in a fairly small range of parameters. Large scale dynamics of the magnetic field result from the interactions of a few modes. The low dimensional nature of these dynamics is not smeared out by the very strong turbulent fluctuations of the flow
Designing synchronization schemes for chaotic fractional-order unified systems
International Nuclear Information System (INIS)
Wang Junwei; Zhang Yanbin
2006-01-01
Synchronization in chaotic fractional-order differential systems is studied both theoretically and numerically. Two schemes are designed to achieve chaos synchronization of so-called unified chaotic systems and the corresponding numerical algorithms are established. Some sufficient conditions on synchronization are also derived based on the Laplace transformation theory. Computer simulations are used for demonstration
Horseshoes in a Chaotic System with Only One Stable Equilibrium
Huan, Songmei; Li, Qingdu; Yang, Xiao-Song
To confirm the numerically demonstrated chaotic behavior in a chaotic system with only one stable equilibrium reported by Wang and Chen, we resort to Poincaré map technique and present a rigorous computer-assisted verification of horseshoe chaos by virtue of topological horseshoes theory.
Modelling chaotic Hamiltonian systems as a Markov Chain ...
African Journals Online (AJOL)
The behaviour of chaotic Hamiltonian system has been characterised qualitatively in recent times by its appearance on the Poincaré section and quantitatively by the Lyapunov exponent. Studying the dynamics of the two chaotic Hamiltonian systems: the Henon-Heiles system and non-linearly coupled oscillators as their ...
Chaotic Motion of Nonlinearly Coupled Quintic Oscillators | Adeloye ...
African Journals Online (AJOL)
With a fixed energy, we investigate the motion of two nonlinearly coupled quintic oscillators for various values of the coupling strength with the aid of the Poincare surface of section. It is observed that chaotic motion sets in for coupling strength as low as 0.001. The degree of chaoticity generally increases as the coupling ...
Localized chaoticity in two linearly coupled inverted double-well ...
African Journals Online (AJOL)
Two linearly coupled inverted double-well oscillators for a fixed energy and varying coupling strength were studied. The dynamics yielded a chaotic system in which the Poincare surface was characterised by two non-mixing regions, one of regular motion and the other region that became chaotic as the coupling increased.
Active control versus recursive backstepping control of a chaotic ...
African Journals Online (AJOL)
In this paper active controllers and recursive backstepping controllers are designed for a third order chaotic system. The performances of these controllers in the control of the dynamics of the chaotic system are investigated numerically and are found to be effective. Comparison of their transient performances show that the ...
Modification for collection of master-slave synchronized chaotic systems
International Nuclear Information System (INIS)
Guo Rongwei; Li Gang
2009-01-01
In this paper, based on the adaptive-feedback control method, we synchronize two identical chaotic systems. In comparison with the previous methods such as the open-plus-closed-loop (OPCL) method, the present control scheme is simple, and therefore it is easily implemented in practice. At last, a group of chaotic systems are used to demonstrate the effectiveness of this method.
Does the classically chaotic Henon–Heiles oscillator exhibit ...
Indian Academy of Sciences (India)
–12]. In contrast to a classically chaotic system, where the exponential divergence of trajectories in phase-space is an unambiguous and confirmatory signature of chaos. [15–17], the decision about whether a quantum system is chaotic or not is ...
Chaotic neoclassical separatrix dissipation in parametric drift-wave decay.
Kabantsev, A A; Tsidulko, Yu A; Driscoll, C F
2014-02-07
Experiments and theory characterize a parametric decay instability between plasma drift waves when the nonlinear coupling is modified by an electrostatic barrier. Novel mode coupling terms representing enhanced dissipation and mode phase shifts are caused by chaotic separatrix crossings on the wave-ruffled separatrix. Experimental determination of these coupling terms is in broad agreement with new chaotic neoclassical transport analyses.
Partial synchronization and spontaneous spatial ordering in coupled chaotic systems
International Nuclear Information System (INIS)
Ying Zhang; Gang Hu; Cerdeira, Hilda A.; Shigang Chen; Braun, Thomas; Yugui Yao
2000-11-01
A model of many symmetrically and locally coupled chaotic oscillators is studied. Partial chaotic synchronizations associated with spontaneous spatial ordering are demonstrated. Very rich patterns of the system are revealed, based on partial synchronization analysis. The stabilities of different partially synchronous spatiotemporal structures and some novel dynamical behaviors of these states are discussed both numerically and analytically. (author)
PSO algorithm enhanced with Lozi Chaotic Map - Tuning experiment
Energy Technology Data Exchange (ETDEWEB)
Pluhacek, Michal; Senkerik, Roman; Zelinka, Ivan [Tomas Bata University in Zlín, Faculty of Applied Informatics Department of Informatics and Artificial Intelligence nám. T.G. Masaryka 5555, 760 01 Zlín (Czech Republic)
2015-03-10
In this paper it is investigated the effect of tuning of control parameters of the Lozi Chaotic Map employed as a chaotic pseudo-random number generator for the particle swarm optimization algorithm. Three different benchmark functions are selected from the IEEE CEC 2013 competition benchmark set. The Lozi map is extensively tuned and the performance of PSO is evaluated.
Transition to a pair of chaotic symmetric flows
International Nuclear Information System (INIS)
Chen Zhimin; Price, W.G.
2006-01-01
The complexity of transition to chaotic flow is discussed. It is shown that many different bifurcation processes may coexist and join together to excite the chaotic flow. The profile of this nonlinear dynamical behaviour is developed on the basis of a four-mode truncation model
Chaos synchronization between two different chaotic dynamical systems
International Nuclear Information System (INIS)
Park, Ju H.
2006-01-01
This work presents chaos synchronization between two different chaotic systems by nonlinear control laws. First, synchronization problem between Genesio system and Rossler system has been investigated, and then the similar approach is applied to the synchronization problem between Genesio system and a new chaotic system developed recently in the literature. The control performances are verified by two numerical examples
The Smallest Transistor-Based Nonautonomous Chaotic Circuit
DEFF Research Database (Denmark)
Lindberg, Erik; Murali, K.; Tamasevicius, Arunas
2005-01-01
A nonautonomous chaotic circuit based on one transistor, two capacitors, and two resistors is described. The mechanism behind the chaotic performance is based on “disturbance of integration.” The forward part and the reverse part of the bipolar transistor are “fighting” about the charging...
A new chaotic Hopfield network with piecewise linear activation function
International Nuclear Information System (INIS)
Peng-Sheng, Zheng; Wan-Sheng, Tang; Jian-Xiong, Zhang
2010-01-01
This paper presents a new chaotic Hopfield network with a piecewise linear activation function. The dynamic of the network is studied by virtue of the bifurcation diagram, Lyapunov exponents spectrum and power spectrum. Numerical simulations show that the network displays chaotic behaviours for some well selected parameters
Lag synchronization of chaotic systems with time-delayed linear
Indian Academy of Sciences (India)
In this paper, the lag synchronization of chaotic systems with time-delayed linear terms via impulsive control is investigated. Based on the stability theory of impulsive delayed differential equations, some sufficient conditions are obtained guaranteeing the synchronized behaviours between two delayed chaotic systems.
Towards generalized synchronization of strictly different chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Femat, R. [Matematicas Aplicadas y Sistemas Computacionales, IPICYT, Apdo. Postal 3-90, 78291 Tangamanga, San Luis Potosi S.L.P. (Mexico)]. E-mail: rfemat@ipicyt.edu.mx; Kocarev, L. [Institute for Nonlinear Science, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0402 (United States)]. E-mail: lkocarev@ucsd.edu; Gerven, L. van [Department of Mechanical Engineering, Technische Universiteit Eindhoven (Netherlands); Monsivais-Perez, M.E. [Matematicas Aplicadas y Sistemas Computacionales, IPICYT, Camino a la Presa San Jose 2055, 78216 Lomas 4a Sec., San Luis Potosi S.L.P. (Mexico)
2005-07-11
This contribution addresses the problem of the generalized synchronization (GS) in different chaotic systems, and departs from chaotic systems in a triangular from, which can be derived from Lie derivatives. A state-feedback (full knowledge of both master and slave systems) scheme is designed, which achieves GS. The work includes illustrative examples; moreover an experimental setup is used to corroborate the obtained results.
Secure Image Encryption Based On a Chua Chaotic Noise Generator
Directory of Open Access Journals (Sweden)
A. S. Andreatos
2013-10-01
Full Text Available This paper presents a secure image cryptography telecom system based on a Chua's circuit chaotic noise generator. A chaotic system based on synchronised Master–Slave Chua's circuits has been used as a chaotic true random number generator (CTRNG. Chaotic systems present unpredictable and complex behaviour. This characteristic, together with the dependence on the initial conditions as well as the tolerance of the circuit components, make CTRNGs ideal for cryptography. In the proposed system, the transmitter mixes an input image with chaotic noise produced by a CTRNG. Using thresholding techniques, the chaotic signal is converted to a true random bit sequence. The receiver must be able to reproduce exactly the same chaotic noise in order to subtract it from the received signal. This becomes possible with synchronisation between the two Chua's circuits: through the use of specific techniques, the trajectory of the Slave chaotic system can be bound to that of the Master circuit producing (almost identical behaviour. Additional blocks have been used in order to make the system highly parameterisable and robust against common attacks. The whole system is simulated in Matlab. Simulation results demonstrate satisfactory performance, as well as, robustness against cryptanalysis. The system works with both greyscale and colour jpg images.
Nonlinear observer based phase synchronization of chaotic systems
International Nuclear Information System (INIS)
Meng Juan; Wang Xingyuan
2007-01-01
This Letter analyzes the phase synchronization problem of autonomous chaotic systems. Based on the nonlinear state observer algorithm and the pole placement technique, a phase synchronization scheme is designed. The phase synchronization of a new chaotic system is achieved by using this observer controller. Numerical simulations further demonstrate the effectiveness of the proposed phase synchronization scheme
Scaling Features of Multimode Motions in Coupled Chaotic Oscillators
DEFF Research Database (Denmark)
Pavlov, A.N.; Sosnovtseva, Olga; Mosekilde, Erik
2003-01-01
Two different methods (the WTMM- and DFA-approaches) are applied to investigate the scaling properties in the return-time sequences generated by a system of two coupled chaotic oscillators. Transitions from twomode asynchronous dynamics (torus or torus-Chaos) to different states of chaotic phase ...
Adaptive control and synchronization of a fractional-order chaotic ...
Indian Academy of Sciences (India)
In this paper, the chaotic dynamics of a three-dimensional fractional-order chaotic sys- tem is investigated. ... So, the fractional description is closer to reality. One of the ..... For the augmented systems (14) and (16), the candidate function can.
PSO algorithm enhanced with Lozi Chaotic Map - Tuning experiment
International Nuclear Information System (INIS)
Pluhacek, Michal; Senkerik, Roman; Zelinka, Ivan
2015-01-01
In this paper it is investigated the effect of tuning of control parameters of the Lozi Chaotic Map employed as a chaotic pseudo-random number generator for the particle swarm optimization algorithm. Three different benchmark functions are selected from the IEEE CEC 2013 competition benchmark set. The Lozi map is extensively tuned and the performance of PSO is evaluated
A novel chaotic encryption scheme based on arithmetic coding
International Nuclear Information System (INIS)
Mi Bo; Liao Xiaofeng; Chen Yong
2008-01-01
In this paper, under the combination of arithmetic coding and logistic map, a novel chaotic encryption scheme is presented. The plaintexts are encrypted and compressed by using an arithmetic coder whose mapping intervals are changed irregularly according to a keystream derived from chaotic map and plaintext. Performance and security of the scheme are also studied experimentally and theoretically in detail
International Nuclear Information System (INIS)
Delande, Dominique; Zakrzewski, Jakub
2003-01-01
Statistics of tunneling rates in the presence of chaotic classical dynamics is discussed on a realistic example: a hydrogen atom placed in parallel, uniform, static electric, and magnetic fields, where tunneling is followed by ionization along the fields direction. Depending on the magnetic quantum number, one may observe either a standard Porter-Thomas distribution of tunneling rates or, for strong scarring by a periodic orbit parallel to the external fields, strong deviations from it. For the latter case, a simple model based on random matrix theory gives the correct distribution
Energy Technology Data Exchange (ETDEWEB)
Hramov, Alexander E., E-mail: aeh@nonlin.sgu.r [Faculty of Nonlinear Processes, Saratov State University, 83, Astrakhanskaya, Saratov, 410012 (Russian Federation); Koronovskii, Alexey A., E-mail: alkor@nonlin.sgu.r [Faculty of Nonlinear Processes, Saratov State University, 83, Astrakhanskaya, Saratov, 410012 (Russian Federation); Kurkin, Semen, E-mail: KurkinSA@nonlin.sgu.r [Faculty of Nonlinear Processes, Saratov State University, 83, Astrakhanskaya, Saratov, 410012 (Russian Federation)
2010-07-05
In this Letter the results of theoretical investigations of the chaotic microwave oscillator based on the electron beam with a virtual cathode are presented. Nonlinear non-stationary processes in these electron systems are studied by means of numerical analysis of 2.5D model. It was discovered that the non-uniform external magnetic field value controls the dynamical regime of oscillations in the virtual cathode oscillator. The processes of the chaotization of output microwave radiation are described and interpreted from the point of view of the formation and interaction of electron structures (bunches) in the electron beams. The numerical results have shown that the investigated electron system with virtual cathode could be considered as a promising controlled source of wideband chaotic oscillations in the microwave range.
Linguistic fuzzy control of the Welander problem in the chaotic regime
International Nuclear Information System (INIS)
Theler, German; Urdapilleta, Eugenio; Bonetto, Fabian J.
2007-01-01
As natural convection provides an efficient and completely passive heat removal system, natural circulation loops are a matter of great interest in the subject of advanced nuclear reactor design. However, under certain circumstances thermal-fluid dynamical instabilities may appear, threatening the reactor safety as a whole. On the other hand, fuzzy logic controllers provide and ideal framework to approach highly non-linear control problems. In the present work we introduce the basic ideas of the fuzzy logic theory and analyse the natural convection system known as the Welander problem, that is one of the simplest configurations of single-phase thermalhydraulic loops in which chaos actually occurs. Finally, we design a linguistic fuzzy controller that is able to stabilise the circulation flow in conditions that, if the controller was not present, would be otherwise non-periodic unstable. (author) [es
Silk, Daniel; Kirk, Paul D W; Barnes, Chris P; Toni, Tina; Rose, Anna; Moon, Simon; Dallman, Margaret J; Stumpf, Michael P H
2011-10-04
Chaos and oscillations continue to capture the interest of both the scientific and public domains. Yet despite the importance of these qualitative features, most attempts at constructing mathematical models of such phenomena have taken an indirect, quantitative approach, for example, by fitting models to a finite number of data points. Here we develop a qualitative inference framework that allows us to both reverse-engineer and design systems exhibiting these and other dynamical behaviours by directly specifying the desired characteristics of the underlying dynamical attractor. This change in perspective from quantitative to qualitative dynamics, provides fundamental and new insights into the properties of dynamical systems.
A New Simple Chaotic Circuit Based on Memristor
Wu, Renping; Wang, Chunhua
In this paper, a new memristor is proposed, and then an emulator built from off-the-shelf solid state components imitating the behavior of the proposed memristor is presented. Multisim simulation and breadboard experiment are done on the emulator, exhibiting a pinched hysteresis loop in the voltage-current plane when the emulator is driven by a periodic excitation voltage. In addition, a new simple chaotic circuit is designed by using the proposed memristor and other circuit elements. It is exciting that this circuit with only a linear negative resistor, a capacitor, an inductor and a memristor can generate a chaotic attractor. The dynamical behaviors of the proposed chaotic system are analyzed by Lyapunov exponents, phase portraits and bifurcation diagrams. Finally, an electronic circuit is designed to implement the chaotic system. For the sake of simple circuit topology, the proposed chaotic circuit can be easily manufactured at low cost.
Spectral Properties of Chaotic Signals Generated by the Bernoulli Map
Directory of Open Access Journals (Sweden)
Rafael A. da Costa
2014-11-01
Full Text Available In the last decades, the use of chaotic signals as broadband carriers has been considered in Telecommunications. Despite the relevance of the frequency domain analysis in this field, there are few studies that are concerned with spectral properties of chaotic signals. Bearing this in mind, this paper aims the characterization of the power spectral density (PSD of chaotic orbits generated by Bernoulli maps. We obtain analytic expressions for autocorrelation sequence, PSD and essential bandwidth for chaotic orbits generated by this map as function of the family parameter and Lyapunov exponent. Moreover, we verify that analytical expressions match numerical results. We conclude that the power of the generated orbits is concentrated in low frequencies for all parameters values. Besides, it is possible to obtain chaotic narrowband signals.
A Novel Audio Cryptosystem Using Chaotic Maps and DNA Encoding
Directory of Open Access Journals (Sweden)
S. J. Sheela
2017-01-01
Full Text Available Chaotic maps have good potential in security applications due to their inherent characteristics relevant to cryptography. This paper introduces a new audio cryptosystem based on chaotic maps, hybrid chaotic shift transform (HCST, and deoxyribonucleic acid (DNA encoding rules. The scheme uses chaotic maps such as two-dimensional modified Henon map (2D-MHM and standard map. The 2D-MHM which has sophisticated chaotic behavior for an extensive range of control parameters is used to perform HCST. DNA encoding technology is used as an auxiliary tool which enhances the security of the cryptosystem. The performance of the algorithm is evaluated for various speech signals using different encryption/decryption quality metrics. The simulation and comparison results show that the algorithm can achieve good encryption results and is able to resist several cryptographic attacks. The various types of analysis revealed that the algorithm is suitable for narrow band radio communication and real-time speech encryption applications.
Encoding and decoding messages with chaotic lasers
International Nuclear Information System (INIS)
Alsing, P.M.; Gavrielides, A.; Kovanis, V.; Roy, R.; Thornburg, K.S. Jr.
1997-01-01
We investigate the structure of the strange attractor of a chaotic loss-modulated solid-state laser utilizing return maps based on a combination of intensity maxima and interspike intervals, as opposed to those utilizing Poincare sections defined by the intensity maxima of the laser (I=0,Ie<0) alone. We find both experimentally and numerically that a simple, intrinsic relationship exists between an intensity maximum and the pair of preceding and succeeding interspike intervals. In addition, we numerically investigate encoding messages on the output of a chaotic transmitter laser and its subsequent decoding by a similar receiver laser. By exploiting the relationship between the intensity maxima and the interspike intervals, we demonstrate that the method utilized to encode the message is vital to the system close-quote s ability to hide the signal from unwanted deciphering. In this work alternative methods are studied in order to encode messages by modulating the magnitude of pumping of the transmitter laser and also by driving its loss modulation with more than one frequency. copyright 1997 The American Physical Society
Qualitative identification of chaotic systems behaviours
International Nuclear Information System (INIS)
Vicha, T.; Dohnal, M.
2008-01-01
There are only three qualitative values positive, negative and zero. This means that there is a maximal number of qualitatively distinguishable scenarios, prescribed by the number of variables and the highest qualitative derivative taken into consideration. There are several chaos related tasks, which can be solved with great difficulties on the numerical level if multidimensional problems are studied. One of them is the identification of all qualitatively different behaviours. To make sure that all distinctive qualitative scenarios are identified a qualitative interpretation of a classical quantitative phase portrait is used. The highest derivatives are usually the second derivatives as it is not possible to safely identify higher derivatives if tasks related to ecology or economics are studied. Two classical models are discussed - Damped oscillation (non chaotic) and Lorenz model (chaotic). There are 191 scenarios of the Lorenz model if only the second derivatives are considered. If the third derivatives are taken into consideration then the number of scenarios is 2619. Complete qualitative results are given in details
Resonant forcing of multidimensional chaotic map dynamics.
Foster, Glenn; Hübler, Alfred W; Dahmen, Karin
2007-03-01
We study resonances of chaotic map dynamics. We use the calculus of variations to determine the additive forcing function that induces the largest response. We find that resonant forcing functions complement the separation of nearby trajectories, in that the product of the displacement of nearby trajectories and the resonant forcing is a conserved quantity. As a consequence, the resonant function will have the same periodicity as the displacement dynamics, and if the displacement dynamics is irregular, then the resonant forcing function will be irregular as well. Furthermore, we show that resonant forcing functions of chaotic systems decrease exponentially, where the rate equals the negative of the largest Lyapunov exponent of the unperturbed system. We compare the response to optimal forcing with random forcing and find that the optimal forcing is particularly effective if the largest Lyapunov exponent is significantly larger than the other Lyapunov exponents. However, if the largest Lyapunov exponent is much larger than unity, then the optimal forcing decreases rapidly and is only as effective as a single-push forcing.
Light matter interaction in chaotic resonators
Liu, Changxu
2016-05-11
Chaos is a complex dynamics with exponential sensitivity to the initial conditions. Since the study of three-body problem by Henri Poincare, chaos has been extensively studied in many systems, ranging from electronics to fluids, brains and more recently photonics. Chaos is a ubiquitous phenomenon in Nature, from the gigantic oceanic waves to the disordered scales of white beetles at nanoscale. The presence of chaos is often unwanted in applications, as it introduces unpredictability,which makes it difficult to predict or explain experimental results. Inspired by how chaos permeates the natural world, this thesis investigates on how the interaction between light and chaotic structure can enhance the performance of photonics devices. With a proper design of the lighter-mater interaction in chaotic resonators, I illustrate how chaos can be used to enhance the ability of an optical cavity to store electromagnetic energy, realize a blackbody system composed of gold nanoparticles, localize light beyond the diffraction limit and control the phase transition of super-radiance.
Chaotic Universe, Friedmannian on the average 2
Energy Technology Data Exchange (ETDEWEB)
Marochnik, L S [AN SSSR, Moscow. Inst. Kosmicheskikh Issledovanij
1980-11-01
The cosmological solutions are found for the equations for correlators, describing a statistically chaotic Universe, Friedmannian on the average in which delta-correlated fluctuations with amplitudes h >> 1 are excited. For the equation of state of matter p = n epsilon, the kind of solutions depends on the position of maximum of the spectrum of the metric disturbances. The expansion of the Universe, in which long-wave potential and vortical motions and gravitational waves (modes diverging at t ..-->.. 0) had been excited, tends asymptotically to the Friedmannian one at t ..-->.. identity and depends critically on n: at n < 0.26, the solution for the scalefactor is situated higher than the Friedmannian one, and lower at n > 0.26. The influence of finite at t ..-->.. 0 long-wave fluctuation modes leads to an averaged quasiisotropic solution. The contribution of quantum fluctuations and of short-wave parts of the spectrum of classical fluctuations to the expansion law is considered. Their influence is equivalent to the contribution from an ultrarelativistic gas with corresponding energy density and pressure. The restrictions are obtained for the degree of chaos (the spectrum characteristics) compatible with the observed helium abundance, which could have been retained by a completely chaotic Universe during its expansion up to the nucleosynthesis epoch.
Chaotic synchronization of two complex nonlinear oscillators
International Nuclear Information System (INIS)
Mahmoud, Gamal M.; Mahmoud, Emad E.; Farghaly, Ahmed A.; Aly, Shaban A.
2009-01-01
Synchronization is an important phenomenon commonly observed in nature. It is also often artificially induced because it is desirable for a variety of applications in physics, applied sciences and engineering. In a recent paper [Mahmoud GM, Mohamed AA, Aly SA. Strange attractors and chaos control in periodically forced complex Duffing's oscillators. Physica A 2001;292:193-206], a system of periodically forced complex Duffing's oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. Their connection to solutions of the nonlinear Schroedinger equation has also been pointed out. In this paper, we study the remarkable phenomenon of chaotic synchronization on these oscillator systems, using active control and global synchronization techniques. We derive analytical expressions for control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set initial conditions, the differences between the drive and response systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.
Chaotic inflation with curvaton induced running
DEFF Research Database (Denmark)
Sloth, Martin Snoager
2014-01-01
While dust contamination now appears as a likely explanation of the apparent tension between the recent BICEP2 data and the Planck data, we will here explore the consequences of a large running in the spectral index as suggested by the BICEP2 collaboration as an alternative explanation of the app......While dust contamination now appears as a likely explanation of the apparent tension between the recent BICEP2 data and the Planck data, we will here explore the consequences of a large running in the spectral index as suggested by the BICEP2 collaboration as an alternative explanation...... of the apparent tension, but which would be in conflict with prediction of the simplest model of chaotic inflation. The large field chaotic model is sensitive to UV physics, and the nontrivial running of the spectral index suggested by the BICEP2 collaboration could therefore, if true, be telling us some...... the possibility that the running could be due to some other less UV sensitive degree of freedom. As an example, we ask if it is possible that the curvature perturbation spectrum has a contribution from a curvaton, which makes up for the large running in the spectrum. We find that this effect could mask...
Applications of tripled chaotic maps in cryptography
International Nuclear Information System (INIS)
Behnia, S.; Akhshani, A.; Akhavan, A.; Mahmodi, H.
2009-01-01
Security of information has become a major issue during the last decades. New algorithms based on chaotic maps were suggested for protection of different types of multimedia data, especially digital images and videos in this period. However, many of them fundamentally were flawed by a lack of robustness and security. For getting higher security and higher complexity, in the current paper, we introduce a new kind of symmetric key block cipher algorithm that is based on tripled chaotic maps. In this algorithm, the utilization of two coupling parameters, as well as the increased complexity of the cryptosystem, make a contribution to the development of cryptosystem with higher security. In order to increase the security of the proposed algorithm, the size of key space and the computational complexity of the coupling parameters should be increased as well. Both the theoretical and experimental results state that the proposed algorithm has many capabilities such as acceptable speed and complexity in the algorithm due to the existence of two coupling parameters and high security. Note that the ciphertext has a flat distribution and has the same size as the plaintext. Therefore, it is suitable for practical use in secure communications.
Resonance and Chaotic Trajectories in Magnetic Field Reversed Configuration
Energy Technology Data Exchange (ETDEWEB)
A.S. Landsman; S.A. Cohen; M. Edelman; G.M. Zaslavsky
2005-04-13
The nonlinear dynamics of a single ion in a field-reversed configuration (FRC) were investigated. FRC is a toroidal fusion device which uses a specific type of magnetic field to confine ions. As a result of angular invariance, the full three-dimensional Hamiltonian system can be expressed as two coupled, highly nonlinear oscillators. Due to the high nonlinearity in the equations of motion, the behavior of the system is extremely complex, showing different regimes, depending on the values of the conserved canonical angular momentum and the geometry of the fusion vessel. Perturbation theory and averaging were used to derive the unperturbed Hamiltonian and frequencies of the two degrees of freedom. The derived equations were then used to find resonances and compare to Poincar{copyright} surface-of-section plots. A regime was found where the nonlinear resonances were clearly separated by KAM [Kolmogorov-Arnold-Mosher] curves. The structure of the observed island chains was explained. The condition for the destruction of KAM curves and the onset of strong chaos was derived, using Chirikov island overlap criterion, and shown qualitatively to depend both on the canonical angular momentum and geometry of the device. After a brief discussion of the adiabatic regime the paper goes on to explore the degenerate regime that sets in at higher values of angular momenta. In this regime, the unperturbed Hamiltonian can be approximated as two uncoupled linear oscillators. In this case, the system is near-integrable, except in cases of a universal resonance, which results in large island structures, due to the smallness of nonlinear terms, which bound the resonance. The linear force constants, dominant in this regime, were derived and the geometry for a large one-to-one resonance identified. The above analysis showed good agreement with numerical simulations and was able to explain characteristic features of the dynamics.
Resonance and Chaotic Trajectories in Magnetic Field Reversed Configuration
International Nuclear Information System (INIS)
Landsman, A.S.; Cohen, S.A.; Edelman, M.; Zaslavsky, G.M.
2005-01-01
The nonlinear dynamics of a single ion in a field-reversed configuration (FRC) were investigated. FRC is a toroidal fusion device which uses a specific type of magnetic field to confine ions. As a result of angular invariance, the full three-dimensional Hamiltonian system can be expressed as two coupled, highly nonlinear oscillators. Due to the high nonlinearity in the equations of motion, the behavior of the system is extremely complex, showing different regimes, depending on the values of the conserved canonical angular momentum and the geometry of the fusion vessel. Perturbation theory and averaging were used to derive the unperturbed Hamiltonian and frequencies of the two degrees of freedom. The derived equations were then used to find resonances and compare to Poincar(copyright) surface-of-section plots. A regime was found where the nonlinear resonances were clearly separated by KAM [Kolmogorov-Arnold-Mosher] curves. The structure of the observed island chains was explained. The condition for the destruction of KAM curves and the onset of strong chaos was derived, using Chirikov island overlap criterion, and shown qualitatively to depend both on the canonical angular momentum and geometry of the device. After a brief discussion of the adiabatic regime the paper goes on to explore the degenerate regime that sets in at higher values of angular momenta. In this regime, the unperturbed Hamiltonian can be approximated as two uncoupled linear oscillators. In this case, the system is near-integrable, except in cases of a universal resonance, which results in large island structures, due to the smallness of nonlinear terms, which bound the resonance. The linear force constants, dominant in this regime, were derived and the geometry for a large one-to-one resonance identified. The above analysis showed good agreement with numerical simulations and was able to explain characteristic features of the dynamics
Unitary Housing Regimes in Transition
DEFF Research Database (Denmark)
Bengtsson, Bo; Jensen, Lotte
2013-01-01
Path dependence is strong in housing institutions and policy. In both Denmark and Sweden, today’s universal and ‘unitary’ (Kemeny) housing regimes can be traced back to institutions that were introduced fifty years back in history or more. Recently, universal and unitary housing systems...... in Scandinavia, and elsewhere, are under challenge from strong political and economic forces. These challenges can be summarized as economic cutbacks, privatization and Europeanization. Although both the Danish and the Swedish housing system are universal and unitary in character, they differ considerably...... in institutional detail. Both systems have corporatist features, however in Denmark public housing is based on local tenant democracy and control, and in Sweden on companies owned and controlled by the municipalities, combined with a centralized system of rent negotiations. In the paper the present challenges...
International Nuclear Information System (INIS)
Jung, Jinwoo; Lee, Jewon; Song, Hanjung
2011-01-01
This paper presents a fully integrated circuit implementation of an operational amplifier (op-amp) based chaotic neuron model with a bipolar output function, experimental measurements, and analyses of its chaotic behavior. The proposed chaotic neuron model integrated circuit consists of several op-amps, sample and hold circuits, a nonlinear function block for chaotic signal generation, a clock generator, a nonlinear output function, etc. Based on the HSPICE (circuit program) simulation results, approximated empirical equations for analyses were formulated. Then, the chaotic dynamical responses such as bifurcation diagrams, time series, and Lyapunov exponent were calculated using these empirical equations. In addition, we performed simulations about two chaotic neuron systems with four synapses to confirm neural network connections and got normal behavior of the chaotic neuron such as internal state bifurcation diagram according to the synaptic weight variation. The proposed circuit was fabricated using a 0.8-μm single poly complementary metal-oxide semiconductor technology. Measurements of the fabricated single chaotic neuron with ±2.5 V power supplies and a 10 kHz sampling clock frequency were carried out and compared with the simulated results.
'CANDLE' burnup regime after LWR regime
International Nuclear Information System (INIS)
Sekimoto, Hiroshi; Nagata, Akito
2008-01-01
CANDLE (Constant Axial shape of Neutron flux, nuclide densities and power shape During Life of Energy producing reactor) burnup strategy can derive many merits. From safety point of view, the change of excess reactivity along burnup is theoretically zero, and the core characteristics, such as power feedback coefficients and power peaking factor, are not changed along burnup. Application of this burnup strategy to neutron rich fast reactors makes excellent performances. Only natural or depleted uranium is required for the replacing fuels. About 40% of natural or depleted uranium undergoes fission without the conventional reprocessing and enrichment. If the LWR produced energy of X Joules, the CANDLE reactor can produce about 50X Joules from the depleted uranium left at the enrichment facility for the LWR fuel. If we can say LWRs have produced energy sufficient for full 20 years, we can produce the energy for 1000 years by using the CANDLE reactors with depleted uranium. We need not mine any uranium ore, and do not need reprocessing facility. The burnup of spent fuel becomes 10 times. Therefore, the spent fuel amount per produced energy is also reduced to one-tenth. The details of the scenario of CANDLE burnup regime after LWR regime will be presented at the symposium. (author)
Advanced data assimilation in strongly nonlinear dynamical systems
Miller, Robert N.; Ghil, Michael; Gauthiez, Francois
1994-01-01
Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.
Directory of Open Access Journals (Sweden)
Petar eTomov
2014-09-01
Full Text Available The cerebral cortex exhibits neural activity even in the absence of externalstimuli. This self-sustained activity is characterized by irregular firing ofindividual neurons and population oscillations with a broad frequency range.Questions that arise in this context, are: What are the mechanismsresponsible for the existence of neuronal spiking activity in the cortexwithout external input? Do these mechanisms depend on the structural organization of the cortical connections? Do they depend onintrinsic characteristics of the cortical neurons? To approach the answers to these questions, we have used computer simulations of cortical network models. Our networks have hierarchical modular architecture and are composedof combinations of neuron models that reproduce the firing behavior of the five main cortical electrophysiological cell classes: regular spiking (RS, chattering (CH, intrinsically bursting (IB, low threshold spiking (LTS and fast spiking (FS. The population of excitatory neurons is built of RS cells(always present and either CH or IB cells. Inhibitoryneurons belong to the same class, either LTS or FS. Long-lived self-sustained activity states in our networksimulations display irregular single neuron firing and oscillatoryactivity similar to experimentally measured ones. The duration of self-sustained activity strongly depends on the initial conditions,suggesting a transient chaotic regime. Extensive analysis of the self-sustainedactivity states showed that their lifetime expectancy increases with the numberof network modules and is favored when the network is composed of excitatory neurons of the RS and CH classes combined with inhibitory neurons of the LTS class. These results indicate that the existence and properties of the self-sustained cortical activity states depend on both the topology of the network and the neuronal mixture that comprises the network.
Proshutinsky, Andrey; Dukhovskoy, Dmitry; Timmermans, Mary-Louise; Krishfield, Richard; Bamber, Jonathan L
2015-10-13
Between 1948 and 1996, mean annual environmental parameters in the Arctic experienced a well-pronounced decadal variability with two basic circulation patterns: cyclonic and anticyclonic alternating at 5 to 7 year intervals. During cyclonic regimes, low sea-level atmospheric pressure (SLP) dominated over the Arctic Ocean driving sea ice and the upper ocean counterclockwise; the Arctic atmosphere was relatively warm and humid, and freshwater flux from the Arctic Ocean towards the subarctic seas was intensified. By contrast, during anticylonic circulation regimes, high SLP dominated driving sea ice and the upper ocean clockwise. Meanwhile, the atmosphere was cold and dry and the freshwater flux from the Arctic to the subarctic seas was reduced. Since 1997, however, the Arctic system has been under the influence of an anticyclonic circulation regime (17 years) with a set of environmental parameters that are atypical for this regime. We discuss a hypothesis explaining the causes and mechanisms regulating the intensity and duration of Arctic circulation regimes, and speculate how changes in freshwater fluxes from the Arctic Ocean and Greenland impact environmental conditions and interrupt their decadal variability. © 2015 The Authors.
Directory of Open Access Journals (Sweden)
Gavril PANDI
2011-03-01
Full Text Available The influenced flow regimes. The presence and activities ofhumanity influences the uniform environmental system, and in this context, therivers water resources. In concordance with this, the natural runoff regime suffersbigger and deeper changes. The nature of these changes depending on the type anddegree of water uses. The multitude of the use cause different types of influence,whit different quantitative aspects. In the same time, the influences havequalitative connotations, too, regarding to the modifications of the yearly watervolume runoff. So the natural runoff regime is modified. After analyzing thedistribution laws of the monthly runoff, there have been differenced four types ofinfluenced runoff regimes. In the excess type the influenced runoff is bigger thanthe natural, continuously in the whole year. The deficient type is characterized byinverse rapports like the first type, in the whole year. In the sinusoidal type, theinfluenced runoff is smaller than the natural in the period when the water isretained in the lake reservoirs, and in the depletion period the situation inverts. Atthe irregular type the ratio between influenced and natural runoff is changeable ina random meaner monthly. The recognition of the influenced regime and the gradeof influence are necessary in the evaluation and analysis of the usable hydrologicalriver resources, in the flood defence activities, in the complex scheme of thehydrographic basins, in the environment design and so on.
Calculating hadronic properties in strong QCD
International Nuclear Information System (INIS)
Pennington, M.R.
1996-01-01
This talk gives a brief review of the progress that has been made in calculating the properties of hadrons in strong QCD. In keeping with this meeting I will concentrate on those properties that can be studied with electromagnetic probes. Though perturbative QCD is highly successful, it only applies in a limited kinematic regime, where hard scattering occur, and the quarks move in the interaction region as if they are free, pointlike objects. However, the bulk of strong interactions are governed by the long distance regime, where the strong interaction is strong. It is this regime of length scales of the order of a Fermi, that determines the spectrum of light hadrons and their properties. The calculation of these properties requires an understanding of non-perturbative QCD, of confinement and chiral symmetry breaking. (author)
An efficient three-party password-based key agreement protocol using extended chaotic maps
International Nuclear Information System (INIS)
Shu Jian
2015-01-01
Three-party password-based key agreement protocols allow two users to authenticate each other via a public channel and establish a session key with the aid of a trusted server. Recently, Farash et al. [Farash M S, Attari M A 2014 “An efficient and provably secure three-party password-based authenticated key exchange protocol based on Chebyshev chaotic maps”, Nonlinear Dynamics 77(7): 399–411] proposed a three-party key agreement protocol by using the extended chaotic maps. They claimed that their protocol could achieve strong security. In the present paper, we analyze Farash et al.’s protocol and point out that this protocol is vulnerable to off-line password guessing attack and suffers communication burden. To handle the issue, we propose an efficient three-party password-based key agreement protocol using extended chaotic maps, which uses neither symmetric cryptosystems nor the server’s public key. Compared with the relevant schemes, our protocol provides better performance in terms of computation and communication. Therefore, it is suitable for practical applications. (paper)
COMPARISON OF CHAOTIC AND FRACTAL PROPERTIES OF POLAR FACULAE WITH SUNSPOT ACTIVITY
Energy Technology Data Exchange (ETDEWEB)
Deng, L. H.; Xiang, Y. Y.; Dun, G. T. [Yunnan Observatories, Chinese Academy of Sciences, Kunming 650216 (China); Li, B., E-mail: wooden@escience.cn [Shandong Provincial Key Laboratory of Optical Astronomy and Solar-Terrestrial Environment, School of Space Science and Physics, Shandong University at Weihai, Weihai 264209 (China)
2016-01-15
The solar magnetic activity is governed by a complex dynamo mechanism and exhibits a nonlinear dissipation behavior in nature. The chaotic and fractal properties of solar time series are of great importance to understanding the solar dynamo actions, especially with regard to the nonlinear dynamo theories. In the present work, several nonlinear analysis approaches are proposed to investigate the nonlinear dynamical behavior of the polar faculae and sunspot activity for the time interval from 1951 August to 1998 December. The following prominent results are found: (1) both the high- and the low-latitude solar activity are governed by a three-dimensional chaotic attractor, and the chaotic behavior of polar faculae is the most complex, followed by that of the sunspot areas, and then the sunspot numbers; (2) both the high- and low-latitude solar activity exhibit a high degree of persistent behavior, and their fractal nature is due to such long-range correlation; (3) the solar magnetic activity cycle is predictable in nature, but the high-accuracy prediction should only be done for short- to mid-term due to its intrinsically dynamical complexity. With the help of the Babcock–Leighton dynamo model, we suggest that the nonlinear coupling of the polar magnetic fields with strong active-region fields exhibits a complex manner, causing the statistical similarities and differences between the polar faculae and the sunspot-related indicators.
DEFF Research Database (Denmark)
Nielsen, Max
2006-01-01
Supply in fisheries is traditionally known for its backward bending nature, owing to externalities in production. Such a supply regime, however, exist only for pure open access fisheries. Since most fisheries worldwide are neither pure open access, nor optimally managed, rather between the extremes......, the traditional understanding of supply regimes in fisheries needs modification. This paper identifies through a case study of the East Baltic cod fishery supply regimes in fisheries, taking alternative fisheries management schemes and mesh size limitations into account. An age-structured Beverton-Holt based bio......-economic supply model with mesh sizes is developed. It is found that in the presence of realistic management schemes, the supply curves are close to vertical in the relevant range. Also, the supply curve under open access with mesh size limitations is almost vertical in the relevant range, owing to constant...
Kemih, K.; Halimi, M.; Ghanes, M.; Zhang, G.
2011-12-01
In this paper, we study the design and implementation of analog secure communication systems via synchronized chaotic Chua's circuit with sliding mode observer. For this, we adopt an approach based on an inclusion of the message in the transmitter and in the receiver; we use a sliding mode observer with un-known input in order to recover the information. Finally, an analog electronic circuit with Multisim software is designed to physically realize the complete system (transmitter-receiver).
Amplification and displacement of chaotic attractors by means of unidirectional chaotic driving
González-Miranda, J. M.
1998-06-01
Chaotic systems, when used to drive copies of themselves (or parts of themselves) may induce interesting behaviors in the driven system. In case the later exhibits invariance under amplification or translation, they may show amplification (reduction), or displacement of the attractor. It is shown how the behavior to be obtained is implied by the symmetries involved. Two explicit examples are studied to show how these phenomena manifest themselves under perfect and imperfect coupling.
Identifying and Evaluating Chaotic Behavior in Hydro-Meteorological Processes
Directory of Open Access Journals (Sweden)
Soojun Kim
2015-01-01
Full Text Available The aim of this study is to identify and evaluate chaotic behavior in hydro-meteorological processes. This study poses the two hypotheses to identify chaotic behavior of the processes. First, assume that the input data is the significant factor to provide chaotic characteristics to output data. Second, assume that the system itself is the significant factor to provide chaotic characteristics to output data. For solving this issue, hydro-meteorological time series such as precipitation, air temperature, discharge, and storage volume were collected in the Great Salt Lake and Bear River Basin, USA. The time series in the period of approximately one year were extracted from the original series using the wavelet transform. The generated time series from summation of sine functions were fitted to each series and used for investigating the hypotheses. Then artificial neural networks had been built for modeling the reservoir system and the correlation dimension was analyzed for the evaluation of chaotic behavior between inputs and outputs. From the results, we found that the chaotic characteristic of the storage volume which is output is likely a byproduct of the chaotic behavior of the reservoir system itself rather than that of the input data.
Non-reversible evolution of quantum chaotic system. Kinetic description
International Nuclear Information System (INIS)
Chotorlishvili, L.; Skrinnikov, V.
2008-01-01
It is well known that the appearance of non-reversibility in classical chaotic systems is connected with a local instability of phase trajectories relatively to a small change of initial conditions and parameters of the system. Classical chaotic systems reveal an exponential sensitivity to these changes. This leads to an exponential growth of initial error with time, and as the result after the statistical averaging over this error, the dynamics of the system becomes non-reversible. In spite of this, the question about the origin of non-reversibility in quantum case remains actual. The point is that the classical notion of instability of phase trajectories loses its sense during quantum consideration. The current work is dedicated to the clarification of the origin of non-reversibility in quantum chaotic systems. For this purpose we study a non-stationary dynamics of the chaotic quantum system. By analogy with classical chaos, we consider an influence of a small unavoidable error of the parameter of the system on the non-reversibility of the dynamics. It is shown in the Letter that due to the peculiarity of chaotic quantum systems, the statistical averaging over the small unavoidable error leads to the non-reversible transition from the pure state into the mixed one. The second part of the Letter is dedicated to the kinematic description of the chaotic quantum-mechanical system. Using the formalism of superoperators, a muster kinematic equation for chaotic quantum system was obtained from Liouville equation under a strict mathematical consideration
Direct numerical simulation of electrokinetic instability and transition to chaotic motion
Demekhin, E. A.; Nikitin, N. V.; Shelistov, V. S.
2013-12-01
A new type of instability—electrokinetic instability—and an unusual transition to chaotic motion near a charge-selective surface (semiselective electric membrane, electrode, or system of micro-/nanochannels) was studied by the numerical integration of the Nernst-Planck-Poisson-Stokes system and a weakly nonlinear analysis near the threshold of instability. A special finite-difference method was used for the space discretization along with a semi-implicit 31/3-step Runge-Kutta scheme for the integration in time. Two kinds of initial conditions were considered: (a) white-noise initial conditions to mimic "room disturbances" and subsequent natural evolution of the solution, and (b) an artificial monochromatic ion distribution with a fixed wave number to simulate regular wave patterns. The results were studied from the viewpoint of hydrodynamic stability and bifurcation theory. The threshold of electroconvective movement was found by the linear spectral stability theory, the results of which were confirmed by numerical simulation of the entire system. Our weakly nonlinear analysis and numerical integration of the entire system predict possibility of both kinds of bifurcations at the critical point, supercritical and subcritical, depending on the system parameters. The following regimes, which replace each other as the potential drop between the selective surfaces increases, were obtained: one-dimensional steady solution, two-dimensional steady electroconvective vortices (stationary point in a proper phase space), unsteady vortices aperiodically changing their parameters (homoclinic contour), periodic motion (limit cycle), and chaotic motion. The transition to chaotic motion does not include Hopf bifurcation. The numerical resolution of the thin concentration polarization layer showed spike-like charge profiles along the surface, which could be, depending on the regime, either steady or aperiodically coalescent. The numerical investigation confirmed the
Direct numerical simulation of electrokinetic instability and transition to chaotic motion
International Nuclear Information System (INIS)
Demekhin, E. A.; Nikitin, N. V.; Shelistov, V. S.
2013-01-01
A new type of instability—electrokinetic instability—and an unusual transition to chaotic motion near a charge-selective surface (semiselective electric membrane, electrode, or system of micro-/nanochannels) was studied by the numerical integration of the Nernst-Planck-Poisson-Stokes system and a weakly nonlinear analysis near the threshold of instability. A special finite-difference method was used for the space discretization along with a semi-implicit 31/3 -step Runge-Kutta scheme for the integration in time. Two kinds of initial conditions were considered: (a) white-noise initial conditions to mimic “room disturbances” and subsequent natural evolution of the solution, and (b) an artificial monochromatic ion distribution with a fixed wave number to simulate regular wave patterns. The results were studied from the viewpoint of hydrodynamic stability and bifurcation theory. The threshold of electroconvective movement was found by the linear spectral stability theory, the results of which were confirmed by numerical simulation of the entire system. Our weakly nonlinear analysis and numerical integration of the entire system predict possibility of both kinds of bifurcations at the critical point, supercritical and subcritical, depending on the system parameters. The following regimes, which replace each other as the potential drop between the selective surfaces increases, were obtained: one-dimensional steady solution, two-dimensional steady electroconvective vortices (stationary point in a proper phase space), unsteady vortices aperiodically changing their parameters (homoclinic contour), periodic motion (limit cycle), and chaotic motion. The transition to chaotic motion does not include Hopf bifurcation. The numerical resolution of the thin concentration polarization layer showed spike-like charge profiles along the surface, which could be, depending on the regime, either steady or aperiodically coalescent. The numerical investigation confirmed the
Direct numerical simulation of electrokinetic instability and transition to chaotic motion
Energy Technology Data Exchange (ETDEWEB)
Demekhin, E. A., E-mail: edemekhi@gmail.com [Laboratory of Micro- and Nanofluidics, Moscow State University, Moscow 119192 (Russian Federation); Department of Computation Mathematics and Computer Science, Kuban State University, Krasnodar 350040 (Russian Federation); Institute of Mechanics, Moscow State University, Moscow 117192 (Russian Federation); Nikitin, N. V. [Institute of Mechanics, Moscow State University, Moscow 117192 (Russian Federation); Shelistov, V. S. [Institute of Mechanics, Moscow State University, Moscow 117192 (Russian Federation); Scientific Research Department, Kuban State University, Krasnodar 350040 (Russian Federation)
2013-12-15
A new type of instability—electrokinetic instability—and an unusual transition to chaotic motion near a charge-selective surface (semiselective electric membrane, electrode, or system of micro-/nanochannels) was studied by the numerical integration of the Nernst-Planck-Poisson-Stokes system and a weakly nonlinear analysis near the threshold of instability. A special finite-difference method was used for the space discretization along with a semi-implicit 31/3 -step Runge-Kutta scheme for the integration in time. Two kinds of initial conditions were considered: (a) white-noise initial conditions to mimic “room disturbances” and subsequent natural evolution of the solution, and (b) an artificial monochromatic ion distribution with a fixed wave number to simulate regular wave patterns. The results were studied from the viewpoint of hydrodynamic stability and bifurcation theory. The threshold of electroconvective movement was found by the linear spectral stability theory, the results of which were confirmed by numerical simulation of the entire system. Our weakly nonlinear analysis and numerical integration of the entire system predict possibility of both kinds of bifurcations at the critical point, supercritical and subcritical, depending on the system parameters. The following regimes, which replace each other as the potential drop between the selective surfaces increases, were obtained: one-dimensional steady solution, two-dimensional steady electroconvective vortices (stationary point in a proper phase space), unsteady vortices aperiodically changing their parameters (homoclinic contour), periodic motion (limit cycle), and chaotic motion. The transition to chaotic motion does not include Hopf bifurcation. The numerical resolution of the thin concentration polarization layer showed spike-like charge profiles along the surface, which could be, depending on the regime, either steady or aperiodically coalescent. The numerical investigation confirmed the
Classical wave experiments on chaotic scattering
International Nuclear Information System (INIS)
Kuhl, U; Stoeckmann, H-J; Weaver, R
2005-01-01
We review recent research on the transport properties of classical waves through chaotic systems with special emphasis on microwaves and sound waves. Inasmuch as these experiments use antennas or transducers to couple waves into or out of the systems, scattering theory has to be applied for a quantitative interpretation of the measurements. Most experiments concentrate on tests of predictions from random matrix theory and the random plane wave approximation. In all studied examples a quantitative agreement between experiment and theory is achieved. To this end it is necessary, however, to take absorption and imperfect coupling into account, concepts that were ignored in most previous theoretical investigations. Classical phase space signatures of scattering are being examined in a small number of experiments
Learning FCM by chaotic simulated annealing
International Nuclear Information System (INIS)
Alizadeh, Somayeh; Ghazanfari, Mehdi
2009-01-01
Fuzzy cognitive map (FCM) is a directed graph, which shows the relations between essential components in complex systems. It is a very convenient, simple, and powerful tool, which is used in numerous areas of application. Experts who are familiar with the system components and their relations can generate a related FCM. There is a big gap when human experts cannot produce FCM or even there is no expert to produce the related FCM. Therefore, a new mechanism must be used to bridge this gap. In this paper, a novel learning method is proposed to construct FCM by using Chaotic simulated annealing (CSA). The proposed method not only is able to construct FCM graph topology but also is able to extract the weight of the edges from input historical data. The efficiency of the proposed method is shown via comparison of its results of some numerical examples with those of Simulated annealing (SA) method.
Chaotic Behavior in a Switched Dynamical System
Directory of Open Access Journals (Sweden)
Fatima El Guezar
2008-01-01
Full Text Available We present a numerical study of an example of piecewise linear systems that constitute a class of hybrid systems. Precisely, we study the chaotic dynamics of the voltage-mode controlled buck converter circuit in an open loop. By considering the voltage input as a bifurcation parameter, we observe that the obtained simulations show that the buck converter is prone to have subharmonic behavior and chaos. We also present the corresponding bifurcation diagram. Our modeling techniques are based on the new French native modeler and simulator for hybrid systems called Scicos (Scilab connected object simulator which is a Scilab (scientific laboratory package. The followed approach takes into account the hybrid nature of the circuit.
Controller Synthesis for Periodically Forced Chaotic Systems
Basso, Michele; Genesio, Roberto; Giovanardi, Lorenzo
Delayed feedback controllers are an appealing tool for stabilization of periodic orbits in chaotic systems. Despite their conceptual simplicity, specific and reliable design procedures are difficult to obtain, partly also because of their inherent infinite-dimensional structure. This chapter considers the use of finite dimensional linear time invariant controllers for stabilization of periodic solutions in a general class of sinusoidally forced nonlinear systems. For such controllers — which can be interpreted as rational approximations of the delayed ones — we provide a computationally attractive synthesis technique based on Linear Matrix Inequalities (LMIs), by mixing results concerning absolute stability of nonlinear systems and robustness of uncertain linear systems. The resulting controllers prove to be effective for chaos suppression in electronic circuits and systems, as shown by two different application examples.
Chaotic waves in Hall thruster plasma
International Nuclear Information System (INIS)
Peradzynski, Zbigniew; Barral, S.; Kurzyna, J.; Makowski, K.; Dudeck, M.
2006-01-01
The set of hyperbolic equations of the fluid model describing the acceleration of plasma in a Hall thruster is analyzed. The characteristic feature of the flow is the existence of a trapped characteristic; i.e. there exists a characteristic line, which never intersects the boundary of the flow region in the thruster. To study the propagation of short wave perturbations, the approach of geometrical optics (like WKB) can be applied. This can be done in a linear as well as in a nonlinear version. The nonlinear version describes the waves of small but finite amplitude. As a result of such an approach one obtains so called transport equation, which are governing the wave amplitude. Due to the existence of trapped characteristics this transport equation appears to have chaotic (turbulent) solutions in both, linear and nonlinear versions
Logistic chaotic maps for binary numbers generations
International Nuclear Information System (INIS)
Kanso, Ali; Smaoui, Nejib
2009-01-01
Two pseudorandom binary sequence generators, based on logistic chaotic maps intended for stream cipher applications, are proposed. The first is based on a single one-dimensional logistic map which exhibits random, noise-like properties at given certain parameter values, and the second is based on a combination of two logistic maps. The encryption step proposed in both algorithms consists of a simple bitwise XOR operation of the plaintext binary sequence with the keystream binary sequence to produce the ciphertext binary sequence. A threshold function is applied to convert the floating-point iterates into binary form. Experimental results show that the produced sequences possess high linear complexity and very good statistical properties. The systems are put forward for security evaluation by the cryptographic committees.
Study of chaos in chaotic satellite systems
Khan, Ayub; Kumar, Sanjay
2018-01-01
In this paper, we study the qualitative behaviour of satellite systems using bifurcation diagrams, Poincaré section, Lyapunov exponents, dissipation, equilibrium points, Kaplan-Yorke dimension etc. Bifurcation diagrams with respect to the known parameters of satellite systems are analysed. Poincaré sections with different sowing axes of the satellite are drawn. Eigenvalues of Jacobian matrices for the satellite system at different equilibrium points are calculated to justify the unstable regions. Lyapunov exponents are estimated. From these studies, chaos in satellite system has been established. Solution of equations of motion of the satellite system are drawn in the form of three-dimensional, two-dimensional and time series phase portraits. Phase portraits and time series display the chaotic nature of the considered system.
Bose, Chandan; Sarkar, Sunetra
2018-04-01
The present study investigates the complex vortex interactions in two-dimensional flow-field behind a symmetric NACA0012 airfoil undergoing a prescribed periodic pitching-plunging motion in low Reynolds number regime. The flow-field transitions from periodic to chaotic through a quasi-periodic route as the plunge amplitude is gradually increased. This study unravels the role of the complex interactions that take place among the main vortex structures in making the unsteady flow-field transition from periodicity to chaos. The leading-edge separation plays a key role in providing the very first trigger for aperiodicity. Subsequent mechanisms like shredding, merging, splitting, and collision of vortices in the near-field that propagate and sustain the disturbance have also been followed and presented. These fundamental mechanisms are seen to give rise to spontaneous and irregular formation of new vortex couples at arbitrary locations, which are the primary agencies for sustaining chaos in the flow-field. The interactions have been studied for each dynamical state to understand the course of transition in the flow-field. The qualitative changes observed in the flow-field are manifestation of changes in the underlying dynamical system. The overall dynamics are established in the present study by means of robust quantitative measures derived from classical and non-classical tools from the dynamical system theory. As the present analysis involves a high fidelity multi-unknown system, non-classical dynamical tools such as recurrence-based time series methods are seen to be very efficient. Moreover, their application is novel in the context of pitch-plunge flapping flight.
Nonlinear Dynamics, Chaotic and Complex Systems
Infeld, E.; Zelazny, R.; Galkowski, A.
2011-04-01
Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet
Regularized forecasting of chaotic dynamical systems
International Nuclear Information System (INIS)
Bollt, Erik M.
2017-01-01
While local models of dynamical systems have been highly successful in terms of using extensive data sets observing even a chaotic dynamical system to produce useful forecasts, there is a typical problem as follows. Specifically, with k-near neighbors, kNN method, local observations occur due to recurrences in a chaotic system, and this allows for local models to be built by regression to low dimensional polynomial approximations of the underlying system estimating a Taylor series. This has been a popular approach, particularly in context of scalar data observations which have been represented by time-delay embedding methods. However such local models can generally allow for spatial discontinuities of forecasts when considered globally, meaning jumps in predictions because the collected near neighbors vary from point to point. The source of these discontinuities is generally that the set of near neighbors varies discontinuously with respect to the position of the sample point, and so therefore does the model built from the near neighbors. It is possible to utilize local information inferred from near neighbors as usual but at the same time to impose a degree of regularity on a global scale. We present here a new global perspective extending the general local modeling concept. In so doing, then we proceed to show how this perspective allows us to impose prior presumed regularity into the model, by involving the Tikhonov regularity theory, since this classic perspective of optimization in ill-posed problems naturally balances fitting an objective with some prior assumed form of the result, such as continuity or derivative regularity for example. This all reduces to matrix manipulations which we demonstrate on a simple data set, with the implication that it may find much broader context.
Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Gundara, G.; Mada Sanjaya, W. S.; Subiyanto
2018-03-01
A 3-D new chaotic attractor with two quadratic nonlinearities is proposed in this paper. The dynamical properties of the new chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new chaotic system has three unstable equilibrium points. The new chaotic attractor is dissipative in nature. As an engineering application, adaptive synchronization of identical new chaotic attractors is designed via nonlinear control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic attractor model.
Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System.
Rozenbaum, Efim B; Ganeshan, Sriram; Galitski, Victor
2017-02-24
It was proposed recently that the out-of-time-ordered four-point correlator (OTOC) may serve as a useful characteristic of quantum-chaotic behavior, because, in the semiclassical limit ℏ→0, its rate of exponential growth resembles the classical Lyapunov exponent. Here, we calculate the four-point correlator C(t) for the classical and quantum kicked rotor-a textbook driven chaotic system-and compare its growth rate at initial times with the standard definition of the classical Lyapunov exponent. Using both quantum and classical arguments, we show that the OTOC's growth rate and the Lyapunov exponent are, in general, distinct quantities, corresponding to the logarithm of the phase-space averaged divergence rate of classical trajectories and to the phase-space average of the logarithm, respectively. The difference appears to be more pronounced in the regime of low kicking strength K, where no classical chaos exists globally. In this case, the Lyapunov exponent quickly decreases as K→0, while the OTOC's growth rate may decrease much slower, showing a higher sensitivity to small chaotic islands in the phase space. We also show that the quantum correlator as a function of time exhibits a clear singularity at the Ehrenfest time t_{E}: transitioning from a time-independent value of t^{-1}lnC(t) at ttime at t>t_{E}. We note that the underlying physics here is the same as in the theory of weak (dynamical) localization [Aleiner and Larkin, Phys. Rev. B 54, 14423 (1996)PRBMDO0163-182910.1103/PhysRevB.54.14423; Tian, Kamenev, and Larkin, Phys. Rev. Lett. 93, 124101 (2004)PRLTAO0031-900710.1103/PhysRevLett.93.124101] and is due to a delay in the onset of quantum interference effects, which occur sharply at a time of the order of the Ehrenfest time.
International Nuclear Information System (INIS)
Provata, A.; Katsaloulis, P.; Verganelakis, D.A.
2012-01-01
Highlights: ► Calculation of human brain multifractal spectra. ► Calculations are based on Diffusion Tensor MRI Images. ► Spectra are modelled by coupled Ikeda map dynamics. ► Coupled lattice Ikeda maps model well only positive multifractal spectra. ► Appropriately modified coupled lattice Ikeda maps give correct spectra. - Abstract: The multifractal spectra of 3d Diffusion Tensor Images (DTI) obtained by magnetic resonance imaging of the human brain are studied. They are shown to deviate substantially from artificial brain images with the same white matter intensity. All spectra, obtained from 12 healthy subjects, show common characteristics indicating non-trivial moments of the intensity. To model the spectra the dynamics of the chaotic Ikeda map are used. The DTI multifractal spectra for positive q are best approximated by 3d coupled Ikeda maps in the fully developed chaotic regime. The coupling constants are as small as α = 0.01. These results reflect not only the white tissue non-trivial architectural complexity in the human brain, but also demonstrate the presence and importance of coupling between neuron axons. The architectural complexity is also mirrored by the deviations in the negative q-spectra, where the rare events dominate. To obtain a good agreement in the DTI negative q-spectrum of the brain with the Ikeda dynamics, it is enough to slightly modify the most rare events of the coupled Ikeda distributions. The representation of Diffusion Tensor Images with coupled Ikeda maps is not unique: similar conclusions are drawn when other chaotic maps (Tent, Logistic or Henon maps) are employed in the modelling of the neuron axons network.
A stream cipher based on a spatiotemporal chaotic system
International Nuclear Information System (INIS)
Li Ping; Li Zhong; Halang, Wolfgang A.; Chen Guanrong
2007-01-01
A stream cipher based on a spatiotemporal chaotic system is proposed. A one-way coupled map lattice consisting of logistic maps is served as the spatiotemporal chaotic system. Multiple keystreams are generated from the coupled map lattice by using simple algebraic computations, and then are used to encrypt plaintext via bitwise XOR. These make the cipher rather simple and efficient. Numerical investigation shows that the cryptographic properties of the generated keystream are satisfactory. The cipher seems to have higher security, higher efficiency and lower computation expense than the stream cipher based on a spatiotemporal chaotic system proposed recently
Transiently chaotic neural networks with piecewise linear output functions
Energy Technology Data Exchange (ETDEWEB)
Chen, S.-S. [Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan (China); Shih, C.-W. [Department of Applied Mathematics, National Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu, Taiwan (China)], E-mail: cwshih@math.nctu.edu.tw
2009-01-30
Admitting both transient chaotic phase and convergent phase, the transiently chaotic neural network (TCNN) provides superior performance than the classical networks in solving combinatorial optimization problems. We derive concrete parameter conditions for these two essential dynamic phases of the TCNN with piecewise linear output function. The confirmation for chaotic dynamics of the system results from a successful application of the Marotto theorem which was recently clarified. Numerical simulation on applying the TCNN with piecewise linear output function is carried out to find the optimal solution of a travelling salesman problem. It is demonstrated that the performance is even better than the previous TCNN model with logistic output function.
Chaotic behaviour and controlling chaos in free electron lasers
International Nuclear Information System (INIS)
Wang Wenjie; Chen Shigang; Du Xiangwan; Wang Guangrui
1995-01-01
Chaos in free electron lasers (FEL) is reviewed. Special attention has been paid to the chaotic behaviour of the electrons and the laser field. The problem of controlling and utilizing chaotic motion of the electrons and the laser field has also been discussed. In order to find out the rules of instability and chaos in FEL, some typical methods of the chaotic theory are used. These methods include making the Poincare surface of section, drawing the phase space diagrams of the electron orbits, calculating the Liapunov exponents, and computing the power spectrum, etc. Finally, some problems in FEL research are discussed (103 refs., 54 figs.)
Adaptive control of chaotic continuous-time systems with delay
Tian, Yu-Chu; Gao, Furong
1998-06-01
A simple delay system governed by a first-order differential-delay equation may behave chaotically, but the conditions for the system to have such behaviors have not been well recognized. In this paper, a set of rules is postulated first for the conditions for the delay system to display chaos. A model-reference adaptive control scheme is then proposed to control the chaotic system state to converge to an arbitrarily given reference trajectory with certain and uncertain system parameters. Numerical examples are given to analyze the chaotic behaviors of the delay system and to demonstrate the effectiveness of the proposed adaptive control scheme.
Statistics of the electromagnetic response of a chaotic reverberation chamber
Directory of Open Access Journals (Sweden)
J.-B. Gros
2015-11-01
Full Text Available This article presents a study of the electromagnetic re- sponse of a chaotic reverberation chamber (RC in the pres- ence of losses. By means of simulations and of experi- ments, the fluctuations in the maxima of the field obtained in a conventional mode-stirred RC are compared with those in a chaotic RC in the neighborhood of the Lowest Useable Frequency (LUF. The present work illustrates that the uni- versal spectral and spatial statistical properties of chaotic RCs allow to meet more adequately the criteria required by the Standard IEC 61000-4-21 to perform tests of electro- magnetic compatibility.
Control of chaotic vibration in automotive wiper systems
International Nuclear Information System (INIS)
Wang Zheng; Chau, K.T.
2009-01-01
Chaotic vibration has been identified in the automotive wiper system at certain wiping speeds. This irregular vibration not only decreases the wiping efficiency, but also degrades the driving comfort. The purpose of this paper is to propose a new approach to stabilize the chaotic vibration in the wiper system. The key is to employ the extended time-delay feedback control in such a way that the applied voltage of the wiper motor is online adjusted according to its armature current feedback. Based on a practical wiper system, it is verified that the proposed approach can successfully stabilize the chaotic vibration, and provide a wide range of wiping speeds
An optical CDMA system based on chaotic sequences
Liu, Xiao-lei; En, De; Wang, Li-guo
2014-03-01
In this paper, a coherent asynchronous optical code division multiple access (OCDMA) system is proposed, whose encoder/decoder is an all-optical generator. This all-optical generator can generate analog and bipolar chaotic sequences satisfying the logistic maps. The formula of bit error rate (BER) is derived, and the relationship of BER and the number of simultaneous transmissions is analyzed. Due to the good property of correlation, this coherent OCDMA system based on these bipolar chaotic sequences can support a large number of simultaneous users, which shows that these chaotic sequences are suitable for asynchronous OCDMA system.
Stabilization and Synchronization of Memristive Chaotic Circuits by Impulsive Control
Directory of Open Access Journals (Sweden)
Limin Zou
2017-01-01
Full Text Available The purpose of this note is to study impulsive control and synchronization of memristor based chaotic circuits shown by Muthuswamy. We first establish a less conservative sufficient condition for the stability of memristor based chaotic circuits. After that, we discuss the effect of errors on stability. Meanwhile, we also discuss impulsive synchronization of two memristor based chaotic systems. Our results are more general and more applicable than the ones shown by Yang, Li, and Huang. Finally, several numerical examples are given to show the effectiveness of our methods.
Chaos synchronization of a new chaotic system via nonlinear control
International Nuclear Information System (INIS)
Zhang Qunjiao; Lu Junan
2008-01-01
This paper investigates chaos synchronization of a new chaotic system [Lue J, Chen G, Cheng D. A new chaotic system and beyond: the generalized Lorenz-like system. Int J Bifurcat Chaos 2004;14:1507-37]. Two kinds of novel nonlinear controllers are designed based on the Lyapunov stability theory. It can be viewed as an improvement to the existing results of reference [Park JH. Chaos synchronization of a chaotic system via nonlinear control. Chaos, Solitons and Fractals 2005;25:579-84] because we use less controllers but realize a global and exponential asymptotical synchronization. Numerical simulations are provided to show the effectiveness and advantage of this method
Cognitive radio resource allocation based on coupled chaotic genetic algorithm
International Nuclear Information System (INIS)
Zu Yun-Xiao; Zhou Jie; Zeng Chang-Chang
2010-01-01
A coupled chaotic genetic algorithm for cognitive radio resource allocation which is based on genetic algorithm and coupled Logistic map is proposed. A fitness function for cognitive radio resource allocation is provided. Simulations are conducted for cognitive radio resource allocation by using the coupled chaotic genetic algorithm, simple genetic algorithm and dynamic allocation algorithm respectively. The simulation results show that, compared with simple genetic and dynamic allocation algorithm, coupled chaotic genetic algorithm reduces the total transmission power and bit error rate in cognitive radio system, and has faster convergence speed
Modified scaling function projective synchronization of chaotic systems
International Nuclear Information System (INIS)
Xu Yu-Hua; Zhou Wu-Neng; Fang Jian-An
2011-01-01
This paper investigates a kind of modified scaling function projective synchronization of uncertain chaotic systems using an adaptive controller. The given scaling function in the new method can be an equilibrium point, a periodic orbit, or even a chaotic attractor in the phase space. Based on LaSalle's invariance set principle, the adaptive control law is derived to make the states of two chaotic systems function projective synchronized. Some numerical examples are also given to show the effectiveness of the proposed method. (general)
2001-01-01
There are at present at least three international regimes of maritime cargo liability in force in different countries of the world - the original Hague rules (1924), the updated version known as the Hague-Visby rules (1968, further amended 1979), and...
Six, Frédérique; Verhoest, Koen
2017-01-01
Within political and administrative sciences generally, trust as a concept is contested, especially in the field of regulatory governance. This groundbreaking book is the first to systematically explore the role and dynamics of trust within regulatory regimes. Conceptualizing, mapping and analyzing
DEFF Research Database (Denmark)
Abrahamson, Peter
2017-01-01
The paper asks if East Asian welfare regimes are still productivist and Confucian? And, have they developed public care policies? The literature is split on the first question but (mostly) confirmative on the second. Care has to a large, but insufficient extent, been rolled out in the region...
Parameter and state estimation of experimental chaotic systems using synchronization
Quinn, John C.; Bryant, Paul H.; Creveling, Daniel R.; Klein, Sallee R.; Abarbanel, Henry D. I.
2009-07-01
We examine the use of synchronization as a mechanism for extracting parameter and state information from experimental systems. We focus on important aspects of this problem that have received little attention previously and we explore them using experiments and simulations with the chaotic Colpitts oscillator as an example system. We explore the impact of model imperfection on the ability to extract valid information from an experimental system. We compare two optimization methods: an initial value method and a constrained method. Each of these involves coupling the model equations to the experimental data in order to regularize the chaotic motions on the synchronization manifold. We explore both time-dependent and time-independent coupling and discuss the use of periodic impulse coupling. We also examine both optimized and fixed (or manually adjusted) coupling. For the case of an optimized time-dependent coupling function u(t) we find a robust structure which includes sharp peaks and intervals where it is zero. This structure shows a strong correlation with the location in phase space and appears to depend on noise, imperfections of the model, and the Lyapunov direction vectors. For time-independent coupling we find the counterintuitive result that often the optimal rms error in fitting the model to the data initially increases with coupling strength. Comparison of this result with that obtained using simulated data may provide one measure of model imperfection. The constrained method with time-dependent coupling appears to have benefits in synchronizing long data sets with minimal impact, while the initial value method with time-independent coupling tends to be substantially faster, more flexible, and easier to use. We also describe a method of coupling which is useful for sparse experimental data sets. Our use of the Colpitts oscillator allows us to explore in detail the case of a system with one positive Lyapunov exponent. The methods we explored are easily
Directory of Open Access Journals (Sweden)
A. V. Malov
2018-01-01
Full Text Available The review article reveals the content of the concept of Food Regime, which is little-known in the Russian academic reference. The author monitored and codified the semantic dynamic of the terminological unit from its original interpretations to modern formulations based on the retrospective analysis. The rehabilitation of the academic merits of D. Puchala and R. Hopkins — authors who used the concept Food Regime for a few years before its universally recognized origin and official scientific debut, was accomplished with help of historical and comparative methods. The author implemented the method of ascension from the abstract to the concrete to demonstrating the classification of Food Regimes compiled on the basis of geopolitical interests in the sphere of international production, consumption, and distribution of foodstuffs. The characteristic features of historically formed Food Regime were described in the chronological order, as well as modern tendencies possessing reformist potential were identified. In particular, it has been established that the idea of Food Sovereignty (which is an alternative to the modern Corporate Food Regime is the subject for acute academic disputes. The discussion between P. McMichael P. and H. Bernstein devoted to the “peasant question” — mobilization frame of the Food Sovereignty strategy was analyzed using the secondary data processing method. Due to the critical analysis, the author comes to the conclusion that it is necessary to follow the principles of the Food Sovereignty strategy to prevent the catastrophic prospects associated with ecosystem degradation, accelerated erosion of soils, the complete disappearance of biodiversity and corporate autoc racy successfully. The author is convinced that the idea of Food Sovereignty can ward off energetic liberalization of nature, intensive privatization of life and rapid monetization of unconditioned human reflexes.
Statistical distribution of components of energy eigenfunctions: from nearly-integrable to chaotic
International Nuclear Information System (INIS)
Wang, Jiaozi; Wang, Wen-ge
2016-01-01
We study the statistical distribution of components in the non-perturbative parts of energy eigenfunctions (EFs), in which main bodies of the EFs lie. Our numerical simulations in five models show that deviation of the distribution from the prediction of random matrix theory (RMT) is useful in characterizing the process from nearly-integrable to chaotic, in a way somewhat similar to the nearest-level-spacing distribution. But, the statistics of EFs reveals some more properties, as described below. (i) In the process of approaching quantum chaos, the distribution of components shows a delay feature compared with the nearest-level-spacing distribution in most of the models studied. (ii) In the quantum chaotic regime, the distribution of components always shows small but notable deviation from the prediction of RMT in models possessing classical counterparts, while, the deviation can be almost negligible in models not possessing classical counterparts. (iii) In models whose Hamiltonian matrices possess a clear band structure, tails of EFs show statistical behaviors obviously different from those in the main bodies, while, the difference is smaller for Hamiltonian matrices without a clear band structure.
Chen, Xin; Fan, Ruihua; Chen, Yiming; Zhai, Hui; Zhang, Pengfei
2017-11-17
The Sachdev-Ye-Kitaev (SYK) model is a concrete solvable model to study non-Fermi liquid properties, holographic duality, and maximally chaotic behavior. In this work, we consider a generalization of the SYK model that contains two SYK models with a different number of Majorana modes coupled by quadratic terms. This model is also solvable, and the solution shows a zero-temperature quantum phase transition between two non-Fermi liquid chaotic phases. This phase transition is driven by tuning the ratio of two mode numbers, and a nonchaotic Fermi liquid sits at the critical point with an equal number of modes. At a finite temperature, the Fermi liquid phase expands to a finite regime. More intriguingly, a different non-Fermi liquid phase emerges at a finite temperature. We characterize the phase diagram in terms of the spectral function, the Lyapunov exponent, and the entropy. Our results illustrate a concrete example of the quantum phase transition and critical behavior between two non-Fermi liquid phases.
Weak and strong chaos in Fermi-Pasta-Ulam models and beyond
Pettini, Marco; Casetti, Lapo; Cerruti-Sola, Monica; Franzosi, Roberto; Cohen, E. G. D.
2005-03-01
We briefly review some of the most relevant results that our group obtained in the past, while investigating the dynamics of the Fermi-Pasta-Ulam (FPU) models. The first result is the numerical evidence of the existence of two different kinds of transitions in the dynamics of the FPU models: (i) A stochasticity threshold (ST), characterized by a value of the energy per degree of freedom below which the overwhelming majority of the phase space trajectories are regular (vanishing Lyapunov exponents). It tends to vanish as the number N of degrees of freedom is increased. (ii) A strong stochasticity threshold (SST), characterized by a value of the energy per degree of freedom at which a crossover appears between two different power laws of the energy dependence of the largest Lyapunov exponent, which phenomenologically corresponds to the transition between weak and strong chaotic regimes. It is stable with N. The second result is the development of a Riemannian geometric theory to explain the origin of Hamiltonian chaos. Starting this theory has been motivated by the inadequacy of the approach based on homoclinic intersections to explain the origin of chaos in systems of arbitrarily large N, or arbitrarily far from quasi-integrability, or displaying a transition between weak and strong chaos. Finally, the third result stems from the search for the transition between weak and strong chaos in systems other than FPU. Actually, we found that a very sharp SST appears as the dynamical counterpart of a thermodynamic phase transition, which in turn has led, in the light of the Riemannian theory of chaos, to the development of a topological theory of phase transitions.
Cluster synchronization modes in an ensemble of coupled chaotic oscillators
DEFF Research Database (Denmark)
Belykh, Vladimir N.; Belykh, Igor V.; Mosekilde, Erik
2001-01-01
Considering systems of diffusively coupled identical chaotic oscillators, an effective method to determine the possible states of cluster synchronization and ensure their stability is presented. The method, which may find applications in communication engineering and other fields of science...
Spatial and Transform Domain based Steganography Using Chaotic ...
African Journals Online (AJOL)
pc
2018-03-05
Mar 5, 2018 ... further improve security chaotic maps are used for scrambling the ... I. INTRODUCTION. With the rapid growth of internet network and computer ..... techniques, then we will have two layers of protection. In this scheme, the ...
Experimental Observation of Chaotic Beats in Oscillators Sharing Nonlinearity
Paul Asir, M.; Jeevarekha, A.; Philominathan, P.
This paper deals with the generation of chaotic beats in a system of two forced dissipative LCR oscillators sharing a nonlinear element. The presence of two external periodic excitations and a common nonlinear element in the chosen system enables the facile generation of chaotic beats. Thus rendered chaotic beats were characterized in both time domain and phase space. Lyapunov exponents and envelope of the beats were computed to diagnose the chaotic nature of the signals. The role of common nonlinearity on the complexity of the generated beats is discussed. Real-time experimental hardware implementation has also been done to confirm the subsistence of the phenomenon, for the first time. Extensive Multisim simulations were carried out to understand, a bit more about the shrinkage and revivals of state variables in phase space.
Hybrid synchronization of two independent chaotic systems on ...
Indian Academy of Sciences (India)
Keywords. Hybrid synchronization; complex network; information source; chaotic system. ... encryption and decryption through synchronization. However, the ... Certainly, if the two systems are different, the security would be improved. How.
Cosmic time gauge in quantum cosmology and chaotic inflation model
International Nuclear Information System (INIS)
Hosoya, A.
1986-01-01
The author proposes a cosmic time gauge formalism in quantum cosmology to get an equation for the Schrodinger type. Its application to the chaotic inflation scenario reveals that the uncertainty in the scale factor grows exponentially as the universe inflates
RBF neural network based H∞ synchronization for unknown chaotic ...
Indian Academy of Sciences (India)
, 172 ... the effect of disturbance to an H∞ norm constraint. It is shown that ... unknown chaotic systems; linear matrix inequality (LMI); learning law. 1. Introduction .... (9) is RBFNN H∞ synchronized if the synchronization error e(t) satisfies. ∫ ∞.
Behavioural analysis of a time series– A chaotic approach
Indian Academy of Sciences (India)
Abstract. Out of the various methods available to study the chaotic behaviour, cor- ... that CDM is an efficient method for behavioural study of a time series. ...... Stochastic Environmental Research and Risk Assessment, 27(6): 1371–1381.
Synchronization Between Two Different Switched Chaotic Systems By Switching Control
Directory of Open Access Journals (Sweden)
Du Li Ming
2016-01-01
Full Text Available This paper is concerned with the synchronization problem of two different switched chaotic systems, considering the general case that the master-slave switched chaotic systems have uncertainties. Two basic problems are considered: one is projective synchronization of switched chaotic systems under arbitrary switching; the other is projective synchronization of switched chaotic systems by design of switching when synchronization cannot achieved by using any subsystems alone. For the two problems, common Lyapunov function method and multiple Lyapunov function method are used respectively, an adaptive control scheme has been presented, some sufficient synchronization conditions are attainted, and the switching signal is designed. Finally, the numerical simulation is provide to show the effectiveness of our method.
Autonomous third-order duffing-holmes type chaotic oscillator
DEFF Research Database (Denmark)
Lindberg, Erik; Tamaseviciute, E; Mykolaitis, G
2009-01-01
feedback loop. In contrast to many other autonomous chaotic oscillators, including linear unstable resonators and nonlinear damping loops, the novel circuit is based on nonlinear resonator and linear damping loop in the negative feedback. SPICE simulation and hardware experimental investigations...
Global chaos synchronization of new chaotic systems via nonlinear control
International Nuclear Information System (INIS)
Chen, H.-K.
2005-01-01
Nonlinear control is an effective method for making two identical chaotic systems or two different chaotic systems be synchronized. However, this method assumes that the Lyapunov function of error dynamic (e) of synchronization is always formed as V (e) = 1/2e T e. In this paper, modification based on Lyapunov stability theory to design a controller is proposed in order to overcome this limitation. The method has been applied successfully to make two identical new systems and two different chaotic systems (new system and Lorenz system) globally asymptotically synchronized. Since the Lyapunov exponents are not required for the calculation, this method is effective and convenient to synchronize two identical systems and two different chaotic systems. Numerical simulations are also given to validate the proposed synchronization approach
Cryptanalysis of a discrete-time synchronous chaotic encryption system
International Nuclear Information System (INIS)
Arroyo, David; Alvarez, Gonzalo; Li Shujun; Li Chengqing; Nunez, Juana
2008-01-01
Recently a chaotic cryptosystem based on discrete-time synchronization has been proposed. Some weaknesses of that new encryption system are addressed and exploited in order to successfully cryptanalyze the system
A new transiently chaotic flow with ellipsoid equilibria
Panahi, Shirin; Aram, Zainab; Jafari, Sajad; Pham, Viet-Thanh; Volos, Christos; Rajagopal, Karthikeyan
2018-03-01
In this article, a simple autonomous transiently chaotic flow with cubic nonlinearities is proposed. This system represents some unusual features such as having a surface of equilibria. We shall describe some dynamical properties and behaviours of this system in terms of eigenvalue structures, bifurcation diagrams, time series, and phase portraits. Various behaviours of this system such as periodic and transiently chaotic dynamics can be shown by setting special parameters in proper values. Our system belongs to a newly introduced category of transiently chaotic systems: systems with hidden attractors. Transiently chaotic behaviour of our proposed system has been implemented and tested by the OrCAD-PSpise software. We have found a proper qualitative similarity between circuit and simulation results.
Lag synchronization of chaotic systems with time-delayed linear ...
Indian Academy of Sciences (India)
delayed linear terms via impulsive control is investigated. Based on the stability theory of impulsive delayed differen- tial equations, some sufficient conditions are obtained guaranteeing the synchronized behaviours between two delayed chaotic ...
Two novel synchronization criterions for a unified chaotic system
International Nuclear Information System (INIS)
Tao Chaohai; Xiong Hongxia; Hu Feng
2006-01-01
Two novel synchronization criterions are proposed in this paper. It includes drive-response synchronization and adaptive synchronization schemes. Moreover, these synchronization criterions can be applied to a large class of chaotic systems and are very useful for secure communication
Suemitsu, Yoshikazu; Nara, Shigetoshi
2004-09-01
Chaotic dynamics introduced into a neural network model is applied to solving two-dimensional mazes, which are ill-posed problems. A moving object moves from the position at t to t + 1 by simply defined motion function calculated from firing patterns of the neural network model at each time step t. We have embedded several prototype attractors that correspond to the simple motion of the object orienting toward several directions in two-dimensional space in our neural network model. Introducing chaotic dynamics into the network gives outputs sampled from intermediate state points between embedded attractors in a state space, and these dynamics enable the object to move in various directions. System parameter switching between a chaotic and an attractor regime in the state space of the neural network enables the object to move to a set target in a two-dimensional maze. Results of computer simulations show that the success rate for this method over 300 trials is higher than that of random walk. To investigate why the proposed method gives better performance, we calculate and discuss statistical data with respect to dynamical structure.
A chaotic stream cipher and the usage in video protection
International Nuclear Information System (INIS)
Lian Shiguo; Sun Jinsheng; Wang Jinwei; Wang Zhiquan
2007-01-01
In this paper, a chaotic stream cipher is constructed and used to encrypt video data selectively. The stream cipher based on a discrete piecewise linear chaotic map satisfies the security requirement of cipher design. The video encryption scheme based on the stream cipher is secure in perception, efficient and format compliant, which is suitable for practical video protection. The video encryption scheme's performances prove the stream cipher's practicability
Experimental observations of EMI effects in autonomous Chua's chaotic circuit
International Nuclear Information System (INIS)
Kilic, Recai; Saracoglu, O. Galip; Yildirim, Fatma
2007-01-01
This paper deals with the experimentally investigation of EMI effects in autonomous Chua's chaotic circuit. We realized this experimental investigation by constructing an experimental setup subject to a Chua's circuit and applying a 5-30 MHz/100-200 mV EMI signal to the input pins of voltage Op-Amps used for realizing nonlinear resistor in Chua's circuit. In addition, we also experimentally investigated whether EMI signals affect the chaos synchronization between two Chua's chaotic circuits or not
Chaotic time series prediction: From one to another
International Nuclear Information System (INIS)
Zhao Pengfei; Xing Lei; Yu Jun
2009-01-01
In this Letter, a new local linear prediction model is proposed to predict a chaotic time series of a component x(t) by using the chaotic time series of another component y(t) in the same system with x(t). Our approach is based on the phase space reconstruction coming from the Takens embedding theorem. To illustrate our results, we present an example of Lorenz system and compare with the performance of the original local linear prediction model.
An exponential observer for the generalized Rossler chaotic system
International Nuclear Information System (INIS)
Sun, Y.-J.
2009-01-01
In this paper, the generalized Rossler chaotic system is considered and the state observation problem of such a system is investigated. Based on the time-domain approach, a state observer for the generalized Rossler chaotic system is developed to guarantee the global exponential stability of the resulting error system. Moreover, the guaranteed exponential convergence rate can be arbitrarily pre-specified. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the obtained result.
A novel secret image sharing scheme based on chaotic system
Li, Li; Abd El-Latif, Ahmed A.; Wang, Chuanjun; Li, Qiong; Niu, Xiamu
2012-04-01
In this paper, we propose a new secret image sharing scheme based on chaotic system and Shamir's method. The new scheme protects the shadow images with confidentiality and loss-tolerance simultaneously. In the new scheme, we generate the key sequence based on chaotic system and then encrypt the original image during the sharing phase. Experimental results and analysis of the proposed scheme demonstrate a better performance than other schemes and confirm a high probability to resist brute force attack.
Existence of a new three-dimensional chaotic attractor
International Nuclear Information System (INIS)
Wang Jiezhi; Chen Zengqiang; Yuan Zhuzhi
2009-01-01
In this paper, one heteroclinic orbit of a new three-dimensional continuous autonomous chaotic system, whose chaotic attractor belongs to the conjugate Lue attractor, is found. The series expression of the heteroclinic orbit of Shil'nikov type is derived by using the undetermined coefficient method. The uniform convergence of the precise series expansions of this heteroclinic orbits is proved. According to the Shil'nikov theorem, this system clearly has Smale horseshoes and the horseshoe chaos.