Spatiotemporal chaos from bursting dynamics
International Nuclear Information System (INIS)
Berenstein, Igal; De Decker, Yannick
2015-01-01
In this paper, we study the emergence of spatiotemporal chaos from mixed-mode oscillations, by using an extended Oregonator model. We show that bursting dynamics consisting of fast/slow mixed mode oscillations along a single attractor can lead to spatiotemporal chaotic dynamics, although the spatially homogeneous solution is itself non-chaotic. This behavior is observed far from the Hopf bifurcation and takes the form of a spatiotemporal intermittency where the system locally alternates between the fast and the slow phases of the mixed mode oscillations. We expect this form of spatiotemporal chaos to be generic for models in which one or several slow variables are coupled to activator-inhibitor type of oscillators
Noise tolerant spatiotemporal chaos computing.
Kia, Behnam; Kia, Sarvenaz; Lindner, John F; Sinha, Sudeshna; Ditto, William L
2014-12-01
We introduce and design a noise tolerant chaos computing system based on a coupled map lattice (CML) and the noise reduction capabilities inherent in coupled dynamical systems. The resulting spatiotemporal chaos computing system is more robust to noise than a single map chaos computing system. In this CML based approach to computing, under the coupled dynamics, the local noise from different nodes of the lattice diffuses across the lattice, and it attenuates each other's effects, resulting in a system with less noise content and a more robust chaos computing architecture.
Spatio-temporal intermittency on the sandpile
International Nuclear Information System (INIS)
Erzan, A.; Sinha, S.
1990-08-01
The self-organized critical state exhibited by a sandpile model is shown to correspond to motion on an attractor characterized by an invariant distribution of the height variable. The largest Lyapunov exponent is equal to zero. The model nonetheless displays intermittent chaos, with a multifractal distribution of local expansion coefficients in history space. Laminar spatio-temporal regions are interrupted by chaotic bursts caused by avalanches. We introduce the concept of local histories in configuration space and show that their expansion parameters also exhibit a multifractal distribution in time and space. (author). 22 refs, 5 figs
Dynamic characterizers of spatiotemporal intermittency
Gupte, Neelima; Jabeen, Zahera
2006-01-01
Systems of coupled sine circle maps show regimes of spatiotemporally intermittent behaviour with associated scaling exponents which belong to the DP class, as well as regimes of spatially intermittent behaviour (with associated regular dynamical behaviour) which do not belong to the DP class. Both types of behaviour are seen along the bifurcation boundaries of the synchronized solutions, and contribute distinct signatures to the dynamical characterizers of the system, viz. the distribution of...
Spatiotemporal chaos involving wave instability.
Berenstein, Igal; Carballido-Landeira, Jorge
2017-01-01
In this paper, we investigate pattern formation in a model of a reaction confined in a microemulsion, in a regime where both Turing and wave instability occur. In one-dimensional systems, the pattern corresponds to spatiotemporal intermittency where the behavior of the systems alternates in both time and space between stationary Turing patterns and traveling waves. In two-dimensional systems, the behavior initially may correspond to Turing patterns, which then turn into wave patterns. The resulting pattern also corresponds to a chaotic state, where the system alternates in both space and time between standing wave patterns and traveling waves, and the local dynamics may show vanishing amplitude of the variables.
Shape of power spectrum of intermittent chaos
International Nuclear Information System (INIS)
So, B.C.; Mori, H.
1984-01-01
Power spectra of intermittent chaos are calculated analytically. It is found that the power spectrum near onset point consists of a large number of Lorentzian lines with two peaks around frequencies ω = 0 and ω = ω 0 , where ω 0 is a fundamental frequency of a periodic orbit before the onset point, and furthermore the envelope of lines around ω = 0 obeys the power law 1/ + ω +2 , whereas the envelope around ω 0 obeys 1/ + ω-ω 0 +4 . The universality of these power law dependence in a certain class of intermittent chaos are clarified from a phenomenological view point. (author)
Transition to turbulence via spatiotemporal intermittency in stimulated Raman backscattering
International Nuclear Information System (INIS)
Skoric, M.M.; Jovanovic, M.S.; Rajkovic, M.R.
1996-01-01
The spatiotemporal evolution of stimulated Raman backscattering in a bounded, uniform, weakly dissipative plasma is studied. The nonlinear model of a three-wave interaction involves a quadratic coupling of slowly varying complex amplitudes of the laser pump, the backscattered and the electron plasma wave. The corresponding set of coupled partial differential equations with nonlinear phase detuning that is taken into account is solved numerically in space time with fixed nonzero source boundary conditions. The study of the above open, convective, weakly confined system reveals a quasiperiodic transition to spatiotemporal chaos via spatiotemporal intermittency. In the analysis of transitions a dual scheme borrowed from fields of nonlinear dynamics and statistical physics is applied. An introduction of a nonlinear three-wave interaction to a growing family of paradigmatic equations which exhibit a route to turbulence via spatiotemporal intermittency is outlined in this work. copyright 1996 The American Physical Society
Chaos synchronization based on intermittent state observer
Institute of Scientific and Technical Information of China (English)
Li Guo-Hui; Zhou Shi-Ping; Xu De-Ming
2004-01-01
This paper describes the method of synchronizing slave to the master trajectory using an intermittent state observer by constructing a synchronizer which drives the response system globally tracing the driving system asymptotically. It has been shown from the theory of synchronization error-analysis that a satisfactory result of chaos synchronization is expected under an appropriate intermittent period and state observer. Compared with continuous control method,the proposed intermittent method can target the desired orbit more efficiently. The application of the method is demonstrated on the hyperchaotic Rossler systems. Numerical simulations show that the length of the synchronization interval rs is of crucial importance for our scheme, and the method is robust with respect to parameter mismatch.
Chaos as an intermittently forced linear system.
Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kaiser, Eurika; Kutz, J Nathan
2017-05-30
Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth's magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.
Spatiotemporal chaos in coupled logistic maps
International Nuclear Information System (INIS)
Varella Guedes, Andre; Amorim Savi, Marcelo
2010-01-01
The objective of this work is to investigate the spatiotemporal dynamics of coupled logistic maps. These maps are prototypes of high-dimensional dynamical systems and have been used to describe the evolution and pattern formation in different systems. Here, the logistic map lattice is coupled by a power law and, therefore, each map is influenced by other maps in its neighborhood. The Kolmogorov-Sinai entropy density is employed to quantify the complexity of system behavior, permitting a general qualitative understanding of different aspects of system dynamics. Three kinds of boundary conditions are treated and the influence of initial conditions is also of concern. Non-homogeneous maps are investigated, showing interesting aspects of spatiotemporal dynamics. The idea is to analyze the spatial interaction between two qualitative different types of behavior from a grid that is split into two parts. Numerical simulations show what types of conditions present a greater tendency to develop chaotic, periodic and synchronized responses. It should be highlighted that non-homogeneous grids have situations where a chaotic pattern can emerge from two periodic responses and also situations where a periodic pattern can emerge from chaos.
Intermittency route to chaos in a biochemical system.
De la Fuente, I M; Martinez, L; Veguillas, J
1996-01-01
The numerical analysis of a glycolytic model performed through the construction of a system of three differential-delay equations reveals a phenomenon of intermittency route to chaos. In our biochemical system, the consideration of delay time variations under constant input flux as well as frequency variations of the periodic substrate input flux allows us, in both cases, to observe a type of transition to chaos different from the 'Feigenbaum route'.
International Nuclear Information System (INIS)
Yuan Guoyong; Yang Shiping; Wang Guangrui; Chen Shigang
2008-01-01
Spiral waves and spatiotemporal chaos are sometimes harmful and should be controlled. In this paper spiral waves and spatiotemporal chaos are successfully eliminated by the pulse with a very specific spatiotemporal configuration. The excited position D of spiral waves or spatiotemporal chaos is first recorded at an arbitrary time (t 0 ). When the system at the domain D enters a recovering state, the external pulse is injected into the domain. If the intensity and the working time of the pulse are appropriate, spiral waves and spatiotemporal chaos can finally be eliminated because counter-directional waves can be generated by the pulse. There are two advantages in the method. One is that the tip can be quickly eliminated together with the body of spiral wave, and the other is that the injected pulse may be weak and the duration can be very short so that the original system is nearly not affected, which is important for practical applications
Torus Destruction and Chaos-Chaos Intermittency in a Commodity Distribution Chain
DEFF Research Database (Denmark)
Sosnovtseva, O.; Mosekilde, Erik
1997-01-01
The destruction of two-dimensional tori T2 and the transitions to chaos are studied in a high-dimensional model describing the decision-making behavior of human subjects in a simulated managerial environment (the beer production-distribution model). Two different routes from quasiperiodicity...... to chaos can be distinguished. Intermittency transitions between chaotic and hyperchaotic attractors are characterized, and transients in which the system "pursues the ghost" of a vanished hyperchaotic attractor are studied....
Dynamical topology and statistical properties of spatiotemporal chaos.
Zhuang, Quntao; Gao, Xun; Ouyang, Qi; Wang, Hongli
2012-12-01
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a large extent, the location and movement of these topologically special points determine the qualitative structure of the disordered states. We analyze numerically statistical properties of the topologically special points in one-dimensional spatiotemporal chaos. The probability distribution functions for the number of point, the lifespan, and the distance covered during their lifetime are obtained from numerical simulations. Mathematically, we establish a probabilistic model to describe the dynamics of these topologically special points. In spite of the different definitions in different spatiotemporal chaos, the dynamics of these special points can be described in a uniform approach.
Stochastic resonance based on modulation instability in spatiotemporal chaos.
Han, Jing; Liu, Hongjun; Huang, Nan; Wang, Zhaolu
2017-04-03
A novel dynamic of stochastic resonance in spatiotemporal chaos is presented, which is based on modulation instability of perturbed partially coherent wave. The noise immunity of chaos can be reinforced through this effect and used to restore the coherent signal information buried in chaotic perturbation. A theoretical model with fluctuations term is derived from the complex Ginzburg-Landau equation via Wigner transform. It shows that through weakening the nonlinear threshold and triggering energy redistribution, the coherent component dominates the instability damped by incoherent component. The spatiotemporal output showing the properties of stochastic resonance may provide a potential application of signal encryption and restoration.
Pattern control and suppression of spatiotemporal chaos using geometrical resonance
International Nuclear Information System (INIS)
Gonzalez, J.A.; Bellorin, A.; Reyes, L.I.; Vasquez, C.; Guerrero, L.E.
2004-01-01
We generalize the concept of geometrical resonance to perturbed sine-Gordon, Nonlinear Schroedinger, phi (cursive,open) Greek 4 , and Complex Ginzburg-Landau equations. Using this theory we can control different dynamical patterns. For instance, we can stabilize breathers and oscillatory patterns of large amplitudes successfully avoiding chaos. On the other hand, this method can be used to suppress spatiotemporal chaos and turbulence in systems where these phenomena are already present. This method can be generalized to even more general spatiotemporal systems. A short report of some of our results has been published in [Europhys. Lett. 64 (2003) 743
Routes to spatiotemporal chaos in Kerr optical frequency combs.
Coillet, Aurélien; Chembo, Yanne K
2014-03-01
We investigate the various routes to spatiotemporal chaos in Kerr optical frequency combs, obtained through pumping an ultra-high Q-factor whispering-gallery mode resonator with a continuous-wave laser. The Lugiato-Lefever model is used to build bifurcation diagrams with regards to the parameters that are externally controllable, namely, the frequency and the power of the pumping laser. We show that the spatiotemporal chaos emerging from Turing patterns and solitons display distinctive dynamical features. Experimental spectra of chaotic Kerr combs are also presented for both cases, in excellent agreement with theoretical spectra.
Mode locking and spatiotemporal chaos in periodically driven Gunn diodes
DEFF Research Database (Denmark)
Mosekilde, Erik; Feldberg, Rasmus; Knudsen, Carsten
1990-01-01
oscillation entrains with the external signal. This produces a devil’s staircase of frequency-locked solutions. At higher microwave amplitudes, period doubling and other forms of mode-converting bifurcations can be seen. In this interval the diode also exhibits spatiotemporal chaos. At still higher microwave...
Controlling spatiotemporal chaos in one- and two-dimensional coupled logistic map lattices
International Nuclear Information System (INIS)
Astakhov, V.V.; Anishchenko, V.S.; Strelkova, G.I.; Shabunin, A.V.
1996-01-01
A method of control of spatiotemporal chaos in lattices of coupled maps is proposed in this work. Forms of spatiotemporal perturbations of a system parameter are analytically determined for one- and two-dimensional logistic map lattices with different kinds of coupling to stabilize chosen spatiotemporal states previously unstable. The results are illustrated by numerical simulation. Controlled transition from the regime of spatiotemporal chaos to the previously chosen regular spatiotemporal patterns is demonstrated. copyright 1996 American Institute of Physics
Secondary Instabilities and Spatiotemporal Chaos in Parametric Surface Waves
International Nuclear Information System (INIS)
Zhang, W.; Vinals, J.
1995-01-01
A 2D model is introduced to study the onset of parametric surface waves, their secondary instabilities, and the transition to spatiotemporal chaos. We obtain the stability boundary of a periodic standing wave above onset against Eckhaus, zigzag, and transverse amplitude modulations (TAM), as a function of the control parameter var-epsilon and the wavelength of the pattern. The Eckhaus and TAM boundaries cross at a finite value of var-epsilon, thus explaining the finite threshold for the TAM observed experimentally. At larger values of var-epsilon, a numerical solution reveals a transition to spatiotemporal chaotic states mediated by the TAM instability
Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors
Schöll, Eckehard
2005-08-01
Nonlinear transport phenomena are an increasingly important aspect of modern semiconductor research. This volume deals with complex nonlinear dynamics, pattern formation, and chaotic behavior in such systems. It bridges the gap between two well-established fields: the theory of dynamic systems and nonlinear charge transport in semiconductors. This unified approach helps reveal important electronic transport instabilities. The initial chapters lay a general framework for the theoretical description of nonlinear self-organized spatio-temporal patterns, such as current filaments, field domains, fronts, and analysis of their stability. Later chapters consider important model systems in detail: impact ionization induced impurity breakdown, Hall instabilities, superlattices, and low-dimensional structures. State-of-the-art results include chaos control, spatio-temporal chaos, multistability, pattern selection, activator-inhibitor kinetics, and global coupling, linking fundamental issues to electronic device applications. This book will be of great value to semiconductor physicists and nonlinear scientists alike.
Using Covariant Lyapunov Vectors to Understand Spatiotemporal Chaos in Fluids
Paul, Mark; Xu, Mu; Barbish, Johnathon; Mukherjee, Saikat
2017-11-01
The spatiotemporal chaos of fluids present many difficult and fascinating challenges. Recent progress in computing covariant Lyapunov vectors for a variety of model systems has made it possible to probe fundamental ideas from dynamical systems theory including the degree of hyperbolicity, the fractal dimension, the dimension of the inertial manifold, and the decomposition of the dynamics into a finite number of physical modes and spurious modes. We are interested in building upon insights such as these for fluid systems. We first demonstrate the power of covariant Lyapunov vectors using a system of maps on a lattice with a nonlinear coupling. We then compute the covariant Lyapunov vectors for chaotic Rayleigh-Bénard convection for experimentally accessible conditions. We show that chaotic convection is non-hyperbolic and we quantify the spatiotemporal features of the spectrum of covariant Lyapunov vectors. NSF DMS-1622299 and DARPA/DSO Models, Dynamics, and Learning (MoDyL).
Scale Dependence of Spatiotemporal Intermittence of Rain
Kundu, Prasun K.; Siddani, Ravi K.
2011-01-01
It is a common experience that rainfall is intermittent in space and time. This is reflected by the fact that the statistics of area- and/or time-averaged rain rate is described by a mixed distribution with a nonzero probability of having a sharp value zero. In this paper we have explored the dependence of the probability of zero rain on the averaging space and time scales in large multiyear data sets based on radar and rain gauge observations. A stretched exponential fannula fits the observed scale dependence of the zero-rain probability. The proposed formula makes it apparent that the space-time support of the rain field is not quite a set of measure zero as is sometimes supposed. We also give an ex.planation of the observed behavior in tenus of a simple probabilistic model based on the premise that rainfall process has an intrinsic memory.
Efficient image or video encryption based on spatiotemporal chaos system
International Nuclear Information System (INIS)
Lian Shiguo
2009-01-01
In this paper, an efficient image/video encryption scheme is constructed based on spatiotemporal chaos system. The chaotic lattices are used to generate pseudorandom sequences and then encrypt image blocks one by one. By iterating chaotic maps for certain times, the generated pseudorandom sequences obtain high initial-value sensitivity and good randomness. The pseudorandom-bits in each lattice are used to encrypt the Direct Current coefficient (DC) and the signs of the Alternating Current coefficients (ACs). Theoretical analysis and experimental results show that the scheme has good cryptographic security and perceptual security, and it does not affect the compression efficiency apparently. These properties make the scheme a suitable choice for practical applications.
Control of Spiral Waves and Spatiotemporal Chaos by Exciting Travel Wave Trains
International Nuclear Information System (INIS)
Yuan Guoyong; Wang Guangrui; Chen Shigang
2005-01-01
Spiral waves and spatiotemporal chaos usually are harmful and need to be suppressed. In this paper, a method is proposed to control them. Travel wave trains can be generated by periodic excitations near left boundary, spiral waves and spatiotemporal chaos can be eliminated by the trains for some certain excitation periods. Obvious resonant behavior can be observed from the relation between the periods of the trains and excitation ones. The method is against noise.
Observation of a Pomeau-Manneville intermittent route to chaos in a nonlinear oscillator
International Nuclear Information System (INIS)
Jeffries, C.; Perez, J.
1982-01-01
For a driven nonlinear semiconductor oscillator which shows a period-doubling pitchfork bifurcation route to chaos, we report an additional route to chaos: the Pomeau-Manneville intermittency route, characterized by a periodic (laminar) phase interrupted by bursts of aperiodic behavior. This occurs near a tangent bifurcation as the system driving parameter is reduced by epsilon from the threshold value for a periodic window. Data are presented for the dependence of the average laminar length on epsilon, and also on additive random noise voltage. The results are in reasonable agreement with the intermittency theory of Hirsch, Huberman, and Scalapino. The distribution P(l) is also reported
Study of intermittent bifurcations and chaos in boost PFC converters by nonlinear discrete models
International Nuclear Information System (INIS)
Zhang Hao; Ma Xikui; Xue Bianling; Liu Weizeng
2005-01-01
This paper mainly deals with nonlinear phenomena like intermittent bifurcations and chaos in boost PFC converters under peak-current control mode. Two nonlinear models in the form of discrete maps are derived to describe precisely the nonlinear dynamics of boost PFC converters from two points of view, i.e., low- and high-frequency regimes. Based on the presented discrete models, both the evolution of intermittent behavior and the periodicity of intermittency are investigated in detail from the fast and slow-scale aspects, respectively. Numerical results show that the occurrence of intermittent bifurcations and chaos with half one line period is one of the most distinguished dynamical characteristics. Finally, we make some instructive conclusions, which prove to be helpful in improving the performances of practical circuits
Spatiotemporal chaos in rf-driven Josephson junction series arrays
International Nuclear Information System (INIS)
Dominguez, D.; Cerdeira, H.A.
1995-01-01
We study underdamped Josephson junction series arrays that are globally coupled through a resistive shunting load and driven by an rf bias current. They can be an experimental realization of many phenomena currently studied in globally coupled logistic maps. We study their spatiotemporal dynamics and we find coherent, ordered, partially ordered, turbulent, and quasiperiodic phases. The ordered phase corresponds to giant Shapiro steps in the IV characteristics. In the turbulent phase there is a saturation of the broad-band noise for a large number of junctions. This corresponds to a breakdown of the law of large numbers as seen in globally coupled maps. Coexisting with this phenomenon, we find an emergence of pseudosteps in the IV characteristics. This effect can be experimentally distinguished from the true Shapiro steps, which do not have broad-band noise emission. We study the stability of the breakdown of the law of large numbers against thermal fluctuations. We find that it is stable below a critical temperature T c1 . A measurement of the broad-band noise as a function of temperature T will show three different regimes: below T c1 the broad-band noise decreases when increasing T, and there is turbulence and the breakdown of the law of large numbers. Between T c1 and a second critical temperature T c2 the broad-band noise is constant and the dynamics is dominated by the chaos of the individual junctions. Finally above T c2 all the broad-band noise is due to thermal fluctuations, since it increases linearly with T
Wang, Shi-Hong; Ye, Wei-Ping; Lü, Hua-Ping; Kuang, Jin-Yu; Li, Jing-Hua; Luo, Yun-Lun; Hu, Gang
2003-07-01
Spatiotemporal chaos of a two-dimensional one-way coupled map lattice is used for chaotic cryptography. The chaotic outputs of many space units are used for encryption simultaneously. This system shows satisfactory cryptographic properties of high security, fast encryption (decryption) speed, and robustness against noise disturbances in communication channel. The overall features of this spatiotemporal-chaos-based cryptosystem are better than chaotic cryptosystems known so far, and also than currently used conventional cryptosystems, such as the Advanced Encryption Standard (AES). The project supported by National Natural Science Foundation of China under Grant No. 10175010 and the Special Funds for Major State Basic Research Projects under Grant No. G2000077304
Spatiotemporal chaos of self-replicating spots in reaction-diffusion systems.
Wang, Hongli; Ouyang, Qi
2007-11-23
The statistical properties of self-replicating spots in the reaction-diffusion Gray-Scott model are analyzed. In the chaotic regime of the system, the spots that dominate the spatiotemporal chaos grow and divide in two or decay into the background randomly and continuously. The rates at which the spots are created and decay are observed to be linearly dependent on the number of spots in the system. We derive a probabilistic description of the spot dynamics based on the statistical independence of spots and thus propose a characterization of the spatiotemporal chaos dominated by replicating spots.
Synchronizing spatiotemporal chaos by introducing a finite flat region in the local map
Directory of Open Access Journals (Sweden)
J. Y. Chen
2001-01-01
Full Text Available An approach to synchronize spatiotemporal chaos is proposed. It is achieved by introducing a finite flat region in the local map. By using this scheme, a number of orbits in both the drive and the response subsystems are forced to pass through a fixed point in every dimension. With only an arbitrary phase space variable as drive signal, synchronization of spatiotemporal chaos can be achieved rapidly in the response subsystem. This is an advantage when compared with other synchronization methods that require a linear combination of the original phase space variables.
Extension of spatiotemporal chaos in glow discharge-semiconductor systems.
Akhmet, Marat; Rafatov, Ismail; Fen, Mehmet Onur
2014-12-01
Generation of chaos in response systems is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach, [H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Phys. Rev. E 53, 4528-4535 (1996)] it is verified that the phenomenon is not a chaos synchronization. Simulations demonstrate various aspects of the chaos appearance in both drive and response systems. Chaotic control is through the external circuit equation and governs the electrical potential on the boundary. The expandability of the theory to collectives of glow discharge systems is discussed, and this increases the potential of applications of the results. Moreover, the research completes the previous discussion of the chaos appearance in a glow discharge-semiconductor system [D. D. Šijačić U. Ebert, and I. Rafatov, Phys. Rev. E 70, 056220 (2004).].
Extension of spatiotemporal chaos in glow discharge-semiconductor systems
International Nuclear Information System (INIS)
Akhmet, Marat; Fen, Mehmet Onur; Rafatov, Ismail
2014-01-01
Generation of chaos in response systems is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach, [H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Phys. Rev. E 53, 4528–4535 (1996)] it is verified that the phenomenon is not a chaos synchronization. Simulations demonstrate various aspects of the chaos appearance in both drive and response systems. Chaotic control is through the external circuit equation and governs the electrical potential on the boundary. The expandability of the theory to collectives of glow discharge systems is discussed, and this increases the potential of applications of the results. Moreover, the research completes the previous discussion of the chaos appearance in a glow discharge-semiconductor system [D. D. Šijačić U. Ebert, and I. Rafatov, Phys. Rev. E 70, 056220 (2004).
Security analysis of a one-way hash function based on spatiotemporal chaos
International Nuclear Information System (INIS)
Wang Shi-Hong; Shan Peng-Yang
2011-01-01
The collision and statistical properties of a one-way hash function based on spatiotemporal chaos are investigated. Analysis and simulation results indicate that collisions exist in the original algorithm and, therefore, the original algorithm is insecure and vulnerable. An improved algorithm is proposed to avoid the collisions. (general)
Wave fronts and spatiotemporal chaos in an array of coupled Lorenz oscillators
International Nuclear Information System (INIS)
Pazo, Diego; Montejo, Noelia; Perez-Munuzuri, Vicente
2001-01-01
The effects of coupling strength and single-cell dynamics (SCD) on spatiotemporal pattern formation are studied in an array of Lorenz oscillators. Different spatiotemporal structures (stationary patterns, propagating wave fronts, short wavelength bifurcation) arise for bistable SCD, and two well differentiated types of spatiotemporal chaos for chaotic SCD (in correspondence with the transition from stationary patterns to propagating fronts). Wave-front propagation in the bistable regime is studied in terms of global bifurcation theory, while a short wavelength pattern region emerges through a pitchfork bifurcation
Emergent dynamics of spatio-temporal chaos in a heterogeneous excitable medium.
Bittihn, Philip; Berg, Sebastian; Parlitz, Ulrich; Luther, Stefan
2017-09-01
Self-organized activation patterns in excitable media such as spiral waves and spatio-temporal chaos underlie dangerous cardiac arrhythmias. While the interaction of single spiral waves with different types of heterogeneity has been studied extensively, the effect of heterogeneity on fully developed spatio-temporal chaos remains poorly understood. We investigate how the complexity and stability properties of spatio-temporal chaos in the Bär-Eiswirth model of excitable media depend on the heterogeneity of the underlying medium. We employ different measures characterizing the chaoticity of the system and find that the spatial arrangement of multiple discrete lower excitability regions has a strong impact on the complexity of the dynamics. Varying the number, shape, and spatial arrangement of the heterogeneities, we observe strong emergent effects ranging from increases in chaoticity to the complete cessation of chaos, contrasting the expectation from the homogeneous behavior. The implications of our findings for the development and treatment of arrhythmias in the heterogeneous cardiac muscle are discussed.
Reshaping-induced spatiotemporal chaos in driven, damped sine-Gordon systems
International Nuclear Information System (INIS)
Chacon, R.
2007-01-01
Spatiotemporal chaos arising from the competition between sine-Gordon-breather and kink-antikink-pair solitons by reshaping an ac force is demonstrated. After introducing soliton collective coordinates, Melnikov's method is applied to the resulting effective equation of motion to estimate the parameter-space regions of the ac force where homoclinic bifurcations are induced. The analysis reveals that the chaos-order threshold exhibits sensitivity to small changes in the force shape. Computer simulations of the sine-Gordon system show good agreement with these theoretical predictions
Reshaping-induced spatiotemporal chaos in driven, damped sine-Gordon systems
Energy Technology Data Exchange (ETDEWEB)
Chacon, R. [Departamento de Electronica e Ingenieria Electromecanica, Escuela de Ingenierias Industriales, Universidad de Extremadura, E-06071 Badajoz (Spain)]. E-mail: rchacon@unex.es
2007-03-15
Spatiotemporal chaos arising from the competition between sine-Gordon-breather and kink-antikink-pair solitons by reshaping an ac force is demonstrated. After introducing soliton collective coordinates, Melnikov's method is applied to the resulting effective equation of motion to estimate the parameter-space regions of the ac force where homoclinic bifurcations are induced. The analysis reveals that the chaos-order threshold exhibits sensitivity to small changes in the force shape. Computer simulations of the sine-Gordon system show good agreement with these theoretical predictions.
Intermittency and transition to chaos in the cubical lid-driven cavity flow
Energy Technology Data Exchange (ETDEWEB)
Loiseau, J-Ch [Department of Mechanics, Royal Institute of Technology (KTH), SE-100 44 Stockholm (Sweden); Robinet, J-Ch [Laboratoire DynFluid, Arts et Métiers ParisTech, F-75013 Paris (France); Leriche, E, E-mail: loiseau@mech.kth.se [Laboratoire de Mécanique de Lille, Université Lille 1, F-59655 Villeneuve d’Ascq (France)
2016-12-15
Transition from steady state to intermittent chaos in the cubical lid-driven cavity flow is investigated numerically. Fully three-dimensional stability analyses have revealed that the flow experiences an Andronov–Poincaré–Hopf bifurcation at a critical Reynolds number Re {sub c} = 1914. As for the 2D-periodic lid-driven cavity flows, the unstable mode originates from a centrifugal instability of the primary vortex core. A Reynolds–Orr analysis reveals that the unstable perturbation relies on a combination of the lift-up and anti lift-up mechanisms to extract its energy from the base flow. Once linearly unstable, direct numerical simulations show that the flow is driven toward a primary limit cycle before eventually exhibiting intermittent chaotic dynamics. Though only one eigenpair of the linearized Navier–Stokes operator is unstable, the dynamics during the intermittencies are surprisingly well characterized by one of the stable eigenpairs. (paper)
Choi, Daeyoung; Wishon, Michael J; Chang, C Y; Citrin, D S; Locquet, A
2018-01-01
We observe experimentally two regimes of intermittency on the route to chaos of a semiconductor laser subjected to optical feedback from a long external cavity as the feedback level is increased. The first regime encountered corresponds to multistate intermittency involving two or three states composed of several combinations of periodic, quasiperiodic, and subharmonic dynamics. The second regime is observed for larger feedback levels and involves intermittency between period-doubled and chaotic regimes. This latter type of intermittency displays statistical properties similar to those of on-off intermittency.
Transient spatiotemporal chaos in the Morris-Lecar neuronal ring network
Energy Technology Data Exchange (ETDEWEB)
Keplinger, Keegan, E-mail: keegankeplinger@gmail.com; Wackerbauer, Renate, E-mail: rawackerbauer@alaska.edu [Department of Physics, University of Alaska, Fairbanks, Alaska 99775-5920 (United States)
2014-03-15
Transient behavior is thought to play an integral role in brain functionality. Numerical simulations of the firing activity of diffusively coupled, excitable Morris-Lecar neurons reveal transient spatiotemporal chaos in the parameter regime below the saddle-node on invariant circle bifurcation point. The neighborhood of the chaotic saddle is reached through perturbations of the rest state, in which few initially active neurons at an effective spatial distance can initiate spatiotemporal chaos. The system escapes from the neighborhood of the chaotic saddle to either the rest state or to a state of pulse propagation. The lifetime of the chaotic transients is manipulated in a statistical sense through a singular application of a synchronous perturbation to a group of neurons.
Transient spatiotemporal chaos in the Morris-Lecar neuronal ring network.
Keplinger, Keegan; Wackerbauer, Renate
2014-03-01
Transient behavior is thought to play an integral role in brain functionality. Numerical simulations of the firing activity of diffusively coupled, excitable Morris-Lecar neurons reveal transient spatiotemporal chaos in the parameter regime below the saddle-node on invariant circle bifurcation point. The neighborhood of the chaotic saddle is reached through perturbations of the rest state, in which few initially active neurons at an effective spatial distance can initiate spatiotemporal chaos. The system escapes from the neighborhood of the chaotic saddle to either the rest state or to a state of pulse propagation. The lifetime of the chaotic transients is manipulated in a statistical sense through a singular application of a synchronous perturbation to a group of neurons.
Four dimensional chaos and intermittency in a mesoscopic model of the electroencephalogram.
Dafilis, Mathew P; Frascoli, Federico; Cadusch, Peter J; Liley, David T J
2013-06-01
The occurrence of so-called four dimensional chaos in dynamical systems represented by coupled, nonlinear, ordinary differential equations is rarely reported in the literature. In this paper, we present evidence that Liley's mesoscopic theory of the electroencephalogram (EEG), which has been used to describe brain activity in a variety of clinically relevant contexts, possesses a chaotic attractor with a Kaplan-Yorke dimension significantly larger than three. This accounts for simple, high order chaos for a physiologically admissible parameter set. Whilst the Lyapunov spectrum of the attractor has only one positive exponent, the contracting dimensions are such that the integer part of the Kaplan-Yorke dimension is three, thus giving rise to four dimensional chaos. A one-parameter bifurcation analysis with respect to the parameter corresponding to extracortical input is conducted, with results indicating that the origin of chaos is due to an inverse period doubling cascade. Hence, in the vicinity of the high order, strange attractor, the model is shown to display intermittent behavior, with random alternations between oscillatory and chaotic regimes. This phenomenon represents a possible dynamical justification of some of the typical features of clinically established EEG traces, which can arise in the case of burst suppression in anesthesia and epileptic encephalopathies in early infancy.
Cryptanalysis on an image block encryption algorithm based on spatiotemporal chaos
International Nuclear Information System (INIS)
Wang Xing-Yuan; He Guo-Xiang
2012-01-01
An image block encryption scheme based on spatiotemporal chaos has been proposed recently. In this paper, we analyse the security weakness of the proposal. The main problem of the original scheme is that the generated keystream remains unchanged for encrypting every image. Based on the flaws, we demonstrate a chosen plaintext attack for revealing the equivalent keys with only 6 pairs of plaintext/ciphertext used. Finally, experimental results show the validity of our attack. (general)
Logarithmic bred vectors in spatiotemporal chaos: structure and growth.
Hallerberg, Sarah; Pazó, Diego; López, Juan M; Rodríguez, Miguel A
2010-06-01
Bred vectors are a type of finite perturbation used in prediction studies of atmospheric models that exhibit spatially extended chaos. We study the structure, spatial correlations, and the growth rates of logarithmic bred vectors (which are constructed by using a given norm). We find that, after a suitable transformation, logarithmic bred vectors are roughly piecewise copies of the leading Lyapunov vector. This fact allows us to deduce a scaling law for the bred vector growth rate as a function of its amplitude. In addition, we relate growth rates with the spectrum of Lyapunov exponents corresponding to the most expanding directions. We illustrate our results with simulations of the Lorenz 1996 model.
A novel method for one-way hash function construction based on spatiotemporal chaos
International Nuclear Information System (INIS)
Ren Haijun; Wang Yong; Xie Qing; Yang Huaqian
2009-01-01
A novel hash algorithm based on a spatiotemporal chaos is proposed. The original message is first padded with zeros if needed. Then it is divided into a number of blocks each contains 32 bytes. In the hashing process, each block is partitioned into eight 32-bit values and input into the spatiotemporal chaotic system. Then, after iterating the system for four times, the next block is processed by the same way. To enhance the confusion and diffusion effect, the cipher block chaining (CBC) mode is adopted in the algorithm. The hash value is obtained from the final state value of the spatiotemporal chaotic system. Theoretic analyses and numerical simulations both show that the proposed hash algorithm possesses good statistical properties, strong collision resistance and high efficiency, as required by practical keyed hash functions.
A novel method for one-way hash function construction based on spatiotemporal chaos
Energy Technology Data Exchange (ETDEWEB)
Ren Haijun [College of Software Engineering, Chongqing University, Chongqing 400044 (China); State Key Laboratory of Power Transmission Equipment and System Security and New Technology, Chongqing University, Chongqing 400044 (China)], E-mail: jhren@cqu.edu.cn; Wang Yong; Xie Qing [Key Laboratory of Electronic Commerce and Logistics of Chongqing, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China); Yang Huaqian [Department of Computer and Modern Education Technology, Chongqing Education of College, Chongqing 400067 (China)
2009-11-30
A novel hash algorithm based on a spatiotemporal chaos is proposed. The original message is first padded with zeros if needed. Then it is divided into a number of blocks each contains 32 bytes. In the hashing process, each block is partitioned into eight 32-bit values and input into the spatiotemporal chaotic system. Then, after iterating the system for four times, the next block is processed by the same way. To enhance the confusion and diffusion effect, the cipher block chaining (CBC) mode is adopted in the algorithm. The hash value is obtained from the final state value of the spatiotemporal chaotic system. Theoretic analyses and numerical simulations both show that the proposed hash algorithm possesses good statistical properties, strong collision resistance and high efficiency, as required by practical keyed hash functions.
International Nuclear Information System (INIS)
Quan-Xing, Liu; Gui-Quan, Sun; Zhen, Jin; Bai-Lian, Li
2009-01-01
It has been reported that the minimal spatially extended phytoplankton–zooplankton system exhibits both temporal regular/chaotic behaviour, and spatiotemporal chaos in a patchy environment. As a further investigation by means of computer simulations and theoretical analysis, in this paper we observe that the spiral waves may exist and the spatiotemporal chaos emerge when the parameters are within the mixed Turing–Hopf bifurcation region, which arises from the far-field breakup of the spiral waves over a large range of diffusion coefficients of phytoplankton and zooplankton. Moreover, the spatiotemporal chaos arising from the far-field breakup of spiral waves does not gradually invade the whole space of that region. Our results are confirmed by nonlinear bifurcation of wave trains. We also discuss ecological implications of these spatially structured patterns. (general)
Comment on "On the security of a spatiotemporal chaotic cryptosystem" [Chaos 17, 033117 (2007)].
Wang, Shihong; Hu, Gang
2008-09-01
This paper comments on a recent paper by R. Rhouma and B. Safya [Chaos 17, 033117 (2007)]. They claimed to find some security weakness of the spatiotemporal chaotic cryptosystem suggested by G. Tang et al. [Phys. Lett. A 318, 388 (2003)] and proposed a chosen-plaintext attack to analyze this system. We find that in their analysis, called a "chosen-plaintext attack," they actually act as a legal receiver (with a machine in their hands during the entire decryption process) rather than an attacker and, therefore, the whole reasoning is not valid. (c) 2008 American Institute of Physics.
A Novel Image Encryption Algorithm Based on DNA Encoding and Spatiotemporal Chaos
Directory of Open Access Journals (Sweden)
Chunyan Song
2015-10-01
Full Text Available DNA computing based image encryption is a new, promising field. In this paper, we propose a novel image encryption scheme based on DNA encoding and spatiotemporal chaos. In particular, after the plain image is primarily diffused with the bitwise Exclusive-OR operation, the DNA mapping rule is introduced to encode the diffused image. In order to enhance the encryption, the spatiotemporal chaotic system is used to confuse the rows and columns of the DNA encoded image. The experiments demonstrate that the proposed encryption algorithm is of high key sensitivity and large key space, and it can resist brute-force attack, entropy attack, differential attack, chosen-plaintext attack, known-plaintext attack and statistical attack.
Spatiotemporal chaos and two-dimensional dissipative rogue waves in Lugiato-Lefever model
Panajotov, Krassimir; Clerc, Marcel G.; Tlidi, Mustapha
2017-06-01
Driven nonlinear optical cavities can exhibit complex spatiotemporal dynamics. We consider the paradigmatic Lugiato-Lefever model describing driven nonlinear optical resonator. This model is one of the most-studied nonlinear equations in optics. It describes a large spectrum of nonlinear phenomena from bistability, to periodic patterns, localized structures, self-pulsating localized structures and to a complex spatiotemporal behavior. The model is considered also as prototype model to describe several optical nonlinear devices such as Kerr media, liquid crystals, left handed materials, nonlinear fiber cavity, and frequency comb generation. We focus our analysis on a spatiotemporal chaotic dynamics in one-dimension. We identify a route to spatiotemporal chaos through an extended quasiperiodicity. We have estimated the Kaplan-Yorke dimension that provides a measure of the strange attractor complexity. Likewise, we show that the Lugiato-Leferver equation supports rogues waves in two-dimensional settings. We characterize rogue-wave formation by computing the probability distribution of the pulse height. Contribution to the Topical Issue "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.
Control of spatio-temporal on-off intermittency in random driving diffusively coupled map lattices
International Nuclear Information System (INIS)
Ziabakhsh Deilami, M.; Rahmani Cherati, Z.; Jahed Motlagh, M.R.
2009-01-01
In this paper, we propose feedback methods for controlling spatio-temporal on-off intermittency which is an aperiodic switching between an 'off' state and an 'on' state. Diffusively coupled map lattice with spatially non-uniform random driving is used for showing spatio-temporal on-off intermittency. For this purpose, we apply three different feedbacks. First, we use a linear feedback which is a simple method but has a long transient time. To overcome this problem, two nonlinear feedbacks based on prediction strategy are proposed. An important advantage of the methods is that the feedback signal is vanished when control is realized. Simulation results show that all methods have suppressed the chaotic behavior.
Dynamic video encryption algorithm for H.264/AVC based on a spatiotemporal chaos system.
Xu, Hui; Tong, Xiao-Jun; Zhang, Miao; Wang, Zhu; Li, Ling-Hao
2016-06-01
Video encryption schemes mostly employ the selective encryption method to encrypt parts of important and sensitive video information, aiming to ensure the real-time performance and encryption efficiency. The classic block cipher is not applicable to video encryption due to the high computational overhead. In this paper, we propose the encryption selection control module to encrypt video syntax elements dynamically which is controlled by the chaotic pseudorandom sequence. A novel spatiotemporal chaos system and binarization method is used to generate a key stream for encrypting the chosen syntax elements. The proposed scheme enhances the resistance against attacks through the dynamic encryption process and high-security stream cipher. Experimental results show that the proposed method exhibits high security and high efficiency with little effect on the compression ratio and time cost.
Spatio-temporal chaos and thermal noise in Josephson junction series arrays
International Nuclear Information System (INIS)
Dominguez, D.; Cerdeira, H.A.
1995-01-01
We study underdamped Josephson junction series arrays that are globally coupled through a resistive shunting load and driven by an rf bias current. We find that they can be an experimental realization of many phenomena currently studied in globally coupled logistic map. Depending on the bias current the array can show Shapiro steps but also spatio-temporal chaos or ''turbulence'' in the IV characteristics. In the turbulent phase there is a saturation of the broad band noise for a large number of junctions. This corresponds to a break down of the law of large numbers as seen in globally coupled maps. We study this phenomenon as a function of thermal noise. We find that when increasing the temperature the broad band noise decreases. (author). 8 refs, 1 fig
Finding equilibrium in the spatiotemporal chaos of the complex Ginzburg-Landau equation
Ballard, Christopher C.; Esty, C. Clark; Egolf, David A.
2016-11-01
Equilibrium statistical mechanics allows the prediction of collective behaviors of large numbers of interacting objects from just a few system-wide properties; however, a similar theory does not exist for far-from-equilibrium systems exhibiting complex spatial and temporal behavior. We propose a method for predicting behaviors in a broad class of such systems and apply these ideas to an archetypal example, the spatiotemporal chaotic 1D complex Ginzburg-Landau equation in the defect chaos regime. Building on the ideas of Ruelle and of Cross and Hohenberg that a spatiotemporal chaotic system can be considered a collection of weakly interacting dynamical units of a characteristic size, the chaotic length scale, we identify underlying, mesoscale, chaotic units and effective interaction potentials between them. We find that the resulting equilibrium Takahashi model accurately predicts distributions of particle numbers. These results suggest the intriguing possibility that a class of far-from-equilibrium systems may be well described at coarse-grained scales by the well-established theory of equilibrium statistical mechanics.
International Nuclear Information System (INIS)
Ghorai, Santu; Poria, Swarup
2016-01-01
Spatiotemporal dynamics of a predator–prey system in presence of spatial diffusion is investigated in presence of additional food exists for predators. Conditions for stability of Hopf as well as Turing patterns in a spatial domain are determined by making use of the linear stability analysis. Impact of additional food is clear from these conditions. Numerical simulation results are presented in order to validate the analytical findings. Finally numerical simulations are carried out around the steady state under zero flux boundary conditions. With the help of numerical simulations, the different types of spatial patterns (including stationary spatial pattern, oscillatory pattern, and spatiotemporal chaos) are identified in this diffusive predator–prey system in presence of additional food, depending on the quantity, quality of the additional food and the spatial domain and other parameters of the model. The key observation is that spatiotemporal chaos can be controlled supplying suitable additional food to predator. These investigations may be useful to understand complex spatiotemporal dynamics of population dynamical models in presence of additional food.
On the angle between the first and second Lyapunov vectors in spatio-temporal chaos
International Nuclear Information System (INIS)
Pazó, D; López, J M; Rodríguez, M A
2013-01-01
In a dynamical system the first Lyapunov vector (LV) is associated with the largest Lyapunov exponent and indicates—at any point on the attractor—the direction of maximal growth in tangent space. The LV corresponding to the second largest Lyapunov exponent generally points in a different direction, but tangencies between both vectors can in principle occur. Here we find that the probability density function (PDF) of the angle ψ spanned by the first and second LVs should be expected to be approximately symmetric around π/4 and to peak at 0 and π/2. Moreover, for small angles we uncover a scaling law for the PDF Q of ψ l = ln ψ with the system size L: Q(ψ l ) = L −1/2 f(ψ l L −1/2 ). We give a theoretical argument that justifies this scaling form and also explains why it should be universal (irrespective of the system details) for spatio-temporal chaos in one spatial dimension. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)
Rybalova, Elena; Semenova, Nadezhda; Strelkova, Galina; Anishchenko, Vadim
2017-06-01
We study the transition from coherence (complete synchronization) to incoherence (spatio-temporal chaos) in ensembles of nonlocally coupled chaotic maps with nonhyperbolic and hyperbolic attractors. As basic models of a partial element we use the Henon map and the Lozi map. We show that the transition to incoherence in a ring of coupled Henon maps occurs through the appearance of phase and amplitude chimera states. An ensemble of coupled Lozi maps demonstrates the coherence-incoherence transition via solitary states and no chimera states are observed in this case.
Bubanja, I. N.; Ivanović-Šašić, A.; Čupić, Ž.; Anić, S.; Kolar-Anić, Lj.
2017-12-01
Chaotic dynamic states with intermittent oscillations were generated in a Bray-Liebhafsky (BL) oscillatory reaction in an isothermal open reactor i.e., in the continuously-fed well-stirred tank reactor (CSTR) when the inflow concentration of potassium iodate was the control parameter. They are found between periodic oscillations obtained when [KIO3]0 4.10 × 10-2 M. It was shown that the most chaotic states obtained experimentally somewhere in the middle of this region are in high correlation with results obtained by means of largest Lyapunov exponents and phenomenological analysis based on the quantitative characteristics of intermittent oscillations.
Pattern selection and spatio-temporal transition to chaos in Ginzburg-Landau equation
Energy Technology Data Exchange (ETDEWEB)
Nozaki, K; Bekki, N
1983-07-01
It is shown that a modulationally unstable pattern is selected and propagates into an initially unstable motionless state in the 1-D generalized Ginzburg-Landau equation. A further spatio-temporal transition occurs with a sharp interface from the selected unstable pattern to a stabilized pattern or a chaotic state. The distinct transition makes a coherent structure to coexist with a chaotic state. 12 refs., 4 figs.
International Nuclear Information System (INIS)
Brochard, F.; Gravier, E.; Bonhomme, G.
2006-01-01
The spatiotemporal transition scenario of flute instabilities from a regular to a turbulent state is experimentally investigated in the low-β plasma column of a thermionic discharge. The same transition scenario, i.e., the Ruelle-Takens route to turbulence, is found for both the Kelvin-Helmholtz and the Rayleigh-Taylor instabilities. It is demonstrated that the transition can be more or less smooth, according to the discharge mode. In both cases, a strong radial dependence is observed, which is linked to the velocity shear layer in the case of the Kelvin-Helmholtz instability
International Nuclear Information System (INIS)
Xing-Yuan, Wang; Na, Zhang
2010-01-01
Coupled map lattices are taken as examples to study the synchronisation of spatiotemporal chaotic systems. First, a generalised synchronisation of two coupled map lattices is realised through selecting an appropriate feedback function and appropriate range of feedback parameter. Based on this method we use the phase compression method to extend the range of the parameter. So, we integrate the feedback control method with the phase compression method to implement the generalised synchronisation and obtain an exact range of feedback parameter. This technique is simple to implement in practice. Numerical simulations show the effectiveness and the feasibility of the proposed program. (general)
International Nuclear Information System (INIS)
Chiriac, S.; Dimitriu, D. G.; Sanduloviciu, M.
2007-01-01
Anodic double layer instabilities occur in low-temperature diffusion filament-type discharge plasma by applying a certain positive bias with respect to the plasma potential to an additional electrode. Periodic nonlinear regimes, characterized by proper dynamics of double layers, are sustained if excitation and ionization rates in front of the electrode reach the value for which current limitation effects appear in the static current-voltage characteristic. It was experimentally shown that under specific experimental conditions these ordered spatiotemporal phenomena can evolve into chaotic states by type I intermittency. This transition was verified by the evolution of time series, fast Fourier transform amplitude plots, three-dimensional reconstructed state spaces, power laws, and flickering phenomena spectrum, as well as by the return map and tangent bifurcation
Spatiotemporal chaos in mixed linear-nonlinear two-dimensional coupled logistic map lattice
Zhang, Ying-Qian; He, Yi; Wang, Xing-Yuan
2018-01-01
We investigate a new spatiotemporal dynamics with mixing degrees of nonlinear chaotic maps for spatial coupling connections based on 2DCML. Here, the coupling methods are including with linear neighborhood coupling and the nonlinear chaotic map coupling of lattices, and the former 2DCML system is only a special case in the proposed system. In this paper the criteria such Kolmogorov-Sinai entropy density and universality, bifurcation diagrams, space-amplitude and snapshot pattern diagrams are provided in order to investigate the chaotic behaviors of the proposed system. Furthermore, we also investigate the parameter ranges of the proposed system which holds those features in comparisons with those of the 2DCML system and the MLNCML system. Theoretical analysis and computer simulation indicate that the proposed system contains features such as the higher percentage of lattices in chaotic behaviors for most of parameters, less periodic windows in bifurcation diagrams and the larger range of parameters for chaotic behaviors, which is more suitable for cryptography.
Synchronizing Spatiotemporal Chaos via a Composite Disturbance Observer-Based Sliding Mode Control
Directory of Open Access Journals (Sweden)
Congyan Chen
2014-01-01
Full Text Available The sliding mode control schemes are investigated to synchronize two spatiotemporal chaotic systems, which are two arrays of a large number of coupled chaotic oscillators. Firstly, sliding mode manifolds with the desired performance are designed. The asymptotic convergence to the origin of the synchronization errors is also proved. However, the terms from parameter fluctuations in equivalent controls are usually impossible to be measured directly. So we regard them as lumped disturbances, but, for practical application, it is difficult to obtain the upper bound of lumped disturbances in advance which often results in a conservative sliding mode control law with large control effort, causing a large amount of chattering. To reduce the chattering and improve the performance of the system, a disturbance observer is designed to estimate the lumped disturbances. A composite synchronization controller that consists of a sliding mode feedback part and a feedforward compensation part based on disturbance observer is developed. The numerical simulation results are presented to show the effectiveness of the proposed methods.
Astel, Aleksander M.; Bigus, Katarzyna; Obolewski, Krystian; Glińska-Lewczuk, Katarzyna
2016-12-01
Ionic profile, pH, electrolytic conductivity, chemical oxygen demand and concentration of selected heavy metals (Ni, Cu, Zn, Fe and Mn) were determined in water of 11 intermittently closed and open lakes and lagoons (ICOLLs) located in Polish coastline. Multidimensional data set was explored by the use of the self-organizing map (SOM) technique to avoid supervised and predictable division for fully isolated, partially and fully connected lakes. Water quality assessment based on single parameter's mean value allowed classification of majority of lakes to first or second class of purity according to regulation presenting classification approach applicable to uniform parts of surface waters. The SOM-based grouping revealed seven clusters comprising water samples of similar physico-chemical profile. Fully connected lakes were characterized by the highest concentration of components characteristic for sea salts (NaCl, MgCl2, MgSO4, CaSO4, K2SO4 and MgBr2), however spring samples from Łebsko were shifted to another cluster suggesting that intensive surface run-off and fresh-water inflow through Łupawa river decreases an impact of sea water intrusions. Forecasted characteristic of water collected in Resko Przymorskie lake was disturbed by high contamination by nitrites indicating accidental and local contamination due to usage of sodium nitrite for the curing of meat. Some unexpected sources of contamination was discovered in intermittently open and closed lakes. Presumably Zn contamination is due to use of wood preservatives to protect small wooden playgrounds or camping places spread around one of the lake, while increased concentration of Ni could be connected with grass and vegetation burning. Waters of Jamno lake are under the strongest anthropogenic impact due to inefficient removal of phosphates by waste water treatment plant and contamination by Fe and Mn caused by backwashing of absorption filters. Generally, the quality of ICOLLs' water was diversified, while
Zhang, Yinping; Wang, Qing-Guo
2008-12-01
In the referenced paper, there is technical carelessness in the third lemma and in the main result. Hence, it is a possible failure when the result is used to design the intermittent linear state feedback controller for exponential synchronization of two chaotic delayed systems.
Chaos and bifurcations in periodic windows observed in plasmas
International Nuclear Information System (INIS)
Qin, J.; Wang, L.; Yuan, D.P.; Gao, P.; Zhang, B.Z.
1989-01-01
We report the experimental observations of deterministic chaos in a steady-state plasma which is not driven by any extra periodic forces. Two routes to chaos have been found, period-doubling and intermittent chaos. The fine structures in chaos such as periodic windows and bifurcations in windows have also been observed
International Nuclear Information System (INIS)
Medvinskii, Aleksandr B; Tikhonova, Irina A; Tikhonov, D A; Ivanitskii, Genrikh R; Petrovskii, Sergei V; Li, B.-L.; Venturino, E; Malchow, H
2002-01-01
The current turn-of-the-century period witnesses the intensive use of the bioproducts of the World Ocean while at the same time calling for precautions to preserve its ecological stability. This requires that biophysical processes in aquatic systems be comprehensively explored and new methods for monitoring their dynamics be developed. While aquatic and terrestrial ecosystems have much in common in terms of their mathematical description, there are essential differences between them. For example, the mobility of oceanic plankton is mainly controlled by diffusion processes, whereas terrestrial organisms naturally enough obey totally different laws. This paper is focused on the processes underlying the dynamics of spatially inhomogeneous plankton communities. We demonstrate that conceptual reaction-diffusion mathematical models are an appropriate tool for investigating both complex spatio-temporal plankton dynamics and the fractal properties of planktivorous fish school walks. (reviews of topical problems)
Spatiotemporal dynamics of a digital phase-locked loop based coupled map lattice system
Energy Technology Data Exchange (ETDEWEB)
Banerjee, Tanmoy, E-mail: tbanerjee@phys.buruniv.ac.in; Paul, Bishwajit; Sarkar, B. C. [Department of Physics, University of Burdwan, Burdwan, West Bengal 713 104 (India)
2014-03-15
We explore the spatiotemporal dynamics of a coupled map lattice (CML) system, which is realized with a one dimensional array of locally coupled digital phase-locked loops (DPLLs). DPLL is a nonlinear feedback-controlled system widely used as an important building block of electronic communication systems. We derive the phase-error equation of the spatially extended system of coupled DPLLs, which resembles a form of the equation of a CML system. We carry out stability analysis for the synchronized homogeneous solutions using the circulant matrix formalism. It is shown through extensive numerical simulations that with the variation of nonlinearity parameter and coupling strength the system shows transitions among several generic features of spatiotemporal dynamics, viz., synchronized fixed point solution, frozen random pattern, pattern selection, spatiotemporal intermittency, and fully developed spatiotemporal chaos. We quantify the spatiotemporal dynamics using quantitative measures like average quadratic deviation and spatial correlation function. We emphasize that instead of using an idealized model of CML, which is usually employed to observe the spatiotemporal behaviors, we consider a real world physical system and establish the existence of spatiotemporal chaos and other patterns in this system. We also discuss the importance of the present study in engineering application like removal of clock-skew in parallel processors.
Synchronization and suppression of chaos in non-locally coupled ...
Indian Academy of Sciences (India)
Coupled map lattices have been intensively investigated as models to understand many spatiotemporal phenomena observed in extended system, and consequently spatiotemporal chaos. We used the complex order parameter to quantify chaos synchronization for a one-dimensional chain of coupled logistic maps with a ...
Nee, Sean
2018-05-01
Survival analysis in biology and reliability theory in engineering concern the dynamical functioning of bio/electro/mechanical units. Here we incorporate effects of chaotic dynamics into the classical theory. Dynamical systems theory now distinguishes strong and weak chaos. Strong chaos generates Type II survivorship curves entirely as a result of the internal operation of the system, without any age-independent, external, random forces of mortality. Weak chaos exhibits (a) intermittency and (b) Type III survivorship, defined as a decreasing per capita mortality rate: engineering explicitly defines this pattern of decreasing hazard as 'infant mortality'. Weak chaos generates two phenomena from the normal functioning of the same system. First, infant mortality- sensu engineering-without any external explanatory factors, such as manufacturing defects, which is followed by increased average longevity of survivors. Second, sudden failure of units during their normal period of operation, before the onset of age-dependent mortality arising from senescence. The relevance of these phenomena encompasses, for example: no-fault-found failure of electronic devices; high rates of human early spontaneous miscarriage/abortion; runaway pacemakers; sudden cardiac death in young adults; bipolar disorder; and epilepsy.
International Nuclear Information System (INIS)
Steiner, F.
1994-01-01
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace formular is discussed as a sound mathematical basis for the semiclassical quantization of chaos. Two conjectures are presented on the basis of which it is argued that there are unique fluctuation properties in quantum mechanics which are universal and, in a well defined sense, maximally random if the corresponding classical system is strongly chaotic. These properties constitute the quantum mechanical analogue of the phenomenon of chaos in classical mechanics. Thus quantum chaos has been found. (orig.)
International Nuclear Information System (INIS)
Mueller, B.
1997-01-01
The report contains viewgraphs on the following: ergodicity and chaos; Hamiltonian dynamics; metric properties; Lyapunov exponents; KS entropy; dynamical realization; lattice formulation; and numerical results
Energy Technology Data Exchange (ETDEWEB)
Mueller, B.
1997-09-22
The report contains viewgraphs on the following: ergodicity and chaos; Hamiltonian dynamics; metric properties; Lyapunov exponents; KS entropy; dynamical realization; lattice formulation; and numerical results.
International Nuclear Information System (INIS)
Gong Yubing; Xie Yanhang; Lin Xiu; Hao Yinghang; Ma Xiaoguang
2010-01-01
Research highlights: → Chemical delay and chemical coupling can tame chaotic bursting. → Chemical delay-induced transitions from bursting synchronization to intermittent multiple spiking synchronizations. → Chemical coupling-induced different types of delay-dependent firing transitions. - Abstract: Chemical synaptic connections are more common than electric ones in neurons, and information transmission delay is especially significant for the synapses of chemical type. In this paper, we report a phenomenon of ordering spatiotemporal chaos and synchronization transitions by the delays and coupling through chemical synapses of modified Hodgkin-Huxley (MHH) neurons on scale-free networks. As the delay τ is increased, the neurons exhibit transitions from bursting synchronization (BS) to intermittent multiple spiking synchronizations (SS). As the coupling g syn is increased, the neurons exhibit different types of firing transitions, depending on the values of τ. For a smaller τ, there are transitions from spatiotemporal chaotic bursting (SCB) to BS or SS; while for a larger τ, there are transitions from SCB to intermittent multiple SS. These findings show that the delays and coupling through chemical synapses can tame the chaotic firings and repeatedly enhance the firing synchronization of neurons, and hence could play important roles in the firing activity of the neurons on scale-free networks.
Hunt, Brian R; Ott, Edward
2015-09-01
In this paper, we propose, discuss, and illustrate a computationally feasible definition of chaos which can be applied very generally to situations that are commonly encountered, including attractors, repellers, and non-periodically forced systems. This definition is based on an entropy-like quantity, which we call "expansion entropy," and we define chaos as occurring when this quantity is positive. We relate and compare expansion entropy to the well-known concept of topological entropy to which it is equivalent under appropriate conditions. We also present example illustrations, discuss computational implementations, and point out issues arising from attempts at giving definitions of chaos that are not entropy-based.
International Nuclear Information System (INIS)
Cejnar, P.
2007-01-01
Chaos is a name given in physics to a branch which, within classical mechanics, studies the consequences of sensitive dependences of the behavior of physical systems on the starting conditions, i.e., the 'butterfly wing effect'. However, how to describe chaotic behavior in the world of quantum particles? It appears that quantum mechanics does not admit the sensitive dependence on the starting conditions, and moreover, predicts a substantial suppression of chaos also at the macroscopic level. Still, the quantum properties of systems that are chaotic in terms of classical mechanics differ basically from the properties of classically arranged systems. This topic is studied by a field of physics referred to as quantum chaos. (author)
Li-Yorke chaos and synchronous chaos in a globally nonlocal coupled map lattice
International Nuclear Information System (INIS)
Khellat, Farhad; Ghaderi, Akashe; Vasegh, Nastaran
2011-01-01
Highlights: → A globally nonlocal coupled map lattice is introduced. → A sufficient condition for the existence of Li-Yorke chaos is determined. → A sufficient condition for synchronous behaviors is obtained. - Abstract: This paper investigates a globally nonlocal coupled map lattice. A rigorous proof to the existence of chaos in the scene of Li-Yorke in that system is presented in terms of the Marotto theorem. Analytical sufficient conditions under which the system is chaotic, and has synchronous behaviors are determined, respectively. The wider regions associated with chaos and synchronous behaviors are shown by simulations. Spatiotemporal chaos, synchronous chaos and some other synchronous behaviors such as fixed points, 2-cycles and 2 2 -cycles are also shown by simulations for some values of the parameters.
Sorensen, Bent
2014-01-01
The first book to consider intermittency as a key point of an energy system, Energy Intermittency describes different levels of variability for traditional and renewable energy sources, presenting detailed solutions for handling energy intermittency through trade, collaboration, demand management, and active energy storage. Addressing energy supply intermittency systematically, this practical text:Analyzes typical time-distributions and intervals between episodes of demand-supply mismatch and explores their dependence on system layouts and energy source characteristicsSimulates scenarios regar
2005-01-01
[figure removed for brevity, see original site] Context image for PIA03200 Iani Chaos This VIS image of Iani Chaos shows the layered deposit that occurs on the floor. It appears that the layers were deposited after the chaos was formed. Image information: VIS instrument. Latitude 2.3S, Longitude 342.3E. 17 meter/pixel resolution. Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
Controlling chaos in the current-driven ion acoustic instability
International Nuclear Information System (INIS)
Fukuyama, T.; Taniguchi, K.; Kawai, Y.
2002-01-01
Control of intermittent chaos caused by the current-driven ion acoustic instability is attempted and the controlling mechanism is investigated. When a small negative dc voltage is applied to the chaotic system as a perturbation, the system changes from a chaotic state to a periodic state while maintaining the instability, indicating that the chaotic state caused by the ion acoustic instability is well controlled by applying a small negative dc voltage. A hysteresis structure is observed on the V-I curve of the mesh grid to which the negative dc voltage to control is applied. Furthermore, when a negative dc voltage is applied to the state which shows a laminar structure existing under same experimental conditions, the system becomes chaotic via a bifurcation. Driven-chaos is excited when a negative dc voltage is applied to the laminar state. Applying a small negative dc voltage leads to controlling intermittent chaos while exciting driven-chaos
Intermittency in the particle production and in the nuclear multifragmentation
International Nuclear Information System (INIS)
Bozek, P.; Ploszajczak, M.
1991-01-01
Intermittency is a manifestation of scale invariance and randomness in physical systems. Intermittency in relativistic heavy-ion collisions and, in particular, the projectile dependence, multiplicity dependence and source-size dependence are discussed in the frame of the model of spatio-temporal intermittency. Moreover, recent theoretical results in intermittency studies of the nuclear multifragmentation are presented. (author) 35 refs., 4 figs., 1 tab
Energy Technology Data Exchange (ETDEWEB)
Bohigas, Oriol [Laboratoire de Physique Theorique et Modeles Statistiques, Orsay (France)
2005-04-18
Are there quantum signatures, for instance in the spectral properties, of the underlying regular or chaotic nature of the corresponding classical motion? Are there universality classes? Within this framework the merging of two at first sight seemingly disconnected fields, namely random matrix theories (RMT) and quantum chaos (QC), is briefly described. Periodic orbit theory (POT) plays a prominent role. Emphasis is given to compound nucleus resonances and binding energies, whose shell effects are examined from this perspective. Several aspects are illustrated with Riemann's {zeta}-function, which has become a testing ground for RMT, QC, POT, and their relationship.
International Nuclear Information System (INIS)
Bohigas, Oriol
2005-01-01
Are there quantum signatures, for instance in the spectral properties, of the underlying regular or chaotic nature of the corresponding classical motion? Are there universality classes? Within this framework the merging of two at first sight seemingly disconnected fields, namely random matrix theories (RMT) and quantum chaos (QC), is briefly described. Periodic orbit theory (POT) plays a prominent role. Emphasis is given to compound nucleus resonances and binding energies, whose shell effects are examined from this perspective. Several aspects are illustrated with Riemann's ζ-function, which has become a testing ground for RMT, QC, POT, and their relationship
[Turbulence and spatio-temporal chaos
International Nuclear Information System (INIS)
1990-01-01
This report discusses Saffman-Taylor instability; cylinder wake; Levy walk and turbulent channel flow; bubble motion and bubble streams; spinal turbulent and wetting; collective behavior of a coupled map system with a conserved quantity; stability of temporally periodic states; generic nonergodic behavior in continuous systems; characterization of unstable periodic orbits; in low-dimensional chaotic attractors and repellers; and Ginzburg-Landau theory for oil-water-surfactant mixture
2003-01-01
[figure removed for brevity, see original site] Released 11 November 2003Aureum Chaos is a large crater that was filled with sediment after its formation. After the infilling of sediment, something occurred that caused the sediment to be broken up into large, slumped blocks and smaller knobs. Currently, it is believed that the blocks and knobs form when material is removed from the subsurface, creating void space. Subsurface ice was probably heated, and the water burst out to the surface, maybe forming a temporary lake. Other areas of chaos terrain have large outflow channels that emanate from them, indicating that a tremendous amount of water was released.Image information: VIS instrument. Latitude -3.2, Longitude 331 East (29 West). 19 meter/pixel resolution.Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
2003-01-01
[figure removed for brevity, see original site] At the easternmost end of Valles Marineris, a rugged, jumbled terrain known as chaos displays a stratigraphy that could be described as precarious. Perched on top of the jumbled blocks is another layer of sedimentary material that is in the process of being eroded off the top. This material is etched by the wind into yardangs before it ultimately is stripped off to reveal the existing chaos.Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.Image information: VIS instrument. Latitude -7.8, Longitude 19.1 East (340.9 West). 19 meter/pixel resolution.
Quantum signatures of chaos or quantum chaos?
Energy Technology Data Exchange (ETDEWEB)
Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu [St. Petersburg State University (Russian Federation)
2016-11-15
A critical analysis of the present-day concept of chaos in quantum systems as nothing but a “quantum signature” of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville–Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stability parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.
Quantum signatures of chaos or quantum chaos?
International Nuclear Information System (INIS)
Bunakov, V. E.
2016-01-01
A critical analysis of the present-day concept of chaos in quantum systems as nothing but a “quantum signature” of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville–Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stability parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.
Critical behavior of the Lyapunov exponent in type-III intermittency
Energy Technology Data Exchange (ETDEWEB)
Alvarez-Llamoza, O. [Departamento de Fisica, FACYT, Universidad de Carabobo, Valencia (Venezuela); Centro de Fisica Fundamental, Grupo de Caos y Sistemas Complejos, Universidad de Los Andes, Merida 5251, Merida (Venezuela)], E-mail: llamoza@ula.ve; Cosenza, M.G. [Centro de Fisica Fundamental, Grupo de Caos y Sistemas Complejos, Universidad de Los Andes, Merida 5251, Merida (Venezuela); Ponce, G.A. [Departamento de Fisica, Universidad Nacional Autonoma de Honduras (Honduras); Departamento de Ciencias Naturales, Universidad Pedagogica Nacional Francisco Morazan, Tegucigalpa (Honduras)
2008-04-15
The critical behavior of the Lyapunov exponent near the transition to robust chaos via type-III intermittency is determined for a family of one-dimensional singular maps. Critical boundaries separating the region of robust chaos from the region where stable fixed points exist are calculated on the parameter space of the system. A critical exponent {beta} expressing the scaling of the Lyapunov exponent is calculated along the critical curve corresponding to the type-III intermittent transition to chaos. It is found that {beta} varies on the interval 0 {<=} {beta} < 1/2 as a function of the order of the singularity of the map. This contrasts with earlier predictions for the scaling behavior of the Lyapunov exponent in type-III intermittency. The variation of the critical exponent {beta} implies a continuous change in the nature of the transition to chaos via type-III intermittency, from a second-order, continuous transition to a first-order, discontinuous transition.
Photonic integrated circuits unveil crisis-induced intermittency.
Karsaklian Dal Bosco, Andreas; Akizawa, Yasuhiro; Kanno, Kazutaka; Uchida, Atsushi; Harayama, Takahisa; Yoshimura, Kazuyuki
2016-09-19
We experimentally investigate an intermittent route to chaos in a photonic integrated circuit consisting of a semiconductor laser with time-delayed optical feedback from a short external cavity. The transition from a period-doubling dynamics to a fully-developed chaos reveals a stage intermittently exhibiting these two dynamics. We unveil the bifurcation mechanism underlying this route to chaos by using the Lang-Kobayashi model and demonstrate that the process is based on a phenomenon of attractor expansion initiated by a particular distribution of the local Lyapunov exponents. We emphasize on the crucial importance of the distribution of the steady-state solutions introduced by the time-delayed feedback on the existence of this intermittent dynamics.
2002-01-01
[figure removed for brevity, see original site] Collapsed terrain in Hydapsis Chaos.This is the source terrain for several outflow channels. Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.VIS Instrument. Latitude 3.2, Longitude 333.2 East. 19 meter/pixel resolution.
Huwe, Terence K.
2009-01-01
"Embracing the chaos" is an ongoing challenge for librarians. Embracing the chaos means librarians must have a plan for responding to the flood of new products, widgets, web tools, and gizmos that students use daily. In this article, the author argues that library instruction and access services have been grappling with that chaos with…
Nonlinear dynamics and chaos in a fractional-order financial system
International Nuclear Information System (INIS)
Chen Weiching
2008-01-01
This study examines the two most attractive characteristics, memory and chaos, in simulations of financial systems. A fractional-order financial system is proposed in this study. It is a generalization of a dynamic financial model recently reported in the literature. The fractional-order financial system displays many interesting dynamic behaviors, such as fixed points, periodic motions, and chaotic motions. It has been found that chaos exists in fractional-order financial systems with orders less than 3. In this study, the lowest order at which this system yielded chaos was 2.35. Period doubling and intermittency routes to chaos in the fractional-order financial system were found
International Nuclear Information System (INIS)
Knop, J.; Vogel, H.; Hupe, W.
1981-01-01
An intermittent hydronephrosis was observed in a 40-year old patient. This disease pattern is due to an incongruity between the formation of urine and the transport capacity in the ureteropelvic junction. The latent impediment of flow becomes manifest with increased urine secretion. Irreversible renal damage can be the result of the repeatedly occurring hydronephrotic crises. (orig.) [de
Complex Nonlinearity Chaos, Phase Transitions, Topology Change and Path Integrals
Ivancevic, Vladimir G
2008-01-01
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to th...
2004-01-01
[figure removed for brevity, see original site] Released 7 May 2004 This daytime visible color image was collected on May 30, 2002 during the Southern Fall season in Atlantis Chaos. The THEMIS VIS camera is capable of capturing color images of the martian surface using its five different color filters. In this mode of operation, the spatial resolution and coverage of the image must be reduced to accommodate the additional data volume produced from the use of multiple filters. To make a color image, three of the five filter images (each in grayscale) are selected. Each is contrast enhanced and then converted to a red, green, or blue intensity image. These three images are then combined to produce a full color, single image. Because the THEMIS color filters don't span the full range of colors seen by the human eye, a color THEMIS image does not represent true color. Also, because each single-filter image is contrast enhanced before inclusion in the three-color image, the apparent color variation of the scene is exaggerated. Nevertheless, the color variation that does appear is representative of some change in color, however subtle, in the actual scene. Note that the long edges of THEMIS color images typically contain color artifacts that do not represent surface variation. Image information: VIS instrument. Latitude -34.5, Longitude 183.6 East (176.4 West). 38 meter/pixel resolution. Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D
2005-01-01
[figure removed for brevity, see original site] The THEMIS VIS camera is capable of capturing color images of the Martian surface using five different color filters. In this mode of operation, the spatial resolution and coverage of the image must be reduced to accommodate the additional data volume produced from using multiple filters. To make a color image, three of the five filter images (each in grayscale) are selected. Each is contrast enhanced and then converted to a red, green, or blue intensity image. These three images are then combined to produce a full color, single image. Because the THEMIS color filters don't span the full range of colors seen by the human eye, a color THEMIS image does not represent true color. Also, because each single-filter image is contrast enhanced before inclusion in the three-color image, the apparent color variation of the scene is exaggerated. Nevertheless, the color variation that does appear is representative of some change in color, however subtle, in the actual scene. Note that the long edges of THEMIS color images typically contain color artifacts that do not represent surface variation. This false color image was collected during Southern Fall and shows part of the Aureum Chaos. Image information: VIS instrument. Latitude -3.6, Longitude 332.9 East (27.1 West). 35 meter/pixel resolution. Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS
Sándor, Bulcsú; Járai-Szabó, Ferenc; Tél, Tamás; Néda, Zoltán
2013-04-01
The dynamics of a spring-block train placed on a moving conveyor belt is investigated both by simple experiments and computer simulations. The first block is connected by a spring to an external static point and, due to the dragging effect of the belt, the blocks undergo complex stick-slip dynamics. A qualitative agreement with the experimental results can be achieved only by taking into account the spatial inhomogeneity of the friction force on the belt's surface, modeled as noise. As a function of the velocity of the conveyor belt and the noise strength, the system exhibits complex, self-organized critical, sometimes chaotic, dynamics and phase transition-like behavior. Noise-induced chaos and intermittency is also observed. Simulations suggest that the maximum complexity of the dynamical states is achieved for a relatively small number of blocks (around five).
A simple spatiotemporal chaotic Lotka-Volterra model
International Nuclear Information System (INIS)
Sprott, J.C.; Wildenberg, J.C.; Azizi, Yousef
2005-01-01
A mathematically simple example of a high-dimensional (many-species) Lotka-Volterra model that exhibits spatiotemporal chaos in one spatial dimension is described. The model consists of a closed ring of identical agents, each competing for fixed finite resources with two of its four nearest neighbors. The model is prototypical of more complicated models in its quasiperiodic route to chaos (including attracting 3-tori), bifurcations, spontaneous symmetry breaking, and spatial pattern formation
Biologically inspired rate control of chaos.
Olde Scheper, Tjeerd V
2017-10-01
The overall intention of chaotic control is to eliminate chaos and to force the system to become stable in the classical sense. In this paper, I demonstrate a more subtle method that does not eliminate all traces of chaotic behaviour; yet it consistently, and reliably, can provide control as intended. The Rate Control of Chaos (RCC) method is derived from metabolic control processes and has several remarkable properties. RCC can control complex systems continuously, and unsupervised, it can also maintain control across bifurcations, and in the presence of significant systemic noise. Specifically, I show that RCC can control a typical set of chaotic models, including the 3 and 4 dimensional chaotic Lorenz systems, in all modes. Furthermore, it is capable of controlling spatiotemporal chaos without supervision and maintains control of the system across bifurcations. This property of RCC allows a dynamic system to operate in parameter spaces that are difficult to control otherwise. This may be particularly interesting for the control of forced systems or dynamic systems that are chaotically perturbed. These control properties of RCC are applicable to a range of dynamic systems, thereby appearing to have far-reaching effects beyond just controlling chaos. RCC may also point to the existence of a biochemical control function of an enzyme, to stabilise the dynamics of the reaction cascade.
International Nuclear Information System (INIS)
Bialas, A.
1993-01-01
The existing data definitely indicate the existence of intermittency, i.e. of self similar structures in the systems of particles created in high-energy collisions. The effect seems universal: it was found in most of the processes investigated and its measures parameters depend only weakly (if at all) on the process in question. Strong HBT effect was found, suggesting that intermittency is related to space-time structure of the pion source rather than to detailed momentum structure of the production amplitudes. There are indications that this space time structure may be fractal, but more data is needed to establish this. The theoretical explanation remains obscure: it seems that both parton cascade and hadronization play an important role. Their interrelation, however, remains a mystery. 5 figs., 19 refs
Erçetin, Şefika; Tekin, Ali
2014-01-01
The present work investigates global politics and political implications of social science and management with the aid of the latest complexity and chaos theories. Until now, deterministic chaos and nonlinear analysis have not been a focal point in this area of research. This book remedies this deficiency by utilizing these methods in the analysis of the subject matter. The authors provide the reader a detailed analysis on politics and its associated applications with the help of chaos theory, in a single edited volume.
National Research Council Canada - National Science Library
Morris, Jr, Gerald W
2007-01-01
.... The study investigates whether chaos theory, part of complexity science, can extract information from Katrina contracting data to help managers make better logistics decisions during disaster relief operations...
Intermittently chaotic oscillations for a differential-delay equation with Gaussian nonlinearity
Hamilton, Ian
1992-01-01
For a differential-delay equation the time dependence of the variable is a function of the variable at a previous time. We consider a differential-delay equation with Gaussian nonlinearity that displays intermittent chaos. Although not the first example of a differential-delay equation that displays such behavior, for this example the intermittency is classified as type III, and the origin of the intermittent chaos may be qualitatively understood from the limiting forms of the equation for large and small variable magnitudes.
Chaos control and taming of turbulence in plasma devices
DEFF Research Database (Denmark)
Klinger, T.; Schröder, C.; Block, D.
2001-01-01
Chaos and turbulence are often considered as troublesome features of plasma devices. In the general framework of nonlinear dynamical systems, a number of strategies have been developed to achieve active control over complex temporal or spatio-temporal behavior. Many of these techniques apply...... to plasma instabilities. In the present paper we discuss recent progress in chaos control and taming of turbulence in three different plasma "model" experiments: (1) Chaotic oscillations in simple plasma diodes, (2) ionization wave turbulence in the positive column of glow discharges, and (3) drift wave...
Suppression of chaos via control of energy flow
Guo, Shengli; Ma, Jun; Alsaedi, Ahmed
2018-03-01
Continuous energy supply is critical and important to support oscillating behaviour; otherwise, the oscillator will die. For nonlinear and chaotic circuits, enough energy supply is also important to keep electric devices working. In this paper, Hamilton energy is calculated for dimensionless dynamical system (e.g., the chaotic Lorenz system) using Helmholtz's theorem. The Hamilton energy is considered as a new variable and then the dynamical system is controlled by using the scheme of energy feedback. It is found that chaos can be suppressed even when intermittent feedback scheme is applied. This scheme is effective to control chaos and to stabilise other dynamical systems.
Murphy, David
2011-01-01
About 20 years ago, while lost in the midst of his PhD research, the author mused over proposed titles for his thesis. He was pretty pleased with himself when he came up with "Chaos Rules" (the implied double meaning was deliberate), or more completely, "Chaos Rules: An Exploration of the Work of Instructional Designers in Distance Education." He…
Chaos Modelling with Computers
Indian Academy of Sciences (India)
Chaos is one of the major scientific discoveries of our times. In fact many scientists ... But there are other natural phenomena that are not predictable though ... characteristics of chaos. ... The position and velocity are all that are needed to determine the motion of a .... a system of equations that modelled the earth's weather ...
International Nuclear Information System (INIS)
Sulman, F.G.; Tal, E.; Pfeifer, Y.; Superstine, E.
1975-01-01
Intermittent hyperthyreosis occurs under various forms of stress, especially heat stress. The clinician may diagnose such cases as masked or apathetic hyperthyroidism or 'forme fruste' hyperthyreosis or thyroid autonomy. As most routine and standard tests may here yield inconsistent results, it is the patients' anamnesis which may provide the clue. Our Bioclimatology Unit has now seen over 100 cases in which thyroid hypersensitivity towards heat was the most prominent syndrome: 10-15% of weather-sensitive patients are affected. The patients complain before or during heat spells of such contradictory symptoms as insomnia, irritability, tension, tachycardia, palpitations, precordial pain, dyspnoe, flushes with sweating or chills, tremor, abdominal pain or diarrhea, polyuria or pollakisuria, weight loss in spite of ravenous appetite, fatigue, exhaustion, depression, adynamia, lack of concentration and confusion. Determination of urinary neurohormones allows a differential diagnosis, intermittent hyperthyreosis being characterized by three cardinal symptoms: tachycardia - every case with more than 80 pulse beats being suspect (not specific); urinary histamine - every case excreting more than 90 μg/day being suspect. Again the drawback of this test is its lack of specificity, as histamine may also be increased in cases of allergy and spondylitis; urinary thyroxine - every case excreting more than 20 μg/day T-4 being suspect. This is the only specific test. Therapy should make use of lithium carbonate and betablockers. Propyl thiouracil is rarely required. (orig.) [de
Experiments on intrinsic and thermally induced chaos in an rf-driven Josephson junction
DEFF Research Database (Denmark)
Davidson, A.; Dueholm, B.; Beasley, M. R.
1986-01-01
We report detailed measurements of low-frequency noise due to microwaves applied to a real Josephson tunnel junction. An intrinsically chaotic region is apparently identified, but the effects of thermal noise are shown to be significant. In particular we show experimental data that we interpret a...... as evidence for thermally activated hopping and thermally affected chaos. The data are only in qualitative accord with recent ideas regarding the effect of thermal noise on intermittent chaos....
International Nuclear Information System (INIS)
Friedrich, H.
1992-01-01
Rapid growth in the study of nonlinear dynamics and chaos in classical mechanics, has led physicists to reappraise their abandonment of this definition of atomic theory in favour of quantum mechanics adopted earlier this century. The concept of chaos in classical mechanics is examined in this paper and manifestations of chaos in quantum mechanics are explored. While quantum mechanics teaches that atomic particles must not be pictured as moving sharply in defined orbits, these precise orbits can be used to describe essential features of the measurable quantum mechanical spectra. (UK)
Chaos applications in telecommunications
Stavroulakis, Peter
2005-01-01
IntroductionPeter StavroulakisChaotic Signal Generation and Transmission Antonio Cândido Faleiros,Waldecir João Perrella,TâniaNunes Rabello,Adalberto Sampaio Santos, andNeiYoshihiro SomaChaotic Transceiver Design Arthur Fleming-DahlChaos-Based Modulation and DemodulationTechniques Francis C.M. Lau and Chi K. TseA Chaos Approach to Asynchronous DS-CDMASystems S. Callegari, G. Mazzini, R. Rovatti, and G. SettiChannel Equalization in Chaotic CommunicationSystems Mahmut CiftciOptical Communications using ChaoticTechniques Gregory D. VanWiggerenAPPENDIX AFundamental Concepts of the Theory ofChaos a
Energy Technology Data Exchange (ETDEWEB)
Maldacena, Juan [School of Natural Sciences, Institute for Advanced Study,1 Einstein Drive, Princeton, NJ (United States); Shenker, Stephen H. [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University,382 Via Pueblo Mall, Stanford, CA (United States); Stanford, Douglas [School of Natural Sciences, Institute for Advanced Study,1 Einstein Drive, Princeton, NJ (United States)
2016-08-17
We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λ{sub L}≤2πk{sub B}T/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.
DEFF Research Database (Denmark)
Lindberg, Erik
1996-01-01
The chaotic behaviour of the Colpitts oscillator reported by M.P. Kennedy is further investigated by means of PSpice simulations. Chaos is also observed with the default Ebers-Moll BJT transistor model with no memory. When the model is extended with memory and losses chaos do not occur and a 3'rd...... order limit cycle is found. If the the forward Early voltage parameter is added chaos is observed again. An examination of the eigenvalues of the oscillator with the simple memoryless Ebers-Moll BJT injection model is presented. By adding bulk resistors to the model stable limit cycles of orders 1, 2, 3...
International Nuclear Information System (INIS)
Shi-Jian, Cang; Zeng-Qiang, Chen; Wen-Juan, Wu
2009-01-01
This paper presents a non-autonomous hyper-chaotic system, which is formed by adding a periodic driving signal to a four-dimensional chaotic model extended from the Lorenz system. The resulting non-autonomous hyper-chaotic system can display any dynamic behaviour among the periodic orbits, intermittency, chaos and hyper-chaos by controlling the frequency of the periodic signal. The phenomenon has been well demonstrated by numerical simulations, bifurcation analysis and electronic circuit realization. Moreover, the system is concrete evidence for the presence of Pomeau–Manneville Type-I intermittency and crisis-induced intermittency. The emergence of a different type of intermittency is similarly subjected to the frequency of periodic forcing. By statistical analysis, power scaling laws consisting in different intermittency are obtained for the lifetime in the laminar state between burst states
Campbell, David
1987-11-01
I provide a brief overview of the current status of the field of deterministic "chaos" stressing its interrelations and applications to other fields and suggesting a number of important open problems for future study.
Quantum manifestations of chaos
International Nuclear Information System (INIS)
Borondo, F.; Benito, R.M.
1998-01-01
The correspondence between classical and quantum mechanics is considered both in the regular and chaotic regimes, and the main results regarding the quantum manifestations of chaos are reviewed. (Author) 16 refs
Energy Technology Data Exchange (ETDEWEB)
Bolotin, IU L; Gonchar, V IU; Truten, V I; Shulga, N F
1986-01-01
It is shown that axial channeling of relativistic electrons can give rise to the effect of dynamic chaos which involves essentially chaotic motion of a particle in the channel. The conditions leading to the effect of dynamic chaos and the manifestations of this effect in physical processes associated with the passage of particles through a crystal are examined using a silicon crystal as an example. 7 references.
Exploiting chaos for applications
Energy Technology Data Exchange (ETDEWEB)
Ditto, William L., E-mail: wditto@hawaii.edu [Department of Physics and Astronomy, University of Hawaii at Mānoa, Honolulu, Hawaii 96822 (United States); Sinha, Sudeshna, E-mail: sudeshna@iisermohali.ac.in [Indian Institute of Science Education and Research (IISER), Mohali, Knowledge City, Sector 81, SAS Nagar, PO Manauli 140306, Punjab (India)
2015-09-15
We discuss how understanding the nature of chaotic dynamics allows us to control these systems. A controlled chaotic system can then serve as a versatile pattern generator that can be used for a range of application. Specifically, we will discuss the application of controlled chaos to the design of novel computational paradigms. Thus, we present an illustrative research arc, starting with ideas of control, based on the general understanding of chaos, moving over to applications that influence the course of building better devices.
Exploiting chaos for applications.
Ditto, William L; Sinha, Sudeshna
2015-09-01
We discuss how understanding the nature of chaotic dynamics allows us to control these systems. A controlled chaotic system can then serve as a versatile pattern generator that can be used for a range of application. Specifically, we will discuss the application of controlled chaos to the design of novel computational paradigms. Thus, we present an illustrative research arc, starting with ideas of control, based on the general understanding of chaos, moving over to applications that influence the course of building better devices.
Nonlinear chaos control and synchronization
Huijberts, H.J.C.; Nijmeijer, H.; Schöll, E.; Schuster, H.G.
2007-01-01
This chapter contains sections titled: Introduction Nonlinear Geometric Control Some Differential Geometric Concepts Nonlinear Controllability Chaos Control Through Feedback Linearization Chaos Control Through Input-Output Linearization Lyapunov Design Lyapunov Stability and Lyapunov's First Method
International Nuclear Information System (INIS)
Destexhe, A.
1994-01-01
Various types of spatiotemporal behavior are described for two-dimensional networks of excitatory and inhibitory neurons with time delayed interactions. It is described how the network behaves as several structural parameters are varied, such as the number of neurons, the connectivity, and the values of synaptic weights. A transition from spatially uniform oscillations to spatiotemporal chaos via intermittentlike behavior is observed. The properties of spatiotemporally chaotic solutions are investigated by evaluating the largest positive Lyapunov exponent and the loss of correlation with distance. Finally, properties of information transport are evaluated during uniform oscillations and spatiotemporal chaos. It is shown that the diffusion coefficient increases significantly in the spatiotemporal phase similar to the increase of transport coefficients at the onset of fluid turbulence. It is proposed that such a property should be seen in other media, such as chemical turbulence or networks of oscillators. The possibility of measuring information transport from appropriate experiments is also discussed
Stochastic Estimation via Polynomial Chaos
2015-10-01
AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic
Enlightenment philosophers’ ideas about chaos
Directory of Open Access Journals (Sweden)
A. V. Kulik
2014-07-01
It is grounded that the philosopher and enlightener Johann Gottfried von Herder advanced an idea of objectivity of process of transformation chaos into order. It is shown that idea of «The law of nature» existing as for ordering chaos opened farreaching prospects for researches of interaction with chaos.
Kasimov, Aslan R.; Faria, Luiz; Rosales, Rodolfo R.
2013-01-01
: steady traveling wave solutions, instability of such solutions, and the onset of chaos. Our model is the first (to our knowledge) to describe chaos in shock waves by a scalar first-order partial differential equation. The chaos arises in the equation
International Nuclear Information System (INIS)
Whelan, N.D.
1993-01-01
Random Matrix Theory successfully describes the statistics of the low-lying spectra of some nuclei but not of others. It is currently believed that this theory applies to systems in which the corresponding classical motion is chaotic. This conjecture is tested for collective nuclei by studying the Interacting Boson Model. Quantum and classical measures of chaos are proposed and found to be in agreement throughout the parameter space of the model. For some parameter values the measures indicate the presence of a previously unknown approximate symmetry. A phenomenon called partial dynamical symmetry is explored and shown to lead to a suppression of chaos. A time dependent function calculated from the quantum spectrum is discussed. This function is sensitive to the extent of chaos and provides a robust method of analyzing experimental spectra
He, Temple; Habib, Salman
2013-09-01
Simple dynamical systems--with a small number of degrees of freedom--can behave in a complex manner due to the presence of chaos. Such systems are most often (idealized) limiting cases of more realistic situations. Isolating a small number of dynamical degrees of freedom in a realistically coupled system generically yields reduced equations with terms that can have a stochastic interpretation. In situations where both noise and chaos can potentially exist, it is not immediately obvious how Lyapunov exponents, key to characterizing chaos, should be properly defined. In this paper, we show how to do this in a class of well-defined noise-driven dynamical systems, derived from an underlying Hamiltonian model.
Economic intermittency in a two-country model of business cycles coupled by investment
International Nuclear Information System (INIS)
Saiki, Y.; Chian, A.C.L.; Yoshida, H.
2011-01-01
Highlights: → Intermittent economic behavior of Keynes-Goodwin type model is investigated. → After a transition the system keeps its memory before the transition. → The intermittent phenomena is examined from the business cycle patterns. → It is concluded that dynamical patterns do not alter much around the transition. - Abstract: Intermittent behavior of economic dynamics is investigated by a two-country model of Keynes-Goodwin type business cycles. Numerical simulations show that after an economic system evolves from weak chaos to strong chaos the system keeps its memory before the transition and its time series alternates episodically between periods of weakly and strongly chaotic fluctuations. In addition, we examine the intermittent phenomena from the view point of business cycle patterns near the crisis point.
Economic intermittency in a two-country model of business cycles coupled by investment
Energy Technology Data Exchange (ETDEWEB)
Saiki, Y., E-mail: saiki@math.sci.hokudai.ac.jp [Department of Mathematics, Hokkaido University, Sapporo 060-0810 (Japan); Chian, A.C.L. [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); California Institute of Technology, Pasadena, CA 91125 (United States); Yoshida, H. [College of Economics, Nihon University, Tokyo 101-8360 (Japan)
2011-06-15
Highlights: > Intermittent economic behavior of Keynes-Goodwin type model is investigated. > After a transition the system keeps its memory before the transition. > The intermittent phenomena is examined from the business cycle patterns. > It is concluded that dynamical patterns do not alter much around the transition. - Abstract: Intermittent behavior of economic dynamics is investigated by a two-country model of Keynes-Goodwin type business cycles. Numerical simulations show that after an economic system evolves from weak chaos to strong chaos the system keeps its memory before the transition and its time series alternates episodically between periods of weakly and strongly chaotic fluctuations. In addition, we examine the intermittent phenomena from the view point of business cycle patterns near the crisis point.
Chaos Modelling with Computers
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 5. Chaos Modelling with Computers Unpredicatable Behaviour of Deterministic Systems. Balakrishnan Ramasamy T S K V Iyer. General Article Volume 1 Issue 5 May 1996 pp 29-39 ...
Neural chaos and schizophrenia
Czech Academy of Sciences Publication Activity Database
Bob, P.; Chládek, Jan; Šusta, M.; Glaslová, K.; Jagla, F.; Kukleta, M.
2007-01-01
Roč. 26, č. 4 (2007), s. 298-305 ISSN 0231-5882 Institutional research plan: CEZ:AV0Z20650511 Keywords : EDA * Lyapunov exponent * schizophrenia * chaos Subject RIV: FL - Psychiatry, Sexuology Impact factor: 1.286, year: 2007
International Nuclear Information System (INIS)
Chirikov, B.V.
1990-01-01
Classification of chaotic patterns in classical Hamiltonian systems is given as a series of levels with increasing disorder. Hamiltonian dynamics is presented, including the renormalization chaos, based upon the fairly simple resonant theory. First estimates for the critical structure and related statistical anomalies in arbitrary dimensions are discussed. 49 refs
Directory of Open Access Journals (Sweden)
Tamás Meszéna
2017-04-01
Full Text Available We are faced with chaotic processes in many segments of our life: meteorology, environmental pollution, financial and economic processes, sociology, mechanics, electronics, biology, chemistry. The spreading of high-performance computers and the development of simulation methods made the examination of these processes easily available. Regular, periodic motions (pendulum, harmonic oscillatory motion, bouncing ball, as taught at secondary level, become chaotic even due minor changes. If it is true that the most considerable achievements of twentieth century physics were the theory of relativity, quantum mechanics and chaos theory, then it is presumably time to think about, examine and test how and to what extent chaos can be presented to the students. Here I would like to introduce a 12 lesson long facultative curriculum framework on chaos designed for students aged seventeen. The investigation of chaos phenomenon in this work is based on a freeware, “Dynamics Solver”. This software, with some assistance from the teacher, is suitable for classroom use at secondary level.
Directory of Open Access Journals (Sweden)
Kratochvíl C.
2007-10-01
Full Text Available The purpose of this article is to provide an elementary introduction to the subject of chaos in the electromechanical drive systems. In this article, we explore chaotic solutions of maps and continuous time systems. These solutions are also bounded like equilibrium, periodic and quasiperiodic solutions.
DEFF Research Database (Denmark)
Lykke, Marianne; Lund, Haakon; Skov, Mette
2016-01-01
CHAOS (Cultural Heritage Archive Open System) provides streaming access to more than 500,000 broadcasts by the Danish Broadcast Corporation from 1931 and onwards. The archive is part of the LARM project with the purpose of enabling researchers to search, annotate, and interact with recordings...
DEFF Research Database (Denmark)
Lykke, Marianne; Skov, Mette; Lund, Haakon
CHAOS (Cultural Heritage Archive Open System) provides streaming access to more than 500.000 broad-casts by the Danish Broadcast Corporation from 1931 and onwards. The archive is part of the LARM project with the purpose of enabling researchers to search, annotate, and interact with recordings...
Jesse A. Logan; Fred P. Hain
1990-01-01
Recent advances in applied mathematical analysis have uncovered a fascinating and unexpected dynamical richness that underlies behavior of even the simplest non-linear mathematical models. Due to the complexity of solutions to these non-linear equations, a new mathematical term, chaos, has been coined to describe the resulting dynamics. This term captures the notion...
Generalized Statistical Mechanics at the Onset of Chaos
Directory of Open Access Journals (Sweden)
Alberto Robledo
2013-11-01
Full Text Available Transitions to chaos in archetypal low-dimensional nonlinear maps offer real and precise model systems in which to assess proposed generalizations of statistical mechanics. The known association of chaotic dynamics with the structure of Boltzmann–Gibbs (BG statistical mechanics has suggested the potential verification of these generalizations at the onset of chaos, when the only Lyapunov exponent vanishes and ergodic and mixing properties cease to hold. There are three well-known routes to chaos in these deterministic dissipative systems, period-doubling, quasi-periodicity and intermittency, which provide the setting in which to explore the limit of validity of the standard BG structure. It has been shown that there is a rich and intricate behavior for both the dynamics within and towards the attractors at the onset of chaos and that these two kinds of properties are linked via generalized statistical-mechanical expressions. Amongst the topics presented are: (i permanently growing sensitivity fluctuations and their infinite family of generalized Pesin identities; (ii the emergence of statistical-mechanical structures in the dynamics along the routes to chaos; (iii dynamical hierarchies with modular organization; and (iv limit distributions of sums of deterministic variables. The occurrence of generalized entropy properties in condensed-matter physical systems is illustrated by considering critical fluctuations, localization transition and glass formation. We complete our presentation with the description of the manifestations of the dynamics at the transitions to chaos in various kinds of complex systems, such as, frequency and size rank distributions and complex network images of time series. We discuss the results.
Chaos in neurons and its application: perspective of chaos engineering.
Hirata, Yoshito; Oku, Makito; Aihara, Kazuyuki
2012-12-01
We review our recent work on chaos in neurons and its application to neural networks from perspective of chaos engineering. Especially, we analyze a dataset of a squid giant axon by newly combining our previous work of identifying Devaney's chaos with surrogate data analysis, and show that an axon can behave chaotically. Based on this knowledge, we use a chaotic neuron model to investigate possible information processing in the brain.
Critical behavior of the Lyapunov exponent in type-III intermittency
International Nuclear Information System (INIS)
Alvarez-Llamoza, O.; Cosenza, M.G.; Ponce, G.A.
2008-01-01
The critical behavior of the Lyapunov exponent near the transition to robust chaos via type-III intermittency is determined for a family of one-dimensional singular maps. Critical boundaries separating the region of robust chaos from the region where stable fixed points exist are calculated on the parameter space of the system. A critical exponent β expressing the scaling of the Lyapunov exponent is calculated along the critical curve corresponding to the type-III intermittent transition to chaos. It is found that β varies on the interval 0 ≤ β < 1/2 as a function of the order of the singularity of the map. This contrasts with earlier predictions for the scaling behavior of the Lyapunov exponent in type-III intermittency. The variation of the critical exponent β implies a continuous change in the nature of the transition to chaos via type-III intermittency, from a second-order, continuous transition to a first-order, discontinuous transition
Energy Technology Data Exchange (ETDEWEB)
Tél, Tamás [Institute for Theoretical Physics, Eötvös University, and MTA-ELTE Theoretical Physics Research Group, Pázmány P. s. 1/A, Budapest H-1117 (Hungary)
2015-09-15
We intend to show that transient chaos is a very appealing, but still not widely appreciated, subfield of nonlinear dynamics. Besides flashing its basic properties and giving a brief overview of the many applications, a few recent transient-chaos-related subjects are introduced in some detail. These include the dynamics of decision making, dispersion, and sedimentation of volcanic ash, doubly transient chaos of undriven autonomous mechanical systems, and a dynamical systems approach to energy absorption or explosion.
Tél, Tamás
2015-09-01
We intend to show that transient chaos is a very appealing, but still not widely appreciated, subfield of nonlinear dynamics. Besides flashing its basic properties and giving a brief overview of the many applications, a few recent transient-chaos-related subjects are introduced in some detail. These include the dynamics of decision making, dispersion, and sedimentation of volcanic ash, doubly transient chaos of undriven autonomous mechanical systems, and a dynamical systems approach to energy absorption or explosion.
2002-01-01
(Released 11 June 2002) The Science This fractured surface belongs to a portion of a region called Gorgonum Chaos located in the southern hemisphere of Mars. Gorgonum Chaos is named after the Gorgons in ancient Greek mythology. The Gorgons were monstrous sisters with snakes for hair, tusks like boars and lolling tongues who lived in caves. As it turns out this is indeed a fitting name for this region of Mars because it contains a high density of gullies that 'snake' their way down the walls of the troughs located in this region of chaos. Upon closer examination one finds that these gullies and alluvial deposits, initially discovered by Mars Global Surveyor, are visible on the trough walls (best seen near the bottom of the image). These gullies appear to emanate from a specific layer in the walls. The gullies have been proposed to have formed by the subsurface release of water. The Story This fractured, almost spooky-looking surface belongs to a region called Gorgonum Chaos in the southern hemisphere of Mars. Chaos is a term used for regions of Mars with distinctive areas of broken terrain like the one seen above. This area of Martian chaos is named after the Gorgons in ancient Greek mythology. The Gorgons were monstrous sisters with snakes for hair, tusks like boars, and lolling tongues, who lived in caves. The Gorgons, including famous sister Medusa, could turn a person to stone, and their writhing, snakelike locks cause revulsion to this day. Given the afflicted nature of this contorted terrain, with all of its twisted, branching channels and hard, stony-looking hills in the top half of the image, this is indeed a fitting name for this region of Mars. The name also has great appeal, because the area contains a high density of gullies that 'snake' their way down the walls of the troughs located in this region of Martian chaos. Gullies are trenches cut into the land as accelerated streams of water (or another liquid) erode the surface. To see these, click on the
International Nuclear Information System (INIS)
Bick, Christian; Kolodziejski, Christoph; Timme, Marc
2014-01-01
Predictive feedback control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive feedback control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we study stalled chaos control, where the application of control is stalled to make use of the chaotic, uncontrolled dynamics, and introduce an adaptation paradigm to overcome this limitation and speed up convergence. This modified control scheme is not only capable of stabilizing more periodic orbits than the original predictive feedback control but also speeds up convergence for typical chaotic maps, as illustrated in both theory and application. The proposed adaptation scheme provides a way to tune parameters online, yielding a broadly applicable, fast chaos control that converges reliably, even for periodic orbits of large period
Schuster, H G
2008-01-01
This long-awaited revised second edition of the standard reference on the subject has been considerably expanded to include such recent developments as novel control schemes, control of chaotic space-time patterns, control of noisy nonlinear systems, and communication with chaos, as well as promising new directions in research. The contributions from leading international scientists active in the field provide a comprehensive overview of our current level of knowledge on chaos control and its applications in physics, chemistry, biology, medicine, and engineering. In addition, they show the overlap with the traditional field of control theory in the engineering community.An interdisciplinary approach of interest to scientists and engineers working in a number of areas
Energy Technology Data Exchange (ETDEWEB)
Hosur, Pavan; Qi, Xiao-Liang [Department of Physics, Stanford University,476 Lomita Mall, Stanford, California 94305 (United States); Roberts, Daniel A. [Center for Theoretical Physics and Department of Physics, Massachusetts Institute of Technology,77 Massachusetts Ave, Cambridge, Massachusetts 02139 (United States); Yoshida, Beni [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada); Walter Burke Institute for Theoretical Physics, California Institute of Technology,1200 E California Blvd, Pasadena CA 91125 (United States)
2016-02-01
We study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back up our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. These results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.
International Nuclear Information System (INIS)
Loskutov, Alexander
2010-01-01
This review introduces most of the concepts used in the study of chaotic phenomena in nonlinear systems and has as its objective to summarize the current understanding of results from the theory of chaotic dynamical systems and to describe the original ideas underlying the study of deterministic chaos. The presentation relies on informal analysis, with abstract mathematical ideas visualized geometrically or by examples from physics. Hyperbolic dynamics, homoclinic trajectories and tangencies, wild hyperbolic sets, and different types of attractors which appear in dynamical systems are considered. The key aspects of ergodic theory are discussed, and the basic statistical properties of chaotic dynamical systems are described. The fundamental difference between stochastic dynamics and deterministic chaos is explained. The review concludes with an investigation of the possibility of studying complex systems on the basis of the analysis of registered signals, i.e. the generated time series. (reviews of topical problems)
Bick, Christian; Kolodziejski, Christoph; Timme, Marc
2014-09-01
Predictive feedback control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive feedback control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we study stalled chaos control, where the application of control is stalled to make use of the chaotic, uncontrolled dynamics, and introduce an adaptation paradigm to overcome this limitation and speed up convergence. This modified control scheme is not only capable of stabilizing more periodic orbits than the original predictive feedback control but also speeds up convergence for typical chaotic maps, as illustrated in both theory and application. The proposed adaptation scheme provides a way to tune parameters online, yielding a broadly applicable, fast chaos control that converges reliably, even for periodic orbits of large period.
Chaos detection and predictability
Gottwald, Georg; Laskar, Jacques
2016-01-01
Distinguishing chaoticity from regularity in deterministic dynamical systems and specifying the subspace of the phase space in which instabilities are expected to occur is of utmost importance in as disparate areas as astronomy, particle physics and climate dynamics. To address these issues there exists a plethora of methods for chaos detection and predictability. The most commonly employed technique for investigating chaotic dynamics, i.e. the computation of Lyapunov exponents, however, may suffer a number of problems and drawbacks, for example when applied to noisy experimental data. In the last two decades, several novel methods have been developed for the fast and reliable determination of the regular or chaotic nature of orbits, aimed at overcoming the shortcomings of more traditional techniques. This set of lecture notes and tutorial reviews serves as an introduction to and overview of modern chaos detection and predictability techniques for graduate students and non-specialists. The book cover...
Energy Technology Data Exchange (ETDEWEB)
Bick, Christian [Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany); Bernstein Center for Computational Neuroscience (BCCN), 37077 Göttingen (Germany); Institute for Mathematics, Georg–August–Universität Göttingen, 37073 Göttingen (Germany); Kolodziejski, Christoph [Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany); III. Physical Institute—Biophysics, Georg–August–Universität Göttingen, 37077 Göttingen (Germany); Timme, Marc [Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany); Institute for Nonlinear Dynamics, Georg–August–Universität Göttingen, 37077 Göttingen (Germany)
2014-09-01
Predictive feedback control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive feedback control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we study stalled chaos control, where the application of control is stalled to make use of the chaotic, uncontrolled dynamics, and introduce an adaptation paradigm to overcome this limitation and speed up convergence. This modified control scheme is not only capable of stabilizing more periodic orbits than the original predictive feedback control but also speeds up convergence for typical chaotic maps, as illustrated in both theory and application. The proposed adaptation scheme provides a way to tune parameters online, yielding a broadly applicable, fast chaos control that converges reliably, even for periodic orbits of large period.
Control of complex dynamics and chaos in distributed parameter systems
Energy Technology Data Exchange (ETDEWEB)
Chakravarti, S.; Marek, M.; Ray, W.H. [Univ. of Wisconsin, Madison, WI (United States)
1995-12-31
This paper discusses a methodology for controlling complex dynamics and chaos in distributed parameter systems. The reaction-diffusion system with Brusselator kinetics, where the torus-doubling or quasi-periodic (two characteristic incommensurate frequencies) route to chaos exists in a defined range of parameter values, is used as an example. Poincare maps are used for characterization of quasi-periodic and chaotic attractors. The dominant modes or topos, which are inherent properties of the system, are identified by means of the Singular Value Decomposition. Tested modal feedback control schemas based on identified dominant spatial modes confirm the possibility of stabilization of simple quasi-periodic trajectories in the complex quasi-periodic or chaotic spatiotemporal patterns.
Czech Academy of Sciences Publication Activity Database
Beran, Zdeněk; Čelikovský, Sergej
2013-01-01
Roč. 23, č. 5 (2013), 1350084-1-1350084-9 ISSN 0218-1274 R&D Projects: GA ČR GA13-20433S Institutional support: RVO:67985556 Keywords : Hyperspace * chaos * shadowing * Bernoulli shift Subject RIV: BC - Control Systems Theory Impact factor: 1.017, year: 2013 http://library.utia.cas.cz/separaty/2013/TR/beran-0392926.pdf
2005-01-01
8 September 2005 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows outcrops of light-toned, sedimentary rock among darker-toned mesas in Aram Chaos. Dark, windblown megaripples -- large ripples -- are also present at this location. Location near: 3.0oN, 21.6oW Image width: width: 3 km (1.9 mi) Illumination from: lower left Season: Northern Autumn
Intermittent search strategies
Bénichou, O.; Loverdo, C.; Moreau, M.; Voituriez, R.
2011-01-01
This review examines intermittent target search strategies, which combine phases of slow motion, allowing the searcher to detect the target, and phases of fast motion during which targets cannot be detected. It is first shown that intermittent search strategies are actually widely observed at various scales. At the macroscopic scale, this is, for example, the case of animals looking for food; at the microscopic scale, intermittent transport patterns are involved in a reaction pathway of DNA-binding proteins as well as in intracellular transport. Second, generic stochastic models are introduced, which show that intermittent strategies are efficient strategies that enable the minimization of search time. This suggests that the intrinsic efficiency of intermittent search strategies could justify their frequent observation in nature. Last, beyond these modeling aspects, it is proposed that intermittent strategies could also be used in a broader context to design and accelerate search processes.
Earnshow, R; Jones, H
1991-01-01
This volume is based upon the presentations made at an international conference in London on the subject of 'Fractals and Chaos'. The objective of the conference was to bring together some of the leading practitioners and exponents in the overlapping fields of fractal geometry and chaos theory, with a view to exploring some of the relationships between the two domains. Based on this initial conference and subsequent exchanges between the editors and the authors, revised and updated papers were produced. These papers are contained in the present volume. We thank all those who contributed to this effort by way of planning and organisation, and also all those who helped in the production of this volume. In particular, we wish to express our appreciation to Gerhard Rossbach, Computer Science Editor, Craig Van Dyck, Production Director, and Nancy A. Rogers, who did the typesetting. A. J. Crilly R. A. Earnshaw H. Jones 1 March 1990 Introduction Fractals and Chaos The word 'fractal' was coined by Benoit Mandelbrot i...
Ruette, Sylvie
2017-01-01
The aim of this book is to survey the relations between the various kinds of chaos and related notions for continuous interval maps from a topological point of view. The papers on this topic are numerous and widely scattered in the literature; some of them are little known, difficult to find, or originally published in Russian, Ukrainian, or Chinese. Dynamical systems given by the iteration of a continuous map on an interval have been broadly studied because they are simple but nevertheless exhibit complex behaviors. They also allow numerical simulations, which enabled the discovery of some chaotic phenomena. Moreover, the "most interesting" part of some higher-dimensional systems can be of lower dimension, which allows, in some cases, boiling it down to systems in dimension one. Some of the more recent developments such as distributional chaos, the relation between entropy and Li-Yorke chaos, sequence entropy, and maps with infinitely many branches are presented in book form for the first time. The author gi...
Kalantari, Bahman
Polynomiography is the algorithmic visualization of iterative systems for computing roots of a complex polynomial. It is well known that iterations of a rational function in the complex plane result in chaotic behavior near its Julia set. In one scheme of computing polynomiography for a given polynomial p(z), we select an individual member from the Basic Family, an infinite fundamental family of rational iteration functions that in particular include Newton's. Polynomiography is an excellent means for observing, understanding, and comparing chaotic behavior for variety of iterative systems. Other iterative schemes in polynomiography are possible and result in chaotic behavior of different kinds. In another scheme, the Basic Family is collectively applied to p(z) and the iterates for any seed in the Voronoi cell of a root converge to that root. Polynomiography reveals chaotic behavior of another kind near the boundary of the Voronoi diagram of the roots. We also describe a novel Newton-Ellipsoid iterative system with its own chaos and exhibit images demonstrating polynomiographies of chaotic behavior of different kinds. Finally, we consider chaos for the more general case of polynomiography of complex analytic functions. On the one hand polynomiography is a powerful medium capable of demonstrating chaos in different forms, it is educationally instructive to students and researchers, also it gives rise to numerous research problems. On the other hand, it is a medium resulting in images with enormous aesthetic appeal to general audiences.
International Nuclear Information System (INIS)
Muñoz, L; Fernández-Ramírez, C; Relaño, A; Retamosa, J
2012-01-01
In the last decade quantum chaos has become a well established discipline with outreach to different fields, from condensed-matter to nuclear physics. The most important signature of quantum chaos is the statistical analysis of the energy spectrum, which distinguishes between systems with integrable and chaotic classical analogues. In recent years, spectral statistical techniques inherited from quantum chaos have been applied successfully to the baryon spectrum revealing its likely chaotic behaviour even at the lowest energies. However, the theoretical spectra present a behaviour closer to the statistics of integrable systems which makes theory and experiment statistically incompatible. The usual statement of missing resonances in the experimental spectrum when compared to the theoretical ones cannot account for the discrepancies. In this communication we report an improved analysis of the baryon spectrum, taking into account the low statistics and the error bars associated with each resonance. Our findings give a major support to the previous conclusions. Besides, analogue analyses are performed in the experimental meson spectrum, with comparison to theoretical models.
Breakdown of universality in transitions to spatiotemporal chaos
DEFF Research Database (Denmark)
Bohr, Tomas; Hecke, Martin van; Mikkelsen, René
2001-01-01
We show that the transition from laminar to active behavior in extended chaotic systems can vary from a continuous transition in the universality class of directed percolation with infinitely many absorbing states to what appears as a first-order transition. The latter occurs when finite lifetime...
Chaos for cardiac arrhythmias through a one-dimensional modulation equation for alternans
Dai, Shu; Schaeffer, David G.
2010-01-01
Instabilities in cardiac dynamics have been widely investigated in recent years. One facet of this work has studied chaotic behavior, especially possible correlations with fatal arrhythmias. Previously chaotic behavior was observed in various models, specifically in the breakup of spiral and scroll waves. In this paper we study cardiac dynamics and find spatiotemporal chaotic behavior through the Echebarria–Karma modulation equation for alternans in one dimension. Although extreme parameter values are required to produce chaos in this model, it seems significant mathematically that chaos may occur by a different mechanism from previous observations. PMID:20590327
Universal signatures of quantum chaos
International Nuclear Information System (INIS)
Aurich, R.; Bolte, J.; Steiner, F.
1994-02-01
We discuss fingerprints of classical chaos in spectra of the corresponding bound quantum systems. A novel quantity to measure quantum chaos in spectra is proposed and a conjecture about its universal statistical behaviour is put forward. Numerical as well as theoretical evidence is provided in favour of the conjecture. (orig.)
Chaos Theory and Post Modernism
Snell, Joel
2009-01-01
Chaos theory is often associated with post modernism. However, one may make the point that both terms are misunderstood. The point of this article is to define both terms and indicate their relationship. Description: Chaos theory is associated with a definition of a theory dealing with variables (butterflies) that are not directly related to a…
Kaszás, Bálint; Feudel, Ulrike; Tél, Tamás
2016-12-01
We investigate the death and revival of chaos under the impact of a monotonous time-dependent forcing that changes its strength with a non-negligible rate. Starting on a chaotic attractor it is found that the complexity of the dynamics remains very pronounced even when the driving amplitude has decayed to rather small values. When after the death of chaos the strength of the forcing is increased again with the same rate of change, chaos is found to revive but with a different history. This leads to the appearance of a hysteresis in the complexity of the dynamics. To characterize these dynamics, the concept of snapshot attractors is used, and the corresponding ensemble approach proves to be superior to a single trajectory description, that turns out to be nonrepresentative. The death (revival) of chaos is manifested in a drop (jump) of the standard deviation of one of the phase-space coordinates of the ensemble; the details of this chaos-nonchaos transition depend on the ratio of the characteristic times of the amplitude change and of the internal dynamics. It is demonstrated that chaos cannot die out as long as underlying transient chaos is present in the parameter space. As a condition for a "quasistatically slow" switch-off, we derive an inequality which cannot be fulfilled in practice over extended parameter ranges where transient chaos is present. These observations need to be taken into account when discussing the implications of "climate change scenarios" in any nonlinear dynamical system.
1998-09-01
GARBO*, R. BALOCCHIt and S. CHILLEMI* *Istituto di Biofisica CNR, Via S. Lorenzo 26, 56127 Pisa, Italy tIstituto di Fisiologia Clinica CNR, Via...Publishing Company DIFFUSION PARAMETER CONTROL OF SPATIOTEMPORAL CHAOS RAUL MONTAGNE* Instituto de Fisica, Facultad de Ciencias & Facultad de Ingenieria
Chaos Criminology: A critical analysis
McCarthy, Adrienne L.
There has been a push since the early 1980's for a paradigm shift in criminology from a Newtonian-based ontology to one of quantum physics. Primarily this effort has taken the form of integrating Chaos Theory into Criminology into what this thesis calls 'Chaos Criminology'. However, with the melding of any two fields, terms and concepts need to be translated properly, which has yet to be done. In addition to proving a translation between fields, this thesis also uses a set of criteria to evaluate the effectiveness of the current use of Chaos Theory in Criminology. While the results of the theory evaluation reveal that the current Chaos Criminology work is severely lacking and in need of development, there is some promise in the development of Marx's dialectical materialism with Chaos Theory.
[Shedding light on chaos theory].
Chou, Shieu-Ming
2004-06-01
Gleick (1987) said that only three twentieth century scientific theories would be important enough to continue be of use in the twenty-first century: The Theory of Relativity, Quantum Theory, and Chaos Theory. Chaos Theory has become a craze which is being used to forge a new scientific system. It has also been extensively applied in a variety of professions. The purpose of this article is to introduce chaos theory and its nursing applications. Chaos is a sign of regular order. This is to say that chaos theory emphasizes the intrinsic potential for regular order within disordered phenomena. It is to be hoped that this article will inspire more nursing scientists to apply this concept to clinical, research, or administrative fields in our profession.
Intermittency in branching models
International Nuclear Information System (INIS)
Chiu, C.B.; Texas Univ., Austin; Hwa, R.C.; Oregon Univ., Eugene
1990-01-01
The intermittency properties of three branching models have been investigated. The factorial moments show power-law behavior as function of small rapidity width. The slopes and energy dependences reveal different characteristics of the models. The gluon model has the weakest intermittency. (orig.)
The design and research of anti-color-noise chaos M-ary communication system
Energy Technology Data Exchange (ETDEWEB)
Fu, Yongqing, E-mail: fuyongqing@hrbeu.edu.cn; Li, Xingyuan; Li, Yanan [College of information and Communication Engineering, Harbin Engineering University, Harbin 150001 (China); Zhang, Lin [College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001 (China)
2016-03-15
Previously a novel chaos M-ary digital communication method based on spatiotemporal chaos Hamilton oscillator has been proposed. Without chaos synchronization circumstance, it has performance improvement in bandwidth efficiency, transmission efficiency and anti-white-noise performance compared with traditional communication method. In this paper, the channel noise influence on chaotic modulation signals and the construction problem of anti-color-noise chaotic M-ary communication system are studied. The formula of zone partition demodulator’s boundary in additive white Gaussian noise is derived, besides, the problem about how to determine the boundary of zone partition demodulator in additive color noise is deeply studied; Then an approach on constructing anti-color-noise chaos M-ary communication system is proposed, in which a pre-distortion filter is added after the chaos baseband modulator in the transmitter and whitening filter is added before zone partition demodulator in the receiver. Finally, the chaos M-ary communication system based on Hamilton oscillator is constructed and simulated in different channel noise. The result shows that the proposed method in this paper can improve the anti-color-noise performance of the whole communication system compared with the former system, and it has better anti-fading and resisting disturbance performance than Quadrature Phase Shift Keying system.
The design and research of anti-color-noise chaos M-ary communication system
International Nuclear Information System (INIS)
Fu, Yongqing; Li, Xingyuan; Li, Yanan; Zhang, Lin
2016-01-01
Previously a novel chaos M-ary digital communication method based on spatiotemporal chaos Hamilton oscillator has been proposed. Without chaos synchronization circumstance, it has performance improvement in bandwidth efficiency, transmission efficiency and anti-white-noise performance compared with traditional communication method. In this paper, the channel noise influence on chaotic modulation signals and the construction problem of anti-color-noise chaotic M-ary communication system are studied. The formula of zone partition demodulator’s boundary in additive white Gaussian noise is derived, besides, the problem about how to determine the boundary of zone partition demodulator in additive color noise is deeply studied; Then an approach on constructing anti-color-noise chaos M-ary communication system is proposed, in which a pre-distortion filter is added after the chaos baseband modulator in the transmitter and whitening filter is added before zone partition demodulator in the receiver. Finally, the chaos M-ary communication system based on Hamilton oscillator is constructed and simulated in different channel noise. The result shows that the proposed method in this paper can improve the anti-color-noise performance of the whole communication system compared with the former system, and it has better anti-fading and resisting disturbance performance than Quadrature Phase Shift Keying system.
Breaking a chaos-noise-based secure communication scheme
Li, Shujun; Álvarez, Gonzalo; Chen, Guanrong; Mou, Xuanqin
2005-03-01
This paper studies the security of a secure communication scheme based on two discrete-time intermittently chaotic systems synchronized via a common random driving signal. Some security defects of the scheme are revealed: 1) The key space can be remarkably reduced; 2) the decryption is insensitive to the mismatch of the secret key; 3) the key-generation process is insecure against known/chosen-plaintext attacks. The first two defects mean that the scheme is not secure enough against brute-force attacks, and the third one means that an attacker can easily break the cryptosystem by approximately estimating the secret key once he has a chance to access a fragment of the generated keystream. Yet it remains to be clarified if intermittent chaos could be used for designing secure chaotic cryptosystems.
International Nuclear Information System (INIS)
Lin, Kevin K; Young, Lai-Sang
2008-01-01
Guided by a geometric understanding developed in earlier works of Wang and Young, we carry out numerical studies of shear-induced chaos in several parallel but different situations. The settings considered include periodic kicking of limit cycles, random kicks at Poisson times and continuous-time driving by white noise. The forcing of a quasi-periodic model describing two coupled oscillators is also investigated. In all cases, positive Lyapunov exponents are found in suitable parameter ranges when the forcing is suitably directed
Lin, Kevin K.; Young, Lai-Sang
2008-05-01
Guided by a geometric understanding developed in earlier works of Wang and Young, we carry out numerical studies of shear-induced chaos in several parallel but different situations. The settings considered include periodic kicking of limit cycles, random kicks at Poisson times and continuous-time driving by white noise. The forcing of a quasi-periodic model describing two coupled oscillators is also investigated. In all cases, positive Lyapunov exponents are found in suitable parameter ranges when the forcing is suitably directed.
2006-01-01
11 January 2006 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows light-toned, layered rock outcrops in Eos Chaos, located near the east end of the Valles Marineris trough system. The outcrops occur in the form of a distinct, circular butte (upper half of image) and a high slope (lower half of image). The rocks might be sedimentary rocks, similar to those found elsewhere exposed in the Valles Marineris system and the chaotic terrain to the east of the region. Location near: 12.9oS, 49.5oW Image width: 3 km (1.9 mi) Illumination from: lower left Season: Southern Summer
Intermittency inhibited by transport: An exactly solvable model
Zanette, Damián H.
1994-04-01
Transport is incorporated in a discrete-time stochastic model of a system undergoing autocatalytic reactions of the type A-->2A and A-->0, whose population field is known to exhibit spatiotemporal intermittency. The temporal evolution is exactly solved, and it is shown that if the transport process is strong enough, intermittency is inhibited. This inhibition is nonuniform, in the sense that, as transport is strengthened, low-order population moments are affected before the high-order ones. Numerical simulations are presented to support the analytical results.
Application of Chaos Theory to Engine Systems
Matsumoto, Kazuhiro; Diebner, Hans H.; Tsuda, Ichiro; Hosoi, Yukiharu
2008-01-01
We focus on the control issue for engine systems from the perspective of chaos theory, which is based on the fact that engine systems have a low-dimensional chaotic dynamics. Two approaches are discussed: controlling chaos and harnessing chaos, respectively. We apply Pyragas' chaos control method to an actual engine system. The experimental results show that the chaotic motion of an engine system may be stabilized to a periodic motion. Alternatively, harnessing chaos for engine systems is add...
Chaos in high-power high-frequency gyrotrons
International Nuclear Information System (INIS)
Airila, M.
2004-01-01
Gyrotron interaction is a complex nonlinear dynamical process, which may turn chaotic in certain circumstances. The emergence of chaos renders dynamical systems unpredictable and causes bandwidth broadening of signals. Such effects would jeopardize the prospect of advanced gyrotrons in fusion. Therefore, it is important to be aware of the possibility of chaos in gyrotrons. There are three different chaos scenarios closely related to the development of high-power gyrotrons: First, the onset of chaos in electron trajectories would lead to difficulties in the design and efficient operation of depressed potential collectors, which are used for efficiency enhancement. Second, the radio-frequency signal could turn chaotic, decreasing the output power and the spectral purity of the output signal. As a result, mode conversion, transmission, and absorption efficiencies would be reduced. Third, spatio-temporal chaos in the resonator field structure can set a limit for the use of large-diameter interaction cavities and high-order TE modes (large azimuthal index) allowing higher generated power. In this thesis, the issues above are addressed with numerical modeling. It is found that chaos in electron residual energies is practically absent in the parameter region corresponding to high efficiency. Accordingly, depressed collectors are a feasible solution also in advanced high-power gyrotrons. A new method is presented for straightforward numerical solution of the one-dimensional self-consistent time-dependent gyrotron equations, and the method is generalized to two dimensions. In 1D, a chart of gyrotron oscillations is calculated. It is shown that the regions of stationary oscillations, automodulation, and chaos have a complicated topology in the plane of generalized gyrotron variables. The threshold current for chaotic oscillations exceeds typical operating currents by a factor of ten. However, reflection of the output signal may significantly lower the threshold. 2D
Intermittent degradation and schizotypy
Directory of Open Access Journals (Sweden)
Matthew W. Roché
2015-06-01
Full Text Available Intermittent degradation refers to transient detrimental disruptions in task performance. This phenomenon has been repeatedly observed in the performance data of patients with schizophrenia. Whether intermittent degradation is a feature of the liability for schizophrenia (i.e., schizotypy is an open question. Further, the specificity of intermittent degradation to schizotypy has yet to be investigated. To address these questions, 92 undergraduate participants completed a battery of self-report questionnaires assessing schizotypy and psychological state variables (e.g., anxiety, depression, and their reaction times were recorded as they did so. Intermittent degradation was defined as the number of times a subject’s reaction time for questionnaire items met or exceeded three standard deviations from his or her mean reaction time after controlling for each item’s information processing load. Intermittent degradation scores were correlated with questionnaire scores. Our results indicate that intermittent degradation is associated with total scores on measures of positive and disorganized schizotypy, but unrelated to total scores on measures of negative schizotypy and psychological state variables. Intermittent degradation is interpreted as potentially derivative of schizotypy and a candidate endophenotypic marker worthy of continued research.
Quantum chaos: entropy signatures
International Nuclear Information System (INIS)
Miller, P.A.; Sarkar, S.; Zarum, R.
1998-01-01
A definition of quantum chaos is given in terms of entropy production rates for a quantum system coupled weakly to a reservoir. This allows the treatment of classical and quantum chaos on the same footing. In the quantum theory the entropy considered is the von Neumann entropy and in classical systems it is the Gibbs entropy. The rate of change of the coarse-grained Gibbs entropy of the classical system with time is given by the Kolmogorov-Sinai (KS) entropy. The relation between KS entropy and the rate of change of von Neumann entropy is investigated for the kicked rotator. For a system which is classically chaotic there is a linear relationship between these two entropies. Moreover it is possible to construct contour plots for the local KS entropy and compare it with the corresponding plots for the rate of change of von Neumann entropy. The quantitative and qualitative similarities of these plots are discussed for the standard map (kicked rotor) and the generalised cat maps. (author)
Quantum mechanical suppression of chaos
International Nuclear Information System (INIS)
Bluemel, R.; Smilansky, U.
1990-01-01
The relation between determinism and predictability is the central issue in the study of 'deterministic chaos'. Much knowledge has been accumulated in the past 10 years about the chaotic dynamics of macroscopic (classical) systems. The implications of chaos in the microscopic quantum world is examined, in other words, how to reconcile the correspondence principle with the inherent uncertainties which reflect the wave nature of quantum dynamics. Recent atomic physics experiments demonstrate clearly that chaos is relevant to the microscopic world. In particular, such experiments emphasise the urgent need to clarify the genuine quantum mechanism which imposes severe limitations on quantum dynamics, and renders it so very different from its classical counterpart. (author)
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
A universal parameterization of chaos in various beam-wave interactions
International Nuclear Information System (INIS)
Lee, Jae Koo; Lee, Hae June; Hur, Min Sup; Bae, InDeog; Yang, Yi
1998-01-01
The comprehensive parameter space of sell-oscillation and its period-doubling route to chaos are shown for a bounded collisionless beam-plasma system. In this parameterization, it is helpful to use a potentially universal parameter in close analogy with free-electron-laser chaos. A common parameter, which is related to the velocity slippage and the ratio of bounce to oscillation frequencies, is shown to have similar significance for different physical systems. This single parameter replaces the dependences on many input parameters, thus suitable for a simplifying and diagnostic measure of nonlinear dynamical and chaotic phenomena for various systems of particle-wave interactions. The results of independent kinetic-simulations verify those of nonlinear fluid-simulations. Other standard routes to chaos via intermittent or quasiperiodic oscillations are also shown for the undriven plasma systems. Some correlation of linear characteristics to nonlinear phenomena was noted. (author)
Topological chaos, braiding and bifurcation of almost-cyclic sets.
Grover, Piyush; Ross, Shane D; Stremler, Mark A; Kumar, Pankaj
2012-12-01
In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in the system through application of the Thurston-Nielsen classification theorem (TNCT). We expand upon earlier work that introduced the application of the TNCT to braiding of almost-cyclic sets, which are individual components of almost-invariant sets [Stremler et al., "Topological chaos and periodic braiding of almost-cyclic sets," Phys. Rev. Lett. 106, 114101 (2011)]. In this context, almost-cyclic sets are periodic regions in the flow with high local residence time that act as stirrers or "ghost rods" around which the surrounding fluid appears to be stretched and folded. In the present work, we discuss the bifurcation of the almost-cyclic sets as a system parameter is varied, which results in a sequence of topologically distinct braids. We show that, for Stokes' flow in a lid-driven cavity, these various braids give good lower bounds on the topological entropy over the respective parameter regimes in which they exist. We make the case that a topological analysis based on spatiotemporal braiding of almost-cyclic sets can be used for analyzing chaos in fluid flows. Hence, we further develop a connection between set-oriented statistical methods and topological methods, which promises to be an important analysis tool in the study of complex systems.
Intermittent Explosive Disorder
Directory of Open Access Journals (Sweden)
Lut Tamam
2011-09-01
Full Text Available Intermittent explosive disorder is an impulse control disorder characterized by the occurrence of discrete episodes of failure to resist aggressive impulses that result in violent assault or destruction of property. Though the prevalence intermittent explosive disorder has been reported to be relatively rare in frontier studies on the field, it is now common opinion that intermittent explosive disorder is far more common than previously thought especially in clinical psychiatry settings. Etiological studies displayed the role of both psychosocial factors like childhood traumas and biological factors like dysfunctional neurotransmitter systems and genetics. In differential diagnosis of the disorder, disorders involving agression as a symptom such as alcohol and drug intoxication, antisocial and borderline personality disorders, personality changes due to general medical conditions and behavioral disorder should be considered. A combination of pharmacological and psychotherapeutic approaches are suggested in the treatment of the disorder. This article briefly reviews the historical background, diagnostic criteria, epidemiology, etiology and treatment of intermittent explosive disorder.
Intermittent heating of buildings
Energy Technology Data Exchange (ETDEWEB)
Kohonen, K
1983-02-01
Conditions for intermittent heating of buildings are considered both theoretically and experimentally. Thermal behaviour of buildings adn rooms in intermittent heating is simulated by a program based on the convective heat balance equation and by simplified RC-models. The preheat times and the heating energy savings compared with continuous heating are presented for typical lightweight, mediumweight and heavyweight classroom and office modules. Formulaes for estimating the oversizing of the radiator network, the maximum heat output of heat exchangers in district heating and the efficiency of heating boilers in intermittent heating are presented. The preheat times and heating energy savings with different heating control systems are determined also experimentally in eight existing buildings. In addition some principles for the planning and application of intermittent heating systems are suggested.
Recent development of chaos theory in topological dynamics
Li, Jian; Ye, Xiangdong
2015-01-01
We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships.
Chaos and reliability in balanced spiking networks with temporal drive.
Lajoie, Guillaume; Lin, Kevin K; Shea-Brown, Eric
2013-05-01
Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: If the same signal is presented many times with the network in different initial states, will the system entrain to the signal in a repeatable way? Reliability is of particular interest in neuroscience, where large, complex networks of excitatory and inhibitory cells are ubiquitous. These networks are known to autonomously produce strongly chaotic dynamics-an obvious threat to reliability. Here, we show that such chaos persists in the presence of weak and strong stimuli, but that even in the presence of chaos, intermittent periods of highly reliable spiking often coexist with unreliable activity. We elucidate the local dynamical mechanisms involved in this intermittent reliability, and investigate the relationship between this phenomenon and certain time-dependent attractors arising from the dynamics. A conclusion is that chaotic dynamics do not have to be an obstacle to precise spike responses, a fact with implications for signal coding in large networks.
Optimal intermittent search strategies
International Nuclear Information System (INIS)
Rojo, F; Budde, C E; Wio, H S
2009-01-01
We study the search kinetics of a single fixed target by a set of searchers performing an intermittent random walk, jumping between different internal states. Exploiting concepts of multi-state and continuous-time random walks we have calculated the survival probability of a target up to time t, and have 'optimized' (minimized) it with regard to the transition probability among internal states. Our model shows that intermittent strategies always improve target detection, even for simple diffusion states of motion
Fu, Yongqing; Li, Xingyuan; Li, Yanan; Yang, Wei; Song, Hailiang
2013-03-01
Chaotic communication has aroused general interests in recent years, but its communication effect is not ideal with the restriction of chaos synchronization. In this paper a new chaos M-ary digital modulation and demodulation method is proposed. By using region controllable characteristics of spatiotemporal chaos Hamilton map in phase plane and chaos unique characteristic, which is sensitive to initial value, zone mapping method is proposed. It establishes the map relationship between M-ary digital information and the region of Hamilton map phase plane, thus the M-ary information chaos modulation is realized. In addition, zone partition demodulation method is proposed based on the structure characteristic of Hamilton modulated information, which separates M-ary information from phase trajectory of chaotic Hamilton map, and the theory analysis of zone partition demodulator's boundary range is given. Finally, the communication system based on the two methods is constructed on the personal computer. The simulation shows that in high speed transmission communications and with no chaos synchronization circumstance, the proposed chaotic M-ary modulation and demodulation method has outperformed some conventional M-ary modulation methods, such as quadrature phase shift keying and M-ary pulse amplitude modulation in bit error rate. Besides, it has performance improvement in bandwidth efficiency, transmission efficiency and anti-noise performance, and the system complexity is low and chaos signal is easy to generate.
Ancient and Current Chaos Theories
Directory of Open Access Journals (Sweden)
Güngör Gündüz
2006-07-01
Full Text Available Chaos theories developed in the last three decades have made very important contributions to our understanding of dynamical systems and natural phenomena. The meaning of chaos in the current theories and in the past is somewhat different from each other. In this work, the properties of dynamical systems and the evolution of chaotic systems were discussed in terms of the views of ancient philosophers. The meaning of chaos in Anaximenes’ philosophy and its role in the Ancient natural philosophy has been discussed in relation to other natural philosophers such as of Anaximander, Parmenides, Heraclitus, Empedocles, Leucippus (i.e. atomists and Aristotle. In addition, the fundamental concepts of statistical mechanics and the current chaos theories were discussed in relation to the views in Ancient natural philosophy. The roots of the scientific concepts such as randomness, autocatalysis, nonlinear growth, information, pattern, etc. in the Ancient natural philosophy were investigated.
Quantum Instantons and Quantum Chaos
Jirari, H.; Kröger, H.; Luo, X. Q.; Moriarty, K. J. M.; Rubin, S. G.
1999-01-01
Based on a closed form expression for the path integral of quantum transition amplitudes, we suggest rigorous definitions of both, quantum instantons and quantum chaos. As an example we compute the quantum instanton of the double well potential.
Cryptography with chaos and shadowing
International Nuclear Information System (INIS)
Smaoui, Nejib; Kanso, Ali
2009-01-01
In this paper, we present a novel approach to encrypt a message (a text composed by some alphabets) using chaos and shadowing. First, we generate a numerical chaotic orbit based on the logistic map, and use the shadowing algorithm of Smaoui and Kostelich [Smaoui N, Kostelich E. Using chaos to shadow the quadratic map for all time. Int J Comput Math 1998;70:117-29] to show that there exists a finite number of true orbits that shadow the numerical orbit. Then, the finite number of maps generated is used in Baptista's algorithm [Baptista MS. Cryptography with chaos. Phys Lett A 1998;240:50-4] to encrypt each character of the message. It is shown that the use of chaos and shadowing in the encryption process enhances the security level.
Chaos and complexity by design
Energy Technology Data Exchange (ETDEWEB)
Roberts, Daniel A. [Center for Theoretical Physics and Department of Physics,Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Yoshida, Beni [Perimeter Institute for Theoretical Physics,Waterloo, Ontario N2L 2Y5 (Canada)
2017-04-20
We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the “frame potential,” which is minimized by unitary k-designs and measures the 2-norm distance between the Haar random unitary ensemble and another ensemble. A natural probe of quantum chaos is out-of-time-order (OTO) four-point correlation functions. We show that the norm squared of a generalization of out-of-time-order 2k-point correlators is proportional to the kth frame potential, providing a quantitative connection between chaos and pseudorandomness. Additionally, we prove that these 2k-point correlators for Pauli operators completely determine the k-fold channel of an ensemble of unitary operators. Finally, we use a counting argument to obtain a lower bound on the quantum circuit complexity in terms of the frame potential. This provides a direct link between chaos, complexity, and randomness.
Chaos and complexity by design
International Nuclear Information System (INIS)
Roberts, Daniel A.; Yoshida, Beni
2017-01-01
We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the “frame potential,” which is minimized by unitary k-designs and measures the 2-norm distance between the Haar random unitary ensemble and another ensemble. A natural probe of quantum chaos is out-of-time-order (OTO) four-point correlation functions. We show that the norm squared of a generalization of out-of-time-order 2k-point correlators is proportional to the kth frame potential, providing a quantitative connection between chaos and pseudorandomness. Additionally, we prove that these 2k-point correlators for Pauli operators completely determine the k-fold channel of an ensemble of unitary operators. Finally, we use a counting argument to obtain a lower bound on the quantum circuit complexity in terms of the frame potential. This provides a direct link between chaos, complexity, and randomness.
Experimental Induction of Genome Chaos.
Ye, Christine J; Liu, Guo; Heng, Henry H
2018-01-01
Genome chaos, or karyotype chaos, represents a powerful survival strategy for somatic cells under high levels of stress/selection. Since the genome context, not the gene content, encodes the genomic blueprint of the cell, stress-induced rapid and massive reorganization of genome topology functions as a very important mechanism for genome (karyotype) evolution. In recent years, the phenomenon of genome chaos has been confirmed by various sequencing efforts, and many different terms have been coined to describe different subtypes of the chaotic genome including "chromothripsis," "chromoplexy," and "structural mutations." To advance this exciting field, we need an effective experimental system to induce and characterize the karyotype reorganization process. In this chapter, an experimental protocol to induce chaotic genomes is described, following a brief discussion of the mechanism and implication of genome chaos in cancer evolution.
Encounters with chaos and fractals
Gulick, Denny
2012-01-01
Periodic Points Iterates of Functions Fixed Points Periodic Points Families of Functions The Quadratic Family Bifurcations Period-3 Points The Schwarzian Derivative One-Dimensional Chaos Chaos Transitivity and Strong Chaos Conjugacy Cantor Sets Two-Dimensional Chaos Review of Matrices Dynamics of Linear FunctionsNonlinear Maps The Hénon Map The Horseshoe Map Systems of Differential Equations Review of Systems of Differential Equations Almost Linearity The Pendulum The Lorenz System Introduction to Fractals Self-Similarity The Sierpiński Gasket and Other "Monsters"Space-Filling Curves Similarity and Capacity DimensionsLyapunov Dimension Calculating Fractal Dimensions of Objects Creating Fractals Sets Metric Spaces The Hausdorff Metric Contractions and Affine Functions Iterated Function SystemsAlgorithms for Drawing Fractals Complex Fractals: Julia Sets and the Mandelbrot Set Complex Numbers and Functions Julia Sets The Mandelbrot Set Computer Programs Answers to Selected Exercises References Index.
Cryptography with chaos and shadowing
Energy Technology Data Exchange (ETDEWEB)
Smaoui, Nejib [Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)], E-mail: nsmaoui64@yahoo.com; Kanso, Ali [Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)], E-mail: akanso@hotmail.com
2009-11-30
In this paper, we present a novel approach to encrypt a message (a text composed by some alphabets) using chaos and shadowing. First, we generate a numerical chaotic orbit based on the logistic map, and use the shadowing algorithm of Smaoui and Kostelich [Smaoui N, Kostelich E. Using chaos to shadow the quadratic map for all time. Int J Comput Math 1998;70:117-29] to show that there exists a finite number of true orbits that shadow the numerical orbit. Then, the finite number of maps generated is used in Baptista's algorithm [Baptista MS. Cryptography with chaos. Phys Lett A 1998;240:50-4] to encrypt each character of the message. It is shown that the use of chaos and shadowing in the encryption process enhances the security level.
Optical digital chaos cryptography
Arenas-Pingarrón, Álvaro; González-Marcos, Ana P.; Rivas-Moscoso, José M.; Martín-Pereda, José A.
2007-10-01
In this work we present a new way to mask the data in a one-user communication system when direct sequence - code division multiple access (DS-CDMA) techniques are used. The code is generated by a digital chaotic generator, originally proposed by us and previously reported for a chaos cryptographic system. It is demonstrated that if the user's data signal is encoded with a bipolar phase-shift keying (BPSK) technique, usual in DS-CDMA, it can be easily recovered from a time-frequency domain representation. To avoid this situation, a new system is presented in which a previous dispersive stage is applied to the data signal. A time-frequency domain analysis is performed, and the devices required at the transmitter and receiver end, both user-independent, are presented for the optical domain.
DEFF Research Database (Denmark)
Lindberg, Erik
1996-01-01
Can we believe in the results of our circuit simulators ? Is it possible to distinguish between results due to numerical chaos and resultsdue to the eventual chaotic nature of our modelsof physical systems ?. Three experiments with SPICE are presented: (1) A "stable" active RCcircuit with poles...... in the right half plane. (2) "Chaotic" steady state behaviour of a non-chaotic dc power supply. (3) Analysis of a Colpitts oscillator with chaotic behaviour. In order to obtain reliable results from the SPICE simulators the users of these programs need insight not only in the use of the programs but also...... in the models of the circuits to be analyzed. If trimmed properly SPICE normally gives the correct result....
Ruelle, David
1991-01-01
Comment expliquer le hasard ? Peut-on rendre raison de l'irraisonnable ? Ce livre, où il est question des jeux de dés, des loteries, des billards, des attracteurs étranges, de l'astrologie et des oracles, du temps qu'il fera, du libre arbitre, de la mécanique quantique, de l'écoulement des fluides, du théorème de Gödel et des limites de l'entendement humain, expose les fondements et les conséquences de la théorie du chaos. David Ruelle est membre de l'Académie des sciences et professeur de physique théorique à l'Institut des hautes études scientifiques de Bures-sur-Yvette.
Multiparticle correlations and intermittency in high energy collisions
International Nuclear Information System (INIS)
Bozek, P.
1992-01-01
The analysis of the intermittency signal observed in high energy experiments is presented using multiparticle distributions and correlation functions. The effect of the dimensional projection of the multiparticle distributions on one or two-dimensional subspace is discussed. The structure of the multiparticle cumulants is analyzed for the DELPHI e + e - annihilation data. The model of spatiotemporal intermittency is discussed in details and is shown to reproduce qualitatively the dependence of the intermittency strength on the target and projectile nuclei. A 1-dimensional (1D) cellular-automaton and a 1D forest-fire model is studied. On the example of the noncritical 1D Ising model the difficulties of the scaled factorial moment (SFM) method in extracting genuine scaling behaviour is illustrated. All these studies could serve as tools to test the sensibility of the SFM method as used in the analysis of the high energy production. (K.A.) 122 refs.; 38 figs.; 3 tabs
Multiparticle correlations and intermittency in high energy collisions
Bozek, P
1992-01-01
In this work the analysis of the intermittency signal observed in high energy experi- ments is done using multiparticle distributions and correlation functions. The effect of the dimensional projection of the multiparticle distributions on one or two-dimensional subspace is discussed. The structure of the multiparticle cumulants is analyzed for the DELPHI e + e~ annihilation data. The language of the self-similar distribution func- tions, which is used in this work, is shown to be largely equivalent to the well known a-model. In the case of the ultrarelativistic nuclear collisions, where the Monte-Carlo simulations fail to reproduce the data, we argue that the observed intermittency pattern is a signal of some nonlinear effect beyond the simple superposition of nucleon-nucleon collisions. The model of spatiotemporal intermittency is discussed in details and is shown to reproduce qualitatively the dependence of t...
Bifurcation, pattern formation and chaos in combustion
International Nuclear Information System (INIS)
Bayliss, A.; Matkowsky, B.J.
1991-01-01
In this paper problems in gaseous combustion and in gasless condensed phase combustion are studied both analytically and numerically. In gaseous combustion we consider the problem of a flame stabilized on a line source of fuel. The authors find both stationary and pulsating axisymmetric solutions as well as stationary and pulsating cellular solutions. The pulsating cellular solutions take the form of either traveling waves or standing waves. Transitions between these patterns occur as parameters related to the curvature of the flame front and the Lewis number are varied. In gasless condensed phase combustion both planar and nonplanar problems are studied. For planar condensed phase combustion we consider two models: accounts for melting and does not. Both models are shown to exhibit a transition from uniformly to pulsating propagating combustion when a parameter related to the activation energy is increased. Upon further increasing this parameter both models undergo a transition to chaos: by intermittency and by a period doubling sequence. In nonplanar condensed phase combustion the nonlinear development of a branch of standing wave solutions is studied and is shown to lead to relaxation oscillations and subsequently to a transition to quasi-periodicity
2012 Symposium on Chaos, Complexity and Leadership
Erçetin, Şefika
2014-01-01
These proceedings from the 2012 symposium on "Chaos, complexity and leadership" reflect current research results from all branches of Chaos, Complex Systems and their applications in Management. Included are the diverse results in the fields of applied nonlinear methods, modeling of data and simulations, as well as theoretical achievements of Chaos and Complex Systems. Also highlighted are Leadership and Management applications of Chaos and Complexity Theory.
Quantum chaos: Statistical relaxation in discrete spectrum
International Nuclear Information System (INIS)
Chirikov, B.V.
1991-01-01
The controversial phenomenon of quantum chaos is discussed using the quantized standard map, or the kicked rotator, as a simple model. The relation to the classical dynamical chaos is tracked down on the basis of the correspondence principle. Various mechanisms of the quantum suppression of classical chaos are considered with an application to the excitation and ionization of Rydberg atoms in a microwave field. Several definitions of the quantum chaos are discussed. (author). 27 refs
Optimal intermittent search strategies
Energy Technology Data Exchange (ETDEWEB)
Rojo, F; Budde, C E [FaMAF, Universidad Nacional de Cordoba, Ciudad Universitaria, X5000HUA Cordoba (Argentina); Wio, H S [Instituto de Fisica de Cantabria, Universidad de Cantabria and CSIC E-39005 Santander (Spain)
2009-03-27
We study the search kinetics of a single fixed target by a set of searchers performing an intermittent random walk, jumping between different internal states. Exploiting concepts of multi-state and continuous-time random walks we have calculated the survival probability of a target up to time t, and have 'optimized' (minimized) it with regard to the transition probability among internal states. Our model shows that intermittent strategies always improve target detection, even for simple diffusion states of motion.
Intermittency and random matrices
Sokoloff, Dmitry; Illarionov, E. A.
2015-08-01
A spectacular phenomenon of intermittency, i.e. a progressive growth of higher statistical moments of a physical field excited by an instability in a random medium, attracted the attention of Zeldovich in the last years of his life. At that time, the mathematical aspects underlying the physical description of this phenomenon were still under development and relations between various findings in the field remained obscure. Contemporary results from the theory of the product of independent random matrices (the Furstenberg theory) allowed the elaboration of the phenomenon of intermittency in a systematic way. We consider applications of the Furstenberg theory to some problems in cosmology and dynamo theory.
Decoherence, determinism and chaos
International Nuclear Information System (INIS)
Noyes, H.P.
1994-01-01
The author claims by now to have made his case that modern work on fractals and chaos theory has already removed the presumption that classical physics is 'deterministic'. Further, he claims that in so far as classical relativistic field theory (i.e. electromagnetism and gravitation) are scale invariant, they are self-consistent only if the idea of 'test-particle' is introduced from outside the theory. Einstein spent the last years of his life trying to use singularities in the metric as 'particles' or to get them out of the non-linearities in a grand unified theory -- in vain. So classical physics in this sense cannot be the fundamental theory. However, the author claims to have shown that if he introduces a 'scale invariance bounded from below' by measurement accuracy, then Tanimura's generalization of the Feynman proof as reconstructed by Dyson allows him to make a consistent classical theory for decoherent sources sinks. Restoring coherence to classical physics via relativistic action-at-a distance is left as a task for the future. Relativistic quantum mechanics, properly reconstructed from a finite and discrete basis, emerges in much better shape. The concept of 'particles has to be replaced by NO-YES particulate events, and particle-antiparticle pair creation and annihilation properly formulated
Quasiperiodic transition to chaos in a plasma
International Nuclear Information System (INIS)
Weixing, D.; Huang Wei; Wang Xiaodong; Yu, C.X.
1993-01-01
The quasiperiodic transition to chaos in an undriven discharge plasma has been investigated. Results from the power spectrum and Lyapunov exponents quantitatively confirm the transition to chaos through quasiperiodicity. A low-dimension strange attractor has been found for this kind of plasma chaos
Further discussion on chaos in duopoly games
International Nuclear Information System (INIS)
Lu, Tianxiu; Zhu, Peiyong
2013-01-01
In this paper, we study Li–Yorke chaos, distributional chaos in a sequence, Li–Yorke sensitivity, sensitivity and distributional chaos of two-dimensional dynamical system of the form Φ(x, y) = (f(y), g(x))
Puzzles in studies of quantum chaos
International Nuclear Information System (INIS)
Xu Gongou
1994-01-01
Puzzles in studies of quantum chaos are discussed. From the view of global properties of quantum states, it is clarified that quantum chaos originates from the break-down of invariant properties of quantum canonical transformations. There exist precise correspondences between quantum and classical chaos
Towards chaos criterion in quantum field theory
Kuvshinov, V. I.; Kuzmin, A. V.
2002-01-01
Chaos criterion for quantum field theory is proposed. Its correspondence with classical chaos criterion in semi-classical regime is shown. It is demonstrated for real scalar field that proposed chaos criterion can be used to investigate stability of classical solutions of field equations.
Quantum chaos: statistical relaxation in discrete spectrum
International Nuclear Information System (INIS)
Chirikov, B.V.
1990-01-01
The controversial phenomenon of quantum chaos is discussed using the quantized standard map, or the kicked rotator, as a simple model. The relation to the classical dynamical chaos is tracked down on the basis of the correspondence principle. Several definitions of the quantum chaos are discussed. 27 refs
Hastily Formed Networks-Chaos to Recovery
2015-09-01
NETWORKS— CHAOS TO RECOVERY by Mark Arezzi September 2015 Thesis Co-Advisors: Douglas J. MacKinnon Brian Steckler THIS PAGE......systems to self-organize, adapt, and exert control over the chaos . Defining the role of communications requires an understanding of complexity, chaos
Chaos in the atomic and subatomic world
International Nuclear Information System (INIS)
Nussenzveig, H.M.
1992-01-01
This work discusses the possibility of the existence of chaos in the quantum level. In the macroscopic scale, chaos can be explained by the use of classical mechanics. The problem is to know whether there is any manifestation of chaos in the evolution of a system following the quantum mechanical laws. (A.C.A.S.)
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.
Influence of solitons in the initial state on chaos in the driven damped sine-Gordon system
Energy Technology Data Exchange (ETDEWEB)
Bishop, A R; Fesser, K; Lomdahl, P S; Trullinger, S E
1983-01-01
The appearance of chaos in the a.c. driven, damped sine-Gordon equation is studied numerically. Several transitions from periodic to chaotic behavior are investigated in detail for flat initial conditions. Spatial structures (breather, kink) in the initial conditions smooth out many of these transitions and give rise to an interesting symbiosis of time and spatial intermittency. This symbiosis appears to be due to the competition between the background tendency towards chaos and the system's preference to maintain a spatial pattern. The way that this competition is relieved is also found to depend very strongly on symmetry in the initial conditions.
Spread-spectrum communication using binary spatiotemporal chaotic codes
International Nuclear Information System (INIS)
Wang Xingang; Zhan Meng; Gong Xiaofeng; Lai, C.H.; Lai, Y.-C.
2005-01-01
We propose a scheme to generate binary code for baseband spread-spectrum communication by using a chain of coupled chaotic maps. We compare the performances of this type of spatiotemporal chaotic code with those of a conventional code used frequently in digital communication, the Gold code, and demonstrate that our code is comparable or even superior to the Gold code in several key aspects: security, bit error rate, code generation speed, and the number of possible code sequences. As the field of communicating with chaos faces doubts in terms of performance comparison with conventional digital communication schemes, our work gives a clear message that communicating with chaos can be advantageous and it deserves further attention from the nonlinear science community
International Nuclear Information System (INIS)
Angius, S.; Bisegni, C.; Ciuffetti, P.
2016-01-01
The paper is aimed to present the !CHAOS open source project aimed to develop a prototype of a national private Cloud Computing infrastructure, devoted to accelerator control systems and large experiments of High Energy Physics (HEP). The !CHAOS project has been financed by MIUR (Italian Ministry of Research and Education) and aims to develop a new concept of control system and data acquisition framework by providing, with a high level of abstraction, all the services needed for controlling and managing a large scientific, or non-scientific, infrastructure. A beta version of the !CHAOS infrastructure will be released at the end of December 2015 and will run on private Cloud infrastructures based on OpenStack.
Angius, S.; Bisegni, C.; Ciuffetti, P.; Di Pirro, G.; Foggetta, L. G.; Galletti, F.; Gargana, R.; Gioscio, E.; Maselli, D.; Mazzitelli, G.; Michelotti, A.; Orrù, R.; Pistoni, M.; Spagnoli, F.; Spigone, D.; Stecchi, A.; Tonto, T.; Tota, M. A.; Catani, L.; Di Giulio, C.; Salina, G.; Buzzi, P.; Checcucci, B.; Lubrano, P.; Piccini, M.; Fattibene, E.; Michelotto, M.; Cavallaro, S. R.; Diana, B. F.; Enrico, F.; Pulvirenti, S.
2016-01-01
The paper is aimed to present the !CHAOS open source project aimed to develop a prototype of a national private Cloud Computing infrastructure, devoted to accelerator control systems and large experiments of High Energy Physics (HEP). The !CHAOS project has been financed by MIUR (Italian Ministry of Research and Education) and aims to develop a new concept of control system and data acquisition framework by providing, with a high level of aaabstraction, all the services needed for controlling and managing a large scientific, or non-scientific, infrastructure. A beta version of the !CHAOS infrastructure will be released at the end of December 2015 and will run on private Cloud infrastructures based on OpenStack.
International Nuclear Information System (INIS)
Soloviev, V.G.
1995-01-01
Order and chaos and order-to-chaos transition are treated in terms of nuclear wave functions. A quasiparticle-phonon interaction is responsible for the fragmentation of one- and many-quasiparticle and phonon states and for the mixing of closely spaced states. Complete damping of one-quasiparticle states cannot be considered as a transition to chaos due to large many-quasiparticle or quasiparticle-phonon terms in their wave functions. An experimental investigation of the strength distribution of many-quasiparticle and quasiparticle-phonon states should uncover a new region of a regularity in nuclei at intermediate excitation energy. A chaotic behaviour of nuclear states can be shifted to higher excitation energies. ((orig.))
Energy Technology Data Exchange (ETDEWEB)
Turiaci, Gustavo J. [Physics Department, Princeton University,Princeton NJ 08544 (United States); Verlinde, Herman [Physics Department, Princeton University,Princeton NJ 08544 (United States); Princeton Center for Theoretical Science, Princeton University,Princeton NJ 08544 (United States)
2016-12-21
We make three observations that help clarify the relation between CFT and quantum chaos. We show that any 1+1-D system in which conformal symmetry is non-linearly realized exhibits two main characteristics of chaos: maximal Lyapunov behavior and a spectrum of Ruelle resonances. We use this insight to identify a lattice model for quantum chaos, built from parafermionic spin variables with an equation of motion given by a Y-system. Finally we point to a relation between the spectrum of Ruelle resonances of a CFT and the analytic properties of OPE coefficients between light and heavy operators. In our model, this spectrum agrees with the quasi-normal modes of the BTZ black hole.
Chaos, decoherence and quantum cosmology
International Nuclear Information System (INIS)
Calzetta, Esteban
2012-01-01
In this topical review we discuss the connections between chaos, decoherence and quantum cosmology. We understand chaos as classical chaos in systems with a finite number of degrees of freedom, decoherence as environment induced decoherence and quantum cosmology as the theory of the Wheeler-DeWitt equation or else the consistent history formulation thereof, first in mini super spaces and later through its extension to midi super spaces. The overall conclusion is that consideration of decoherence is necessary (and probably sufficient) to sustain an interpretation of quantum cosmology based on the wavefunction of the Universe adopting a Wentzel-Kramers-Brillouin form for large Universes, but a definitive account of the semiclassical transition in classically chaotic cosmological models is not available in the literature yet. (topical review)
International Nuclear Information System (INIS)
Turiaci, Gustavo J.; Verlinde, Herman
2016-01-01
We make three observations that help clarify the relation between CFT and quantum chaos. We show that any 1+1-D system in which conformal symmetry is non-linearly realized exhibits two main characteristics of chaos: maximal Lyapunov behavior and a spectrum of Ruelle resonances. We use this insight to identify a lattice model for quantum chaos, built from parafermionic spin variables with an equation of motion given by a Y-system. Finally we point to a relation between the spectrum of Ruelle resonances of a CFT and the analytic properties of OPE coefficients between light and heavy operators. In our model, this spectrum agrees with the quasi-normal modes of the BTZ black hole.
Nuclear spectroscopy and quantum chaos
International Nuclear Information System (INIS)
Sakata, Fumihiko; Marumori, Toshio; Hashimoto, Yukio; Yamamoto, Yoshifumi; Tsukuma, Hidehiko; Iwasawa, Kazuo.
1990-05-01
In this paper, a recent development of INS-TSUKUBA joint research project on large-amplitude collective motion is summerized. The classical theory of nuclear collective dynamics formulated within the time-dependent Hartree-Fock theory is recapitulated and decisive role of the level crossing in the single-particle dynamics on the order-to-chaos transition of collective motion is discussed in detail. Extending the basic idea of the classical theory, we discuss a quantum theory of nuclear collective dynamics which allows us to properly define a concept of quantum chaos for each eigenfunction. By using numerical calculation, we illustrate what the quantum chaos for each eigenfunction means and its relation to usual definition based on the random matrix theory. (author)
Intermittent Testicular Torsion
African Journals Online (AJOL)
2017-06-02
Jun 2, 2017 ... had prior episodes of testicular pain, suggesting that they may have had intermittent torsion before .... None of the patients had antecedent history of sexual exposure, fever, or urinary tract infection .... torsion of the spermatic cord portends an increased risk of acute testicular infarction. J Urol 2008;180 4 ...
1989-01-01
Le mouvement brownien ; la mémoire des atomes ; le chaos ; déterminisme et prédictabilité ; déterminisme et chaos ; les phénomènes de physique et les échelles de longueur ; un ordre caché dans la matière désordonnée ; les verres de spin et l'étude des milieux désordonnés ; la convection ; la croissance fractale ; la physique de la matière hétérogène ; la matière ultradivisée.
Bunimovich, Leonid A; Vela-Arevalo, Luz V
2015-09-01
"Chaos is found in greatest abundance wherever order is being sought.It always defeats order, because it is better organized"Terry PratchettA brief review is presented of some recent findings in the theory of chaotic dynamics. We also prove a statement that could be naturally considered as a dual one to the Poincaré theorem on recurrences. Numerical results demonstrate that some parts of the phase space of chaotic systems are more likely to be visited earlier than other parts. A new class of chaotic focusing billiards is discussed that clearly violates the main condition considered to be necessary for chaos in focusing billiards.
Distributional chaos for linear operators
Czech Academy of Sciences Publication Activity Database
Bernardes Jr., N.C.; Bonilla, A.; Müller, Vladimír; Peris, A.
2013-01-01
Roč. 265, č. 9 (2013), s. 2143-2163 ISSN 0022-1236 R&D Projects: GA ČR GA201/09/0473 Institutional support: RVO:67985840 Keywords : distributional chaos * hypercyclic operators * irregular vectors Subject RIV: BA - General Mathematics Impact factor: 1.152, year: 2013 http://www.sciencedirect.com/science/article/pii/S0022123613002450
International Nuclear Information System (INIS)
Ichikawa, Y.H.
1990-09-01
Plasma exhibits a full of variety of nonlinear phenomena. Active research in nonlinear plasma physics contributed to explore the concepts of soliton and chaos. Structure of soliton equations and dynamics of low dimensional Hamiltonian systems are discussed to emphasize the universality of these novel concepts in the wide branch of science and engineering. (author) 52 refs
Chaos Theory and International Relations
2016-12-01
King Oscar II 12 James E. Glenn, Chaos Theory: The Essentials for Military Applications (Newport, RI...Adolf Hitler in Germany, Alexander’s conquest of the Persian Empire, the arrival of Attila to Europe, the onset of the two Gulf Wars, the Arab Spring
Bright, Jim E. H.; Pryor, Robert G. L.
2011-01-01
The Chaos Theory of Careers (CTC; Pryor & Bright, 2011) construes both individuals and the contexts in which they develop their careers in terms of complex dynamical systems. Such systems perpetually operate under influences of stability and change both internally and in relation to each other. The CTC introduces new concepts to account for…
On the Mechanisms Behind Chaos
DEFF Research Database (Denmark)
Lindberg, Erik
2006-01-01
behind the chaotic behavior, e.g. one group is based on the sudden interrupt of inductive currents, another group is based on the sudden parallel coupling of capacitors with different voltages, and a third group may be based on multiplication of signals. An example of chaos based on disturbance...
Lecar, Myron; Franklin, Fred A.; Holman, Matthew J.; Murray, Norman J.
2001-01-01
The physical basis of chaos in the solar system is now better understood: In all cases investigated so far, chaotic orbits result from overlapping resonances. Perhaps the clearest examples are found in the asteroid belt. Overlapping resonances account for its kirkwood gaps and were used to predict and find evidence for very narrow gaps in the outer belt. Further afield, about one new "short-peroid" comet is discovered each year. They are believed to come from the "Kuiper Belt" (at 40 AU or more) via chaotic orbits produced by mean-motion and secular resonances with Neptune. Finally, the planetary system itself is not immune from chaos. In the inner solar system, overlapping secular resonances have been identified as the possible source of chaos. For example, Mercury in 1012 years, may suffer a close encounter with Venus or plunge into the Sun. In the outer solar system, three-body resonances have been identified as a source of chaos, but on an even longer time scale of 109 times the age of the solar system. On the human time scale, the planets do follow their orbits in a stately procession, and we can predict their trajectories for hundreds of thousands of years. That is because the mavericks, with shorter instability times, have long since been ejected. The solar system is not stable; it is just old!
Synchronicity from Synchronized Chaos
Directory of Open Access Journals (Sweden)
Gregory S. Duane
2015-03-01
Full Text Available The synchronization of loosely-coupled chaotic oscillators, a phenomenon investigated intensively for the last two decades, may realize the philosophical concept of “synchronicity”—the commonplace notion that related eventsmysteriously occur at the same time. When extended to continuous media and/or large discrete arrays, and when general (non-identical correspondences are considered between states, intermittent synchronous relationships indeed become ubiquitous. Meaningful synchronicity follows naturally if meaningful events are identified with coherent structures, defined by internal synchronization between remote degrees of freedom; a condition that has been posited as necessary for synchronizability with an external system. The important case of synchronization between mind and matter is realized if mind is analogized to a computer model, synchronizing with a sporadically observed system, as in meteorological data assimilation. Evidence for the ubiquity of synchronization is reviewed along with recent proposals that: (1 synchronization of different models of the same objective process may be an expeditious route to improved computational modeling and may also describe the functioning of conscious brains; and (2 the nonlocality in quantum phenomena implied by Bell’s theorem may be explained in a variety of deterministic (hidden variable interpretations if the quantum world resides on a generalized synchronization “manifold”.
Chaos and remedial investigations
International Nuclear Information System (INIS)
Galbraith, R.M.
1991-01-01
Current research into the nature of chaos indicates that even for systems that are well known and easily modeled, slight changes in the scale used to measure the input have unpredictable results in the model output. The conduct of a remedial investigation (RI) is dictated by well-established rules of investigation and management, yet small changes in project orientation, regulatory environment, or site conditions have unpredictable consequences to the project. The consequences can lead to either brilliant success or utter failure. The chaotic effect of a change in scale is most often illustrated by an exercise in measuring the length of the coast of Great Britain. If a straight ruler 10-kilometers long is used, the sum of the 10-kilometer increments gives the length of the coast. If the ruler is changed to five kilometers long and the exercise is repeated, the sum of the five-kilometer increments will not be the same as the sum of the 10-kilometer increments. Nor is there a way to predict what the length of the coast will be using any other scale. Several examples from the Fernald Project RI are used to illustrate open-quotes changes in scaleclose quotes in both technical and management situations. Given that there is no way to predict the outcome of scale changes in a RI, technical and project management must be alert to the fact that a scale has changed and the investigation is no longer on the path it was thought to be on. The key to success, therefore, is to develop specific units of measure for a number of activities, in addition to cost and schedule, and track them regularly. An example for tracking a portion of the field investigation is presented. The determination of effective units of measure is perhaps the most difficult aspect of any project. Changes in scale sometimes go unnoticed until suddenly the budget is expended and only a portion of the work is completed. Remedial investigations on large facilities provide new and complex challenges
Quasistatic Dynamics with Intermittency
International Nuclear Information System (INIS)
Leppänen, Juho; Stenlund, Mikko
2016-01-01
We study an intermittent quasistatic dynamical system composed of nonuniformly hyperbolic Pomeau–Manneville maps with time-dependent parameters. We prove an ergodic theorem which shows almost sure convergence of time averages in a certain parameter range, and identify the unique physical family of measures. The theorem also shows convergence in probability in a larger parameter range. In the process, we establish other results that will be useful for further analysis of the statistical properties of the model.
Quasistatic Dynamics with Intermittency
Energy Technology Data Exchange (ETDEWEB)
Leppänen, Juho; Stenlund, Mikko, E-mail: mikko.stenlund@helsinki.fi [University of Helsinki, Department of Mathematics and Statistics (Finland)
2016-06-15
We study an intermittent quasistatic dynamical system composed of nonuniformly hyperbolic Pomeau–Manneville maps with time-dependent parameters. We prove an ergodic theorem which shows almost sure convergence of time averages in a certain parameter range, and identify the unique physical family of measures. The theorem also shows convergence in probability in a larger parameter range. In the process, we establish other results that will be useful for further analysis of the statistical properties of the model.
Hamiltonian Chaos and Fractional Dynamics
International Nuclear Information System (INIS)
Combescure, M
2005-01-01
This book provides an introduction and discussion of the main issues in the current understanding of classical Hamiltonian chaos, and of its fractional space-time structure. It also develops the most complex and open problems in this context, and provides a set of possible applications of these notions to some fundamental questions of dynamics: complexity and entropy of systems, foundation of classical statistical physics on the basis of chaos theory, and so on. Starting with an introduction of the basic principles of the Hamiltonian theory of chaos, the book covers many topics that can be found elsewhere in the literature, but which are collected here for the readers' convenience. In the last three parts, the author develops topics which are not typically included in the standard textbooks; among them are: - the failure of the traditional description of chaotic dynamics in terms of diffusion equations; - he fractional kinematics, its foundation and renormalization group analysis; - 'pseudo-chaos', i.e. kinetics of systems with weak mixing and zero Lyapunov exponents; - directional complexity and entropy. The purpose of this book is to provide researchers and students in physics, mathematics and engineering with an overview of many aspects of chaos and fractality in Hamiltonian dynamical systems. In my opinion it achieves this aim, at least provided researchers and students (mainly those involved in mathematical physics) can complement this reading with comprehensive material from more specialized sources which are provided as references and 'further reading'. Each section contains introductory pedagogical material, often illustrated by figures coming from several numerical simulations which give the feeling of what's going on, and thus is very useful to the reader who is not very familiar with the topics presented. Some problems are included at the end of most sections to help the reader to go deeper into the subject. My one regret is that the book does not
International Nuclear Information System (INIS)
Upadhyay, Ranjit Kumar; Kumari, Nitu; Rai, Vikas
2009-01-01
We show that wave of chaos (WOC) can generate two-dimensional time-independent spatial patterns which can be a potential candidate for understanding planktonic patchiness observed in marine environments. These spatio-temporal patterns were obtained in computer simulations of a minimal model of phytoplankton-zooplankton dynamics driven by forces of diffusion. We also attempt to figure out the average lifetimes of these non-linear non-equilibrium patterns. These spatial patterns serve as a realistic model for patchiness found in aquatic systems (e.g., marine and oceanic). Additionally, spatio-temporal chaos produced by bi-directional WOCs is robust to changes in key parameters of the system; e.g., intra-specific competition among individuals of phytoplankton and the rate of fish predation. The ideas contained in the present paper may find applications in diverse fields of human endeavor.
Spatiotemporal perspective on the decay of turbulence in wall-bounded flows.
Manneville, Paul
2009-02-01
By use of a reduced model focusing on the in-plane dependence of plane Couette flow, it is shown that the turbulent-->laminar relaxation process can be understood as a nucleation problem similar to that occurring at a thermodynamic first-order phase transition. The approach, apt to deal with the large extension of the system considered, challenges the current interpretation in terms of chaotic transients typical of temporal chaos. The study of the distribution of the sizes of laminar domains embedded in turbulent flow proves that an abrupt transition from sustained spatiotemporal chaos to laminar flow can take place at some given value of the Reynolds number Rlow, whether or not the local chaos lifetime, as envisioned within low-dimensional dynamical systems theory, diverges at finite R beyond Rlow.
Meaning Finds a Way: Chaos (Theory) and Composition
Kyburz, Bonnie Lenore
2004-01-01
The explanatory power provided by the chaos theory is explored. A dynamic and reciprocal relationship between culture and chaos theory indicates that the progressive cultural work may be formed by the cross-disciplinary resonance of chaos theory.
Chaos, Chaos Control and Synchronization of a Gyrostat System
GE, Z.-M.; LIN, T.-N.
2002-03-01
The dynamic behavior of a gyrostat system subjected to external disturbance is studied in this paper. By applying numerical results, phase diagrams, power spectrum, period-T maps, and Lyapunov exponents are presented to observe periodic and choatic motions. The effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams. For global analysis, the basins of attraction of each attractor of the system are located by employing the modified interpolated cell mapping (MICM) method. Several methods, the delayed feedback control, the addition of constant torque, the addition of periodic force, the addition of periodic impulse torque, injection of dither signal control, adaptive control algorithm (ACA) control and bang-bang control are used to control chaos effectively. Finally, synchronization of chaos in the gyrostat system is studied.
Effect of chaos on plasma filament dynamics and turbulence in the scrape-off layer
International Nuclear Information System (INIS)
Meyerson, D.; Waelbroeck, F.; Horton, W.; Michoski, C.
2014-01-01
Naturally occurring error fields as well as resonant magnetic perturbations applied for stability control are known to cause magnetic field-line chaos in the scrape-off layer (SOL) region of tokamaks. Here, 2D simulations with the BOUT++ simulation framework are used to investigate the effect of the field-line chaos on the SOL and in particular on its width and peak particle flux. The chaos enters the SOL dynamics only through the connection length, which is evaluated using a Poincaré map. The variation of experimentally relevant quantities, such as the SOL gradient length scale and the intermittency of the particle flux in the SOL, is described as a function of the strength of the magnetic perturbation. It is found that the effect of the chaos is to broaden the profile of the sheath-loss coefficient, which is proportional to the inverse connection length. That is, the SOL transport in a chaotic field is equivalent to that in a model where the sheath-loss coefficient is replaced by its average over the unperturbed flux surfaces. The model does not include the effects of chaotic features other than the parallel connection length
Does chaos assist localization or delocalization?
Tan, Jintao; Lu, Gengbiao; Luo, Yunrong; Hai, Wenhua
2014-12-01
We aim at a long-standing contradiction between chaos-assisted tunneling and chaos-related localization study quantum transport of a single particle held in an amplitude-modulated and tilted optical lattice. We find some near-resonant regions crossing chaotic and regular regions in the parameter space, and demonstrate that chaos can heighten velocity of delocalization in the chaos-resonance overlapping regions, while chaos may aid localization in the other chaotic regions. The degree of localization enhances with increasing the distance between parameter points and near-resonant regions. The results could be useful for experimentally manipulating chaos-assisted transport of single particles in optical or solid-state lattices.
Advances in chaos theory and intelligent control
Vaidyanathan, Sundarapandian
2016-01-01
The book reports on the latest advances in and applications of chaos theory and intelligent control. Written by eminent scientists and active researchers and using a clear, matter-of-fact style, it covers advanced theories, methods, and applications in a variety of research areas, and explains key concepts in modeling, analysis, and control of chaotic and hyperchaotic systems. Topics include fractional chaotic systems, chaos control, chaos synchronization, memristors, jerk circuits, chaotic systems with hidden attractors, mechanical and biological chaos, and circuit realization of chaotic systems. The book further covers fuzzy logic controllers, evolutionary algorithms, swarm intelligence, and petri nets among other topics. Not only does it provide the readers with chaos fundamentals and intelligent control-based algorithms; it also discusses key applications of chaos as well as multidisciplinary solutions developed via intelligent control. The book is a timely and comprehensive reference guide for graduate s...
New advances on chaotic intermittency and its applications
Elaskar, Sergio
2017-01-01
One of the most important routes to chaos is the chaotic intermittency. However, there are many cases that do not agree with the classical theoretical predictions. In this book, an extended theory for intermittency in one-dimensional maps is presented. A new general methodology to evaluate the reinjection probability density function (RPD) is developed in Chapters 5 to 8. The key of this formulation is the introduction of a new function, called M(x), which is used to calculate the RPD function. The function M(x) depends on two integrals. This characteristic reduces the influence on the statistical fluctuations in the data series. Also, the function M(x) is easy to evaluate from the data series, even for a small number of numerical or experimental data. As a result, a more general form for the RPD is found; where the classical theory based on uniform reinjection is recovered as a particular case. The characteristic exponent traditionally used to characterize the intermittency type, is now a function depending ...
Quantum chaos: diffusion photoeffect in hydrogen
Energy Technology Data Exchange (ETDEWEB)
Shepelyanskij, D L
1987-05-01
Ionization process in highly excited hydrogen atom in electromagnetic field is presented in the form of an extraordinary photoeffect, in which ionization at the frequency, being much lower than ionization energy, occurs much quicker than single-photon one. Such a quick ionization is explained by dynamic chaos occurence. Question, related to quantum effect influence on chaotic movement of the electron (quantum chaos) is considered. Electron excitation in the chaos area is described by a diffusional equation.
Discursive Maps at the Edge of Chaos
2017-05-25
Discursive Maps at the Edge of Chaos A Monograph by Major Mathieu Primeau Canadian Army, Royal Canadian Engineer School of Advanced Military...Master’s Thesis 3. DATES COVERED (From - To) JUN 2016 – MAY 2017 4. TITLE AND SUBTITLE Discursive Maps at the Edge of Chaos 5a. CONTRACT NUMBER 5b...meaning of boundaries and polarize conflict towards violence. The edge of chaos is the fine line between disorder and coherence. Discursive maps
Chaos induced by breakup of waves in a spatial epidemic model with nonlinear incidence rate
International Nuclear Information System (INIS)
Sun, Gui-Quan; Jin, Zhen; Liu, Quan-Xing; Li, Li
2008-01-01
Spatial epidemiology is the study of spatial variation in disease risk or incidence, including the spatial patterns of the population. The spread of diseases in human populations can exhibit large scale patterns, underlining the need for spatially explicit approaches. In this paper, the spatiotemporal complexity of a spatial epidemic model with nonlinear incidence rate, which includes the behavioral changes and crowding effect of the infective individuals, is investigated. Based on both theoretical analysis and computer simulations, we find out when, under the parameters which can guarantee a stable limit cycle in the non-spatial model, spiral and target waves can emerge. Moreover, two different kinds of breakup of waves are shown. Specifically, the breakup of spiral waves is from the core and the breakup of target waves is from the far-field, and both kinds of waves become irregular patterns at last. Our results reveal that the spatiotemporal chaos is induced by the breakup of waves. The results obtained confirm that diffusion can form spiral waves, target waves or spatial chaos of high population density, which enrich the findings of spatiotemporal dynamics in the epidemic model
Intermittency in Complex Flows
Ben Mahjoub, Otman; Redondo, Jose M.
2017-04-01
Experimental results of the complex turbulent wake of a cilinder in 2D [1] and 3D flows [2] were used to investigate the scaling of structure functions, similar research was also performed on wave propagation and breaking in the Ocean [3], in the the stratified Atmosphere (ABL) [4] and in a 100large flume (UPC) for both regular and irregular waves, where long time series of waves propagating and generating breaking turbulence velocity rms and higher order measurements were taken in depth. [3,5] by means of a velocimeter SONTEK3-D. The probability distribution functions of the velocity differences and their non Gaussian distribution related to the energy spectrum indicate that irregularity is an important source of turbulence. From Kolmogorov's K41 and K61 intermittency correction: the p th-order longitudinal velocity structure function δul at scale l in the inertial range of three-dimensional fully developed turbulence is related by ⟨δup⟩ = ⟨(u(x+ l)- u(x))p⟩ ˜ ɛp0/3lp/3 l where ⟨...⟩ represents the spatial average over flow domain, with ɛ0 the mean energy dissipation per unit mass and l is the separation distance. The importance of the random nature of the energy dissipation led to the K62 theory of intermittency, but locality and non-homogeneity are key issues. p p/3 p/3 ξd ⟨δul⟩ ˜ ⟨ɛl ⟩l ˜ l and ξp = p 3 + τp/3 , where now ɛl is a fractal energy dissipation at scale l, τp/3 is the scaling of and ξp is the scaling exponent of the velocity structure function of order p. Both in K41 and K62, the structure functions of third order related to skewness is ξ3 = 1. But this is not true either. We show that scaling exponents ξp do deviate from early studies that only investigated homogeneous turbulence, where a large inertial range dominates. The use of multi-fractal analysis and improvements on Structure function calculations on standard Enhanced mixing is an essential property of turbulence and efforts to alter and to control
Intermittency in nuclear multifragmentation
International Nuclear Information System (INIS)
Ploszajczak, M.; Tucholski, A.
1990-07-01
Fluctuations of the fragment size distribution in a percolation model and in nuclear multifragmentation following the breakup of high energy nuclei in the nuclear emulsion are studied using the method of scaled factorial moments. An intermittent patern of fluctuations is found in the data as well as in the percolation lattice calculation. This is a consequence of both a self-similarity in the fragment size distribution and a random character for the scaling law. These fluctuations are in general well-described by percolation model. The multifractal dimensions are calculated and their relevance to the study of possible critical behaviour is pointed out. (orig.)
Controlling Mackey-Glass chaos
Kiss, Gábor; Röst, Gergely
2017-11-01
The Mackey-Glass equation is the representative example of delay induced chaotic behavior. Here, we propose various control mechanisms so that otherwise erratic solutions are forced to converge to the positive equilibrium or to a periodic orbit oscillating around that equilibrium. We take advantage of some recent results of the delay differential literature, when a sufficiently large domain of the phase space has been shown to be attractive and invariant, where the system is governed by monotone delayed feedback and chaos is not possible due to some Poincaré-Bendixson type results. We systematically investigate what control mechanisms are suitable to drive the system into such a situation and prove that constant perturbation, proportional feedback control, Pyragas control, and state dependent delay control can all be efficient to control Mackey-Glass chaos with properly chosen control parameters.
Energy Technology Data Exchange (ETDEWEB)
Fitzpatrick, A. Liam [Department of Physics, Boston University,590 Commonwealth Avenue, Boston, MA 02215 (United States); Kaplan, Jared [Department of Physics and Astronomy, Johns Hopkins University,3400 N. Charles St, Baltimore, MD 21218 (United States)
2016-05-12
We use results on Virasoro conformal blocks to study chaotic dynamics in CFT{sub 2} at large central charge c. The Lyapunov exponent λ{sub L}, which is a diagnostic for the early onset of chaos, receives 1/c corrections that may be interpreted as λ{sub L}=((2π)/β)(1+(12/c)). However, out of time order correlators receive other equally important 1/c suppressed contributions that do not have such a simple interpretation. We revisit the proof of a bound on λ{sub L} that emerges at large c, focusing on CFT{sub 2} and explaining why our results do not conflict with the analysis leading to the bound. We also comment on relationships between chaos, scattering, causality, and bulk locality.
International Nuclear Information System (INIS)
Fitzpatrick, A. Liam; Kaplan, Jared
2016-01-01
We use results on Virasoro conformal blocks to study chaotic dynamics in CFT_2 at large central charge c. The Lyapunov exponent λ_L, which is a diagnostic for the early onset of chaos, receives 1/c corrections that may be interpreted as λ_L=((2π)/β)(1+(12/c)). However, out of time order correlators receive other equally important 1/c suppressed contributions that do not have such a simple interpretation. We revisit the proof of a bound on λ_L that emerges at large c, focusing on CFT_2 and explaining why our results do not conflict with the analysis leading to the bound. We also comment on relationships between chaos, scattering, causality, and bulk locality.
Oestreicher, Christian
2007-01-01
Whether every effect can be precisely linked to a given cause or to a list of causes has been a matter of debate for centuries, particularly during the 17th century, when astronomers became capable of predicting the trajectories of planets. Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely, although they can be predicted to some extent, in line with the chaos theory. Concepts such as deterministic models, sensitivity to initial conditions, strange attractors, and fractal dimensions are inherent to the development of this theory A few situations involving normal or abnormal endogenous rhythms in biology have been analyzed following the principles of chaos theory. This is particularly the case with cardiac arrhythmias, but less so with biological clocks and circadian rhythms.
Magnetic field induced dynamical chaos.
Ray, Somrita; Baura, Alendu; Bag, Bidhan Chandra
2013-12-01
In this article, we have studied the dynamics of a particle having charge in the presence of a magnetic field. The motion of the particle is confined in the x-y plane under a two dimensional nonlinear potential. We have shown that constant magnetic field induced dynamical chaos is possible even for a force which is derived from a simple potential. For a given strength of the magnetic field, initial position, and velocity of the particle, the dynamics may be regular, but it may become chaotic when the field is time dependent. Chaotic dynamics is very often if the field is time dependent. Origin of chaos has been explored using the Hamiltonian function of the dynamics in terms of action and angle variables. Applicability of the present study has been discussed with a few examples.
Controlling Mackey-Glass chaos.
Kiss, Gábor; Röst, Gergely
2017-11-01
The Mackey-Glass equation is the representative example of delay induced chaotic behavior. Here, we propose various control mechanisms so that otherwise erratic solutions are forced to converge to the positive equilibrium or to a periodic orbit oscillating around that equilibrium. We take advantage of some recent results of the delay differential literature, when a sufficiently large domain of the phase space has been shown to be attractive and invariant, where the system is governed by monotone delayed feedback and chaos is not possible due to some Poincaré-Bendixson type results. We systematically investigate what control mechanisms are suitable to drive the system into such a situation and prove that constant perturbation, proportional feedback control, Pyragas control, and state dependent delay control can all be efficient to control Mackey-Glass chaos with properly chosen control parameters.
Oestreicher, Christian
2007-01-01
Whether every effect can be precisely linked to a given cause or to a list of causes has been a matter of debate for centuries, particularly during the 17th century when astronomers became capable of predicting the trajectories of planets. Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely although they can be predicted to some extent in line with the chaos theory Concepts such as deterministic models, sensitivity to initial conditions, strange attractors, and fractal dimensions are inherent to the development of this theory, A few situations involving normal or abnormal endogenous rhythms in biology have been analyzed following the principles of chaos theory This is particularly the case with cardiac arrhythmias, but less so with biological clocks and circadian rhythms. PMID:17969865
International Nuclear Information System (INIS)
Kolesov, Andrei Yu; Rozov, Nikolai Kh
2009-01-01
A new definition of a chaotic invariant set is given for a continuous semiflow in a metric space. It generalizes the well-known definition due to Devaney and allows one to take into account a special feature occurring in the non-compact infinite-dimensional case: so-called turbulent chaos. The paper consists of two sections. The first contains several well-known facts from chaotic dynamics, together with new definitions and results. The second presents a concrete example demonstrating that our definition of chaos is meaningful. Namely, an infinite-dimensional system of ordinary differential equations is investigated having an attractor that is chaotic in the sense of the new definition but not in the sense of Devaney or Knudsen. Bibliography: 65 titles.
PHASE CHAOS IN THE DISCRETE KURAMOTO MODEL
DEFF Research Database (Denmark)
Maistrenko, V.; Vasylenko, A.; Maistrenko, Y.
2010-01-01
The paper describes the appearance of a novel, high-dimensional chaotic regime, called phase chaos, in a time-discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It arises from the nonlinear...... interaction among the oscillators, while the individual oscillators behave periodically when left uncoupled. For the four-dimensional time-discrete Kuramoto model, we outline the region of phase chaos in the parameter plane and determine the regions where phase chaos coexists with different periodic...
The CHAOS-4 geomagnetic field model
DEFF Research Database (Denmark)
Olsen, Nils; Lühr, H.; Finlay, Chris
2014-01-01
We present CHAOS-4, a new version in the CHAOS model series, which aims to describe the Earth's magnetic field with high spatial and temporal resolution. Terms up to spherical degree of at least n = 85 for the lithospheric field, and up to n = 16 for the time-varying core field are robustly...... to the core field, but the high-degree lithospheric field is regularized for n > 85. CHAOS-4 model is derived by merging two submodels: its low-degree part has been derived using similar model parametrization and data sets as used for previous CHAOS models (but of course including more recent data), while its...
The CHAOS-4 Geomagnetic Field Model
DEFF Research Database (Denmark)
Olsen, Nils; Finlay, Chris; Lühr, H.
We present CHAOS-4, a new version in the CHAOS model series, which aims at describing the Earth's magnetic field with high spatial resolution (terms up to spherical degree n=90 for the crustal field, and up to n=16 for the time-varying core field are robustly determined) and high temporal...... between the coordinate systems of the vector magnetometer and of the star sensor providing attitude information). The final CHAOS-4 model is derived by merging two sub-models: its low-degree part has been obtained using similar model parameterization and data sets as used for previous CHAOS models (but...
A quantum harmonic oscillator and strong chaos
International Nuclear Information System (INIS)
Oprocha, Piotr
2006-01-01
It is known that many physical systems which do not exhibit deterministic chaos when treated classically may exhibit such behaviour if treated from the quantum mechanics point of view. In this paper, we will show that an annihilation operator of the unforced quantum harmonic oscillator exhibits distributional chaos as introduced in B Schweizer and J SmItal (1994 Trans. Am. Math. Soc. 344 737-54). Our approach strengthens previous results on chaos in this model and provides a very powerful tool to measure chaos in other (quantum or classical) models
The chaos cookbook a practical programming guide
Pritchard, Joe
2014-01-01
The Chaos Cookbook: A Practical Programming Guide discusses the use of chaos in computer programming. The book is comprised of 11 chapters that tackle various topics relevant to chaos and programming. Chapter 1 reviews the concept of chaos, and Chapter 2 discusses the iterative functions. Chapters 3 and 4 cover differential and Lorenz equations. Chapter 5 talks about strange attractors, while Chapter 6 deals with the fractal link. The book also discusses the Mandelbrot set, and then covers the Julia sets. The other fractal systems and the cellular automata are also explained. The last chapter
Multidimensional intermittency in hadronic collisions
International Nuclear Information System (INIS)
Pan, J.; Hwa, R.C.
1992-06-01
The study of intermittency in high-energy hadronic collisions by the Monte Carlo code ECCO is extended to 3-dimensional phase space. Strong intermittency is found in agreement with the data. Fluctuation in the impact parameter is responsible for the intermittency in lnp T , and the transverse-momentum conservation leads to negative intermittency slopes in the azimuthal angle φ. The Ochs-Wosiek plots are linear in all dimensions having universal slopes. An exponent ν = 1.448 emerges to characterize multiparticle production in pp collisions. The properties of G moments are also examined, and the fractal dimensions determined
International Nuclear Information System (INIS)
Sheridan, T.E.
2005-01-01
Chaotic dynamics is observed experimentally in a complex (dusty) plasma of three particles. A low-frequency sinusoidal modulation of the plasma density excites both the center-of-mass and breathing modes. Low-dimensional chaos is seen for a 1:2 resonance between these modes. A strange attractor with a dimension of 2.48±0.05 is observed. The largest Lyapunov exponent is positive
Chaos, complexity, and random matrices
Cotler, Jordan; Hunter-Jones, Nicholas; Liu, Junyu; Yoshida, Beni
2017-11-01
Chaos and complexity entail an entropic and computational obstruction to describing a system, and thus are intrinsically difficult to characterize. In this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE) Hamiltonians and analytically compute out-of-time-ordered correlation functions (OTOCs) and frame potentials to quantify scrambling, Haar-randomness, and circuit complexity. While our random matrix analysis gives a qualitatively correct prediction of the late-time behavior of chaotic systems, we find unphysical behavior at early times including an O(1) scrambling time and the apparent breakdown of spatial and temporal locality. The salient feature of GUE Hamiltonians which gives us computational traction is the Haar-invariance of the ensemble, meaning that the ensemble-averaged dynamics look the same in any basis. Motivated by this property of the GUE, we introduce k-invariance as a precise definition of what it means for the dynamics of a quantum system to be described by random matrix theory. We envision that the dynamical onset of approximate k-invariance will be a useful tool for capturing the transition from early-time chaos, as seen by OTOCs, to late-time chaos, as seen by random matrix theory.
Kasimov, Aslan R.
2013-03-08
We propose the following model equation, ut+1/2(u2−uus)x=f(x,us) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, x<0, and the shock is located at x=0 for any t≥0. Here, us(t) is the shock state and the source term f is taken to mimic the chemical energy release in detonations. This equation retains the essential physics needed to reproduce many properties of detonations in gaseous reactive mixtures: steady traveling wave solutions, instability of such solutions, and the onset of chaos. Our model is the first (to our knowledge) to describe chaos in shock waves by a scalar first-order partial differential equation. The chaos arises in the equation thanks to an interplay between the nonlinearity of the inviscid Burgers equation and a novel forcing term that is nonlocal in nature and has deep physical roots in reactive Euler equations.
International Nuclear Information System (INIS)
Guszejnov, Dávid; Lazányi, Nóra; Bencze, Attila; Zoletnik, Sándor
2013-01-01
This paper is aimed to contribute to the scientific discussions that have been triggered by the experimental observation of a quadratic relation between the kurtosis and skewness of turbulent fluctuations present in fusion plasmas and other nonlinear physical systems. In this paper, we offer a general statistical model which attributes the observed K=aS 2 +b relation to the varying intermittency of the experimental signals. The model is a two random variable model constructed to catch the essential intermittent feature of the real signal. One of the variables is the amplitude of the underlying intermittent event (e.g., turbulent structure) while the other is connected to the intermittency level of the system. This simple model can attribute physical meaning to the a and b coefficients, as they characterize the spatio-temporal statistics of intermittent events. By constructing a particle-conserving Gaussian model for the underlying coherent structures, the experimentally measured a and b coefficients could be adequately reproduced
Metabolic Effects of Intermittent Fasting.
Patterson, Ruth E; Sears, Dorothy D
2017-08-21
The objective of this review is to provide an overview of intermittent fasting regimens, summarize the evidence on the health benefits of intermittent fasting, and discuss physiological mechanisms by which intermittent fasting might lead to improved health outcomes. A MEDLINE search was performed using PubMed and the terms "intermittent fasting," "fasting," "time-restricted feeding," and "food timing." Modified fasting regimens appear to promote weight loss and may improve metabolic health. Several lines of evidence also support the hypothesis that eating patterns that reduce or eliminate nighttime eating and prolong nightly fasting intervals may result in sustained improvements in human health. Intermittent fasting regimens are hypothesized to influence metabolic regulation via effects on (a) circadian biology, (b) the gut microbiome, and (c) modifiable lifestyle behaviors, such as sleep. If proven to be efficacious, these eating regimens offer promising nonpharmacological approaches to improving health at the population level, with multiple public health benefits.
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
Galloping instability to chaos of cables
Luo, Albert C J
2017-01-01
This book provides students and researchers with a systematic solution for fluid-induced structural vibrations, galloping instability and the chaos of cables. They will also gain a better understanding of stable and unstable periodic motions and chaos in fluid-induced structural vibrations. Further, the results presented here will help engineers effectively design and analyze fluid-induced vibrations.
Path and semimartingale properties of chaos processes
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas; Graversen, Svend-Erik
2010-01-01
The present paper characterizes various properties of chaos processes which in particular include processes where all time variables admit a Wiener chaos expansion of a fixed finite order. The main focus is on the semimartingale property, p-variation and continuity. The general results obtained...
Chaos and fractals. Applications to nuclear engineering
International Nuclear Information System (INIS)
Clausse, A.; Delmastro, D.F.
1990-01-01
This work presents a description of the research lines carried out by the authors on chaos and fractal theories, oriented to the nuclear field. The possibilities that appear in the nuclear security branch where the information deriving from chaos and fractal techniques may help to the development of better criteria and more reliable designs, are of special importance. (Author) [es
Transition to chaos of a vertical collapsible tube conveying air flow
International Nuclear Information System (INIS)
Flores, F Castillo; Cros, A
2009-01-01
'Sky dancers', the large collapsible tubes used as advertising, are studied in this work through a simple experimental device. Our study is devoted to the nonlinear dynamics of this system and to its transition to chaos. Firstly, we have shown that after a collapse occurs, the air fills the tube at a different speed rate from the flow velocity. Secondly, the temporal intermittency is studied as the flow rate is increased. A statistical analysis shows that the chaotic times maintain roughly the same value by increasing air speed. On the other hand, laminar times become shorter, until the system reaches a completely chaotic state.
Transition to chaos of a vertical collapsible tube conveying air flow
Energy Technology Data Exchange (ETDEWEB)
Flores, F Castillo; Cros, A, E-mail: anne_cros@yahoo.co [Departamento de Fisica, Universidad de Guadalajara, 44430 Jalisco (Mexico)
2009-05-01
'Sky dancers', the large collapsible tubes used as advertising, are studied in this work through a simple experimental device. Our study is devoted to the nonlinear dynamics of this system and to its transition to chaos. Firstly, we have shown that after a collapse occurs, the air fills the tube at a different speed rate from the flow velocity. Secondly, the temporal intermittency is studied as the flow rate is increased. A statistical analysis shows that the chaotic times maintain roughly the same value by increasing air speed. On the other hand, laminar times become shorter, until the system reaches a completely chaotic state.
Order and chaos in the nonlinear response of driven nuclear spin systems
Energy Technology Data Exchange (ETDEWEB)
Brun, E; Derighetti, B; Holzner, R; Ravani, M [Zurich Univ. (Switzerland). Inst. fuer Physik
1984-01-01
The authors report on observations of ordered and chaotic behavior of a nonlinear system of strongly polarized nuclear spins inside the tuning coil of an NMR detector. The combined system: spins plus LC-circuit, may act as a nonlinear bistable absorber or a spin-flip laser, depending on the sign of the nuclear spin polarization. For the NMR laser experimental evidence is presented for limit-cycle behavior, sequences of bifurcations which lead to chaos, intermittency, multistability, and pronounced hysteresis effects. The experimental facts are compared with computer solutions of appropriate Bloch equations for the macroscopic order parameters.
Rybalko, S.; Larionov, S.; Poptsova, M.; Loskutov, A.
2011-10-01
Large-scale dynamical properties of complete chromosome DNA sequences of eukaryotes are considered. Using the proposed deterministic models with intermittency and symbolic dynamics we describe a wide spectrum of large-scale patterns inherent in these sequences, such as segmental duplications, tandem repeats, and other complex sequence structures. It is shown that the recently discovered gene number balance on the strands is not of a random nature, and certain subsystems of a complete chromosome DNA sequence exhibit the properties of deterministic chaos.
Fate in intermittent claudication
DEFF Research Database (Denmark)
Jelnes, Rolf; Gaardsting, O; Hougaard Jensen, K
1986-01-01
, or an ankle/arm pressure index below 50% were individually significantly associated with progression of the arteriosclerotic disease. These findings show the importance of peripheral blood pressure measurements in the management of patients with intermittent claudication due to arteriosclerotic disease........ The rate of clinical progression of the arteriosclerotic disease (that is, rest pain or gangrene) of the worst affected leg was 7.5% in the first year after referral. Thereafter the rate was 2.2% a year. An ankle systolic blood pressure below 70 mm Hg, a toe systolic blood pressure below 40 mm Hg...... 113 of the patients (44%) had died. Causes of death were no different from those in the general population. Mortality was twice that of the general population matched for age and sex. Mortality among the men was twice that among the women. In men under 60 mortality was four times that expected...
4th international interdisciplinary chaos symposium
Banerjee, Santo; Caglar, Suleyman; Ozer, Mehmet; Chaos and complex systems
2013-01-01
Complexity Science and Chaos Theory are fascinating areas of scientific research with wide-ranging applications. The interdisciplinary nature and ubiquity of complexity and chaos are features that provides scientists with a motivation to pursue general theoretical tools and frameworks. Complex systems give rise to emergent behaviors, which in turn produce novel and interesting phenomena in science, engineering, as well as in the socio-economic sciences. The aim of all Symposia on Chaos and Complex Systems (CCS) is to bring together scientists, engineers, economists and social scientists, and to discuss the latest insights and results obtained in the area of corresponding nonlinear-system complex (chaotic) behavior. Especially for the “4th International Interdisciplinary Chaos Symposium on Chaos and Complex Systems,” which took place April 29th to May 2nd, 2012 in Antalya, Turkey, the scope of the symposium had been further enlarged so as to encompass the presentation of work from circuits to econophysic...
Chaos the science of predictable random motion
Kautz, Richard
2011-01-01
Based on only elementary mathematics, this engaging account of chaos theory bridges the gap between introductions for the layman and college-level texts. It develops the science of dynamics in terms of small time steps, describes the phenomenon of chaos through simple examples, and concludes with a close look at a homoclinic tangle, the mathematical monster at the heart of chaos. The presentation is enhanced by many figures, animations of chaotic motion (available on a companion CD), and biographical sketches of the pioneers of dynamics and chaos theory. To ensure accessibility to motivated high school students, care has been taken to explain advanced mathematical concepts simply, including exponentials and logarithms, probability, correlation, frequency analysis, fractals, and transfinite numbers. These tools help to resolve the intriguing paradox of motion that is predictable and yet random, while the final chapter explores the various ways chaos theory has been put to practical use.
Semiconductor Lasers Stability, Instability and Chaos
Ohtsubo, Junji
2013-01-01
This third edition of “Semiconductor Lasers, Stability, Instability and Chaos” was significantly extended. In the previous edition, the dynamics and characteristics of chaos in semiconductor lasers after the introduction of the fundamental theory of laser chaos and chaotic dynamics induced by self-optical feedback and optical injection was discussed. Semiconductor lasers with new device structures, such as vertical-cavity surface-emitting lasers and broad-area semiconductor lasers, are interesting devices from the viewpoint of chaotic dynamics since they essentially involve chaotic dynamics even in their free-running oscillations. These topics are also treated with respect to the new developments in the current edition. Also the control of such instabilities and chaos control are critical issues for applications. Another interesting and important issue of semiconductor laser chaos in this third edition is chaos synchronization between two lasers and the application to optical secure communication. One o...
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.
Prediction based chaos control via a new neural network
International Nuclear Information System (INIS)
Shen Liqun; Wang Mao; Liu Wanyu; Sun Guanghui
2008-01-01
In this Letter, a new chaos control scheme based on chaos prediction is proposed. To perform chaos prediction, a new neural network architecture for complex nonlinear approximation is proposed. And the difficulty in building and training the neural network is also reduced. Simulation results of Logistic map and Lorenz system show the effectiveness of the proposed chaos control scheme and the proposed neural network
Homoclinic tubes and chaos in perturbed sine-Gordon equation
International Nuclear Information System (INIS)
Li, Y. Charles
2004-01-01
Sine-Gordon equation under a quasi-periodic perturbation or a chaotic perturbation is studied. Existence of a homoclinic tube is proved. Established are chaos associated with the homoclinic tube, and 'chaos cascade' referring to the embeddings of smaller scale chaos in larger scale chaos
Transport, chaos and plasma physics
International Nuclear Information System (INIS)
Benkadda, S.; Doveil, F.; Elskens, Y.
1993-01-01
This workshop made it possible to gather for the first time plasma physicists, dynamical systems physicists and mathematicians, around a general theme focusing on the characterisation of chaotic transport. The participations have been divided into 4 topics: - dynamical systems and microscopic models of chaotic transport, - magnetic fluctuations and transport in tokamaks, - drift wave turbulence, self-organisation and intermittency, and - Wave-particle interactions
Kasimov, Aslan R; Faria, Luiz M; Rosales, Rodolfo R
2013-03-08
We propose the following model equation, u(t) + 1/2(u(2)-uu(s))x = f(x,u(s)) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, xorder partial differential equation. The chaos arises in the equation thanks to an interplay between the nonlinearity of the inviscid Burgers equation and a novel forcing term that is nonlocal in nature and has deep physical roots in reactive Euler equations.
Chaos control in duffing system
International Nuclear Information System (INIS)
Wang Ruiqi; Deng Jin; Jing Zhujun
2006-01-01
Analytical and numerical results concerning the inhibition of chaos in Duffing's equation with two weak forcing excitations are presented. We theoretically give parameter-space regions by using Melnikov's function, where chaotic states can be suppressed. The intervals of initial phase difference between the two excitations for which chaotic dynamics can be eliminated are given. Meanwhile, the influence of the phase difference on Lyapunov exponents for different frequencies is investigated. Numerical simulation results show the consistence with the theoretical analysis and the chaotic motions can be controlled to period-motions by adjusting parameter of suppressing excitation
Deterministic chaos in entangled eigenstates
Schlegel, K. G.; Förster, S.
2008-05-01
We investigate the problem of deterministic chaos in connection with entangled states using the Bohmian formulation of quantum mechanics. We show for a two particle system in a harmonic oscillator potential, that in a case of entanglement and three energy eigen-values the maximum Lyapunov-parameters of a representative ensemble of trajectories for large times develops to a narrow positive distribution, which indicates nearly complete chaotic dynamics. We also present in short results from two time-dependent systems, the anisotropic and the Rabi oscillator.
Deterministic chaos in entangled eigenstates
Energy Technology Data Exchange (ETDEWEB)
Schlegel, K.G. [Fakultaet fuer Physik, Universitaet Bielefeld, Postfach 100131, D-33501 Bielefeld (Germany)], E-mail: guenter.schlegel@arcor.de; Foerster, S. [Fakultaet fuer Physik, Universitaet Bielefeld, Postfach 100131, D-33501 Bielefeld (Germany)
2008-05-12
We investigate the problem of deterministic chaos in connection with entangled states using the Bohmian formulation of quantum mechanics. We show for a two particle system in a harmonic oscillator potential, that in a case of entanglement and three energy eigen-values the maximum Lyapunov-parameters of a representative ensemble of trajectories for large times develops to a narrow positive distribution, which indicates nearly complete chaotic dynamics. We also present in short results from two time-dependent systems, the anisotropic and the Rabi oscillator.
Deterministic chaos in entangled eigenstates
International Nuclear Information System (INIS)
Schlegel, K.G.; Foerster, S.
2008-01-01
We investigate the problem of deterministic chaos in connection with entangled states using the Bohmian formulation of quantum mechanics. We show for a two particle system in a harmonic oscillator potential, that in a case of entanglement and three energy eigen-values the maximum Lyapunov-parameters of a representative ensemble of trajectories for large times develops to a narrow positive distribution, which indicates nearly complete chaotic dynamics. We also present in short results from two time-dependent systems, the anisotropic and the Rabi oscillator
Decoherence, determinism and chaos revisited
Energy Technology Data Exchange (ETDEWEB)
Noyes, H.P.
1994-11-15
We suggest that the derivation of the free space Maxwell Equations for classical electromagnetism, using a discrete ordered calculus developed by L.H. Kauffman and T. Etter, necessarily pushes the discussion of determinism in natural science down to the level of relativistic quantum mechanics and hence renders the mathematical phenomena studied in deterministic chaos research irrelevant to the question of whether the world investigated by physics is deterministic. We believe that this argument reinforces Suppes` contention that the issue of determinism versus indeterminism should be viewed as a Kantian antinomy incapable of investigation using currently available scientific tools.
Decoherence, determinism and chaos revisited
International Nuclear Information System (INIS)
Noyes, H.P.
1994-01-01
We suggest that the derivation of the free space Maxwell Equations for classical electromagnetism, using a discrete ordered calculus developed by L.H. Kauffman and T. Etter, necessarily pushes the discussion of determinism in natural science down to the level of relativistic quantum mechanics and hence renders the mathematical phenomena studied in deterministic chaos research irrelevant to the question of whether the world investigated by physics is deterministic. We believe that this argument reinforces Suppes' contention that the issue of determinism versus indeterminism should be viewed as a Kantian antinomy incapable of investigation using currently available scientific tools
Merxhani, Branko
2012-01-01
Title: Organizimi i Kaosit (The organization of the chaos) Originally Published: In the monthly review Neo-shqiptarisma, Nr. 1, Tirana, 1930 Language: Albanian The excerpts used are from A. Plasari ed., Formula të Neoshqiptarismës. Përmbledhje shkrimesh (Tirana: Apollonia, 1996), pp. 99–102. About the author Branko Merxhani [1894 Istanbul – 1981, Istanbul]: scholar and writer. He was born in Istanbul and educated in Germany. In all likelihood, only his father was Albanian. By the end of the 1...
International Nuclear Information System (INIS)
Wang Xing-Yuan; Zhang Na; Ren Xiao-Li; Zhang Yong-Lei
2011-01-01
Coupled map lattices (CMLs) are taken as examples to study the synchronization of spatiotemporal chaotic systems. In this paper, we use the nonlinear coupled method to implement the synchronization of two coupled map lattices. Through the appropriate separation of the linear term from the nonlinear term of the spatiotemporal chaotic system, we set the nonlinear term as the coupling function and then we can achieve the synchronization of two coupled map lattices. After that, we implement the secure communication of digital image using this synchronization method. Then, the discrete characteristics of the nonlinear coupling spatiotemporal chaos are applied to the discrete pixel of the digital image. After the synchronization of both the communication parties, the receiver can decrypt the original image. Numerical simulations show the effectiveness and the feasibility of the proposed program. (general)
Indeterminacy and Spatiotemporal Data
DEFF Research Database (Denmark)
Pfoser, D.; Tryfona, N.; Jensen, Christian Søndergaard
2005-01-01
For some spatiotemporal applications, it can be assumed that the modeled world is precise and bounded, and that our record of it is precise. While these simplifying assumptions are sufficient in applications like a land information system, they are unnecessarily crude for many other applications...
Naftidrofuryl for intermittent claudication.
De Backer, T L M; Vander Stichele, R; Lehert, P; Van Bortel, L
2008-04-16
Lifestyle changes and cardiovascular prevention measures are a primary treatment for intermittent claudication (IC). Symptomatic treatment with vasoactive agents (Anatomic Therapeutic Chemical Classification (ATC) for medicines from the World Health Organisation class CO4A) is controversial. To evaluate evidence on the efficacy and safety of oral naftidrofuryl (ATC CO4 21) versus placebo on the pain-free walking distance (PFWD) of people with IC by using a meta-analysis based on individual patient data (IPD). The Cochrane Peripheral Vascular Diseases Group searched their Trials Register (last searched December 2007) and CENTRAL (last searched 2007, Issue 4). We searched MEDLINE, EMBASE, International Pharmaceutical Abstracts, the Science Citation Index and contacted the authors and checked the reference lists of retrieved articles. We asked the manufacturing company for IPD. We included only randomized controlled trials (RCTs) with low or moderate risk of bias for which the IPD were available. We collected data from the electronic data file or from the case report form and checked the data by a statistical quality control procedure. All randomized patients were analyzed following the intention-to-treat (ITT) principle. The geometric mean of the relative improvement in PFWD was calculated for both treatment groups in all identified studies. The effect of the drug was assessed compared with placebo on final walking distance (WDf) using multilevel and random-effect models and adjusting for baseline walking distance (WD0). For the responder analysis, therapeutic success was defined as an improvement of walking distance of at least 50%. We included seven studies in the IPD (n = 1266 patients). One of these studies (n = 183) was only used in the sensitivity analysis so that the main analysis included 1083 patients. The ratio of the relative improvement in PFWD (naftidrofuryl compared with placebo) was 1.37 (95% confidence interval (CI) 1.32 to 1.51, P < 0.001). The
Quantifying chaos for ecological stoichiometry.
Duarte, Jorge; Januário, Cristina; Martins, Nuno; Sardanyés, Josep
2010-09-01
The theory of ecological stoichiometry considers ecological interactions among species with different chemical compositions. Both experimental and theoretical investigations have shown the importance of species composition in the outcome of the population dynamics. A recent study of a theoretical three-species food chain model considering stoichiometry [B. Deng and I. Loladze, Chaos 17, 033108 (2007)] shows that coexistence between two consumers predating on the same prey is possible via chaos. In this work we study the topological and dynamical measures of the chaotic attractors found in such a model under ecological relevant parameters. By using the theory of symbolic dynamics, we first compute the topological entropy associated with unimodal Poincaré return maps obtained by Deng and Loladze from a dimension reduction. With this measure we numerically prove chaotic competitive coexistence, which is characterized by positive topological entropy and positive Lyapunov exponents, achieved when the first predator reduces its maximum growth rate, as happens at increasing δ1. However, for higher values of δ1 the dynamics become again stable due to an asymmetric bubble-like bifurcation scenario. We also show that a decrease in the efficiency of the predator sensitive to prey's quality (increasing parameter ζ) stabilizes the dynamics. Finally, we estimate the fractal dimension of the chaotic attractors for the stoichiometric ecological model.
Invoking the muse: Dada's chaos.
Rosen, Diane
2014-07-01
Dada, a self-proclaimed (anti)art (non)movement, took shape in 1916 among a group of writers and artists who rejected the traditions of a stagnating bourgeoisie. Instead, they adopted means of creative expression that embraced chaos, stoked instability and undermined logic, an outburst that overturned centuries of classical and Romantic aesthetics. Paradoxically, this insistence on disorder foreshadowed a new order in understanding creativity. Nearly one hundred years later, Nonlinear Dynamical Systems theory (NDS) gives renewed currency to Dada's visionary perspective on chance, chaos and creative cognition. This paper explores commonalities between NDS-theory and this early precursor of the nonlinear paradigm, suggesting that their conceptual synergy illuminates what it means to 'be creative' beyond the disciplinary boundaries of either. Key features are discussed within a 5P model of creativity based on Rhodes' 4P framework (Person, Process, Press, Product), to which I add Participant-Viewer for the interactivity of observer-observed. Grounded in my own art practice, several techniques are then put forward as non-methodical methods that invoke creative border zones, those regions where Dada's chance and design are wedded in a dialectical tension of opposites.
DEFF Research Database (Denmark)
Gidofalvi, Gyozo; Pedersen, Torben Bach
2005-01-01
Recent advances in communication and information technology, such as the increasing accuracy of GPS technology and the miniaturization of wireless communication devices pave the road for Location-Based Services (LBS). To achieve high quality for such services, spatio-temporal data mining techniques...... are needed. In this paper, we describe experiences with spatio-temporal rule mining in a Danish data mining company. First, a number of real world spatio-temporal data sets are described, leading to a taxonomy of spatio-temporal data. Second, the paper describes a general methodology that transforms...... the spatio-temporal rule mining task to the traditional market basket analysis task and applies it to the described data sets, enabling traditional association rule mining methods to discover spatio-temporal rules for LBS. Finally, unique issues in spatio-temporal rule mining are identified and discussed....
Markov transitions and the propagation of chaos
International Nuclear Information System (INIS)
Gottlieb, A.
1998-01-01
The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic independence of two random particles in a many-particle system, persists in time, as the number of particles tends to infinity. We establish a necessary and sufficient condition for a family of general n-particle Markov processes to propagate chaos. This condition is expressed in terms of the Markov transition functions associated to the n-particle processes, and it amounts to saying that chaos of random initial states propagates if it propagates for pure initial states. Our proof of this result relies on the weak convergence approach to the study of chaos due to Sztitman and Tanaka. We assume that the space in which the particles live is homomorphic to a complete and separable metric space so that we may invoke Prohorov's theorem in our proof. We also show that, if the particles can be in only finitely many states, then molecular chaos implies that the specific entropies in the n-particle distributions converge to the entropy of the limiting single-particle distribution
Using chaos theory: the implications for nursing.
Haigh, Carol
2002-03-01
The purpose of this paper is to review chaos theory and to examine the role that it may have in the discipline of nursing. In this paper, the fundamental ingredients of chaotic thinking are outlined. The earlier days of chaos thinking were characterized by an almost exclusively physiological focus. By the 21st century, nurse theorists were applying its principles to the organization and evaluation of care delivery with varying levels of success. Whilst the biological use of chaos has focused on pragmatic approaches to knowledge enhancement, nursing has often focused on the mystical aspects of chaos as a concept. The contention that chaos theory has yet to find a niche within nursing theory and practice is examined. The application of chaotic thinking across nursing practice, nursing research and statistical modelling is reviewed. The use of chaos theory as a way of identifying the attractor state of specific systems is considered and the suggestion is made that it is within statistical modelling of services that chaos theory is most effective.
Cheng, Chih-Hao; Chen, Chih-Ying; Chen, Jun-Da; Pan, Da-Kung; Ting, Kai-Ting; Lin, Fan-Yi
2018-04-30
We develop an unprecedented 3D pulsed chaos lidar system for potential intelligent machinery applications. Benefited from the random nature of the chaos, conventional CW chaos lidars already possess excellent anti-jamming and anti-interference capabilities and have no range ambiguity. In our system, we further employ self-homodyning and time gating to generate a pulsed homodyned chaos to boost the energy-utilization efficiency. Compared to the original chaos, we show that the pulsed homodyned chaos improves the detection SNR by more than 20 dB. With a sampling rate of just 1.25 GS/s that has a native sampling spacing of 12 cm, we successfully achieve millimeter-level accuracy and precision in ranging. Compared with two commercial lidars tested side-by-side, namely the pulsed Spectroscan and the random-modulation continuous-wave Lidar-lite, the pulsed chaos lidar that is in compliance with the class-1 eye-safe regulation shows significantly better precision and a much longer detection range up to 100 m. Moreover, by employing a 2-axis MEMS mirror for active laser scanning, we also demonstrate real-time 3D imaging with errors of less than 4 mm in depth.
How to test for partially predictable chaos.
Wernecke, Hendrik; Sándor, Bulcsú; Gros, Claudius
2017-04-24
For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation can split into an initial exponential decrease and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. Both processes can be either of the same or of very different time scales. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall extent of the attractor) for exceedingly long times and remain partially predictable. Standard tests for chaos widely use inter-orbital correlations as an indicator. However, testing partially predictable chaos yields mostly ambiguous results, as this type of chaos is characterized by attractors of fractally broadened braids. For a resolution we introduce a novel 0-1 indicator for chaos based on the cross-distance scaling of pairs of initially close trajectories. This test robustly discriminates chaos, including partially predictable chaos, from laminar flow. Additionally using the finite time cross-correlation of pairs of initially close trajectories, we are able to identify laminar flow as well as strong and partially predictable chaos in a 0-1 manner solely from the properties of pairs of trajectories.
Directory of Open Access Journals (Sweden)
Veres Bálint
2014-12-01
Full Text Available It is commonly known that medial reflections have been initiated by attempts to secure the borders of discrete medial forms and to define the modus operandi of each essentialized medial area. Later on, the focus of study has shifted to plurimedial formations and the interactions between predefined medial genres. In the last few decades, taxonomic approaches to various multi-, inter-, and transmedial phenomena dominated the discussions, which offered invaluable support in mapping the terrain, but at the same time hindered the analysis of the ephemeral, time-dependent aspects of plurimedial operations. While we explore the properties of each medial configuration, we lose sight of the actual historical drivers that produce ever-new configurations. My thesis is that any discourse on intermediality should be paralleled by a discourse on cultural intermittency, and consequently, media studies should involve an approach that focuses on the “ecosystem” of the constantly renewing media configurations from the point of view of their vitalizing potential and capability to trigger heightened experiences. This approach draws much inspiration from K. Ludwig Pfeiffer’s media anthropology that gives orientation in my paper.
Chronic Intermittent Hypoxia Induces Atherosclerosis
Savransky, Vladimir; Nanayakkara, Ashika; Li, Jianguo; Bevans, Shannon; Smith, Philip L.; Rodriguez, Annabelle; Polotsky, Vsevolod Y.
2007-01-01
Rationale: Obstructive sleep apnea, a condition leading to chronic intermittent hypoxia (CIH), is associated with hyperlipidemia, atherosclerosis, and a high cardiovascular risk. A causal link between obstructive sleep apnea and atherosclerosis has not been established.
Some remarks on chaos in topological dynamics
Directory of Open Access Journals (Sweden)
Huoyung Wang
2011-10-01
Full Text Available Bau-Sen Du introduced a notion of chaos which is stronger than Li-Yorke sensitivity. A TDS (X, f is called chaotic if there is a positive e such that for any x and any nonempty open set V of X there is a point y in V such that the pair (x, y is proximal but not e-asymptotic. In this article, we show that a TDS (T, f is transitive but not mixing if and only if (T, f is Li-Yorke sensitive but not chaotic, where T is a tree. Moreover, we compare such chaos with other notions of chaos.
A-coupled-expanding and distributional chaos
International Nuclear Information System (INIS)
Kim, Cholsan; Ju, Hyonhui; Chen, Minghao; Raith, Peter
2015-01-01
The concept of A-coupled-expanding maps is one of the more natural and useful ideas generalized from the horseshoe map which is commonly known as a criterion of chaos. It is well known that distributional chaos is one of the concepts which reflect strong chaotic behavior. In this paper, we focus on the relationship between A-coupled-expanding and distributional chaos. We prove two theorems which give sufficient conditions for a strictly A-coupled-expanding map to be distributionally chaotic in the senses of two kinds, where A is an m × m irreducible transition matrix
Towards CHAOS-5 - How can Swarm contribute?
DEFF Research Database (Denmark)
Finlay, Chris; Olsen, Nils; Tøffner-Clausen, Lars
2014-01-01
The launch of ESA's satellite trio Swarm in November 2013 opens an exciting new chapter in the observation and monitoring of Earth's magnetic field from space. We report preliminary results from an extension of the CHAOS series of geomagnetic field models to include both scalar and vector field...... observations from the three Swarm satellites, along with the most recent quasi-definitive ground observatory data. The fit of this new update CHAOS field model to the Swarm observations will be presented in detail providing useful insight the initial Swarm data. Enhancements of the CHAOS modelling scheme...
Chaos from simple models to complex systems
Cencini, Massimo; Vulpiani, Angelo
2010-01-01
Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theor
Some open questions in 'wave chaos'
International Nuclear Information System (INIS)
Nonnenmacher, Stéphane
2008-01-01
The subject area referred to as 'wave chaos', 'quantum chaos' or 'quantum chaology' has been investigated mostly by the theoretical physics community in the last 30 years. The questions it raises have more recently also attracted the attention of mathematicians and mathematical physicists, due to connections with number theory, graph theory, Riemannian, hyperbolic or complex geometry, classical dynamical systems, probability, etc. After giving a rough account on 'what is quantum chaos?', I intend to list some pending questions, some of them having been raised a long time ago, some others more recent. The choice of problems (and of references) is of course partial and personal. (open problem)
Nuclear physics, symmetries, and quantum chaos
International Nuclear Information System (INIS)
Bunakov, V.E.
1999-01-01
The reasons why the problem of chaos is of great topical interest in modern physics are briefly summarized, and it is indicated that ambiguities in the concept of quantum chaos present the greatest difficulties in these realms. The theory of random matrices and strength functions are generalized to demonstrate that chaotization of a system is associated with the violation of its symmetries. A criterion of quantum chaoticity is formulated in terms of the spreading width Γ spr . In the classical limit, this criterion reduces to Lyapunov's stability criteria. It is shown that the proposed criterion is applicable to standard problems of the modern theory of dynamical chaos
Semiconductor Lasers Stability, Instability and Chaos
Ohtsubo, Junji
2008-01-01
This monograph describes fascinating recent progress in the field of chaos, stability and instability of semiconductor lasers. Applications and future prospects are discussed in detail. The book emphasizes the various dynamics induced in semiconductor lasers by optical and electronic feedback, optical injection, and injection current modulation. Recent results of both theoretical and experimental investigations are presented. Demonstrating applications of semiconductor laser chaos, control and noise, Semiconductor Lasers describes suppression and chaotic secure communications. For those who are interested in optics but not familiar with nonlinear systems, a brief introduction to chaos analysis is presented.
Quantum chaos in the Heisenberg picture
International Nuclear Information System (INIS)
McKellar, B.H.J.; Lancaster, M.; McCaw, J.
2000-01-01
Full text: We explore the possibility of defining quantum chaos in the algebra of quantum mechanical operators. The simple definition of the Lyapunov exponent in terms of a metric on that algebra has the expected properties for the quantum logistic map, as we confirm for the simple spin 1 system. We then show numerically and analytically that the Hamiltonian evolution of finite spin systems does not lead to chaos in this definition, and investigate alternative definitions of quantum chaos in the algebra of operators
Chaos in body-vortex interactions
DEFF Research Database (Denmark)
Pedersen, Johan Rønby; Aref, Hassan
2010-01-01
of a circle is integrable. As the body is made slightly elliptic, a chaotic region grows from an unstable relative equilibrium of the circle-vortex case. The case of a cylindrical body of any shape moving in fluid otherwise at rest is also integrable. A second transition to chaos arises from the limit between...... rocking and tumbling motion of the body known in this case. In both instances, the chaos may be detected both in the body motion and in the vortex motion. The effect of increasing body mass at a fixed body shape is to damp the chaos....
Chua's circuit a paradigm for chaos
1993-01-01
For uninitiated researchers, engineers, and scientists interested in a quick entry into the subject of chaos, this book offers a timely collection of 55 carefully selected papers covering almost every aspect of this subject. Because Chua's circuit is endowed with virtually every bifurcation phenomena reported in the extensive literature on chaos, and because it is the only chaotic system which can be easily built by a novice, simulated in a personal computer, and tractable mathematically, it has become a paradigm for chaos, and a vehicle for illustrating this ubiquitous phenomenon. Its supreme
Multiparticle correlations and intermittency in high energy collisions
International Nuclear Information System (INIS)
Bozek, P.
1992-01-01
An analysis of the intermittency signal observed in high energy experiments is presented using multiparticle distributions and correlation functions. The effect of the dimensional projection of the multiparticle distributions on one or two-dimensional subspace is discussed. The structure of the multiparticle cumulants is analyzed for the DELPHI e + e - annihilation data. The model of spatiotemporal intermittency is discussed in details and is shown to reproduce qualitatively the dependence of the intermittency strength on the target and projectile nuclei. A 1-dimensional (lD) cellular-automaton (CA) and a lD forest-fire model is studied. On the example of the noncritical lD Ising model the difficulties of the scaled factorial moment (SFM) method in extracting genuine scaling behaviour are illustrated. The problem of the finite-size effect in connection to the dimensional projection can be easily exemplified in the case of the 2D critical system with conformal symmetry. (R.P.) 122 refs., 38 figs., 3 tabs
International Nuclear Information System (INIS)
Ge Zhengming; Hsu Maoyuan
2008-01-01
In this paper, chaos excited chaos synchronizations of generalized van der Pol systems with integral and fractional order are studied. Synchronizations of two identified autonomous generalized van der Pol chaotic systems are obtained by replacing their corresponding exciting terms by the same function of chaotic states of a third nonautonomous or autonomous generalized van der Pol system. Numerical simulations, such as phase portraits, Poincare maps and state error plots are given. It is found that chaos excited chaos synchronizations exist for the fractional order systems with the total fractional order both less than and more than the number of the states of the integer order generalized van der Pol system
Sudhakar, N.; Rajasekar, N.; Akhil, Saya; Jyotheeswara Reddy, K.
2017-11-01
The boost converter is the most desirable DC-DC power converter for renewable energy applications for its favorable continuous input current characteristics. In other hand, these DC-DC converters known as practical nonlinear systems are prone to several types of nonlinear phenomena including bifurcation, quasiperiodicity, intermittency and chaos. These undesirable effects has to be controlled for maintaining normal periodic operation of the converter and to ensure the stability. This paper presents an effective solution to control the chaos in solar fed DC-DC boost converter since the converter experiences wide range of input power variation which leads to chaotic phenomena. Controlling of chaos is significantly achieved using optimal circuit parameters obtained through Nelder-Mead Enhanced Bacterial Foraging Optimization Algorithm. The optimization renders the suitable parameters in minimum computational time. The results are compared with the traditional methods. The obtained results of the proposed system ensures the operation of the converter within the controllable region.
Spatiotemporal Stochastic Resonance:Theory and Experiment
Peter, Jung
1996-03-01
The amplification of weak periodic signals in bistable or excitable systems via stochastic resonance has been studied intensively over the last years. We are going one step further and ask: Can noise enhance spatiotemporal patterns in excitable media and can this effect be observed in nature? To this end, we are looking at large, two dimensional arrays of coupled excitable elements. Due to the coupling, excitation can propagate through the array in form of nonlinear waves. We observe target waves, rotating spiral waves and other wave forms. If the coupling between the elements is below a critical threshold, any excitational pattern will die out in the absence of noise. Below this threshold, large scale rotating spiral waves - as they are observed above threshold - can be maintained by a proper level of the noise[1]. Furthermore, their geometric features, such as the curvature can be controlled by the homogeneous noise level[2]. If the noise level is too large, break up of spiral waves and collisions with spontaneously nucleated waves yields spiral turbulence. Driving our array with a spatiotemporal pattern, e.g. a rotating spiral wave, we show that for weak coupling the excitational response of the array shows stochastic resonance - an effect we have termed spatiotemporal stochastic resonance. In the last part of the talk I'll make contact with calcium waves, observed in astrocyte cultures and hippocampus slices[3]. A. Cornell-Bell and collaborators[3] have pointed out the role of calcium waves for long-range glial signaling. We demonstrate the similarity of calcium waves with nonlinear waves in noisy excitable media. The noise level in the tissue is characterized by spontaneous activity and can be controlled by applying neuro-transmitter substances[3]. Noise effects in our model are compared with the effect of neuro-transmitters on calcium waves. [1]P. Jung and G. Mayer-Kress, CHAOS 5, 458 (1995). [2]P. Jung and G. Mayer-Kress, Phys. Rev. Lett.62, 2682 (1995). [3
Spatiotemporal optical solitons
International Nuclear Information System (INIS)
Malomed, Boris A; Mihalache, Dumitru; Wise, Frank; Torner, Lluis
2005-01-01
In the course of the past several years, a new level of understanding has been achieved about conditions for the existence, stability, and generation of spatiotemporal optical solitons, which are nondiffracting and nondispersing wavepackets propagating in nonlinear optical media. Experimentally, effectively two-dimensional (2D) spatiotemporal solitons that overcome diffraction in one transverse spatial dimension have been created in quadratic nonlinear media. With regard to the theory, fundamentally new features of light pulses that self-trap in one or two transverse spatial dimensions and do not spread out in time, when propagating in various optical media, were thoroughly investigated in models with various nonlinearities. Stable vorticity-carrying spatiotemporal solitons have been predicted too, in media with competing nonlinearities (quadratic-cubic or cubic-quintic). This article offers an up-to-date survey of experimental and theoretical results in this field. Both achievements and outstanding difficulties are reviewed, and open problems are highlighted. Also briefly described are recent predictions for stable 2D and 3D solitons in Bose-Einstein condensates supported by full or low-dimensional optical lattices. (review article)
Leveraging Chaos in Continuous Thrust Trajectory Design
National Aeronautics and Space Administration — A trajectory design tool is sought to leverage chaos and nonlinear dynamics present in multi-body gravitational fields to design ultra-low energy transfer...
A Chaos Theory Perspective on International Migration
Directory of Open Access Journals (Sweden)
Anca Tănasie
2017-12-01
Full Text Available This paper aims at providing a different approach to international migration analysis, beyond classical models previously proposed by specialized literature. Chaos theory is getting more and more applied into macroeconomics once traditional linear models or even previous dynamic analysis become less suitable. Modern science sees chaos as unpredictable evolution, maybe even disorder. Still, chaos has got its own rules and can describe many dynamic phenomena within our world. Thus, we test whether international migration data falls under the rules of chaos and whether recent developments within the “European migration crisis” (the total daily migration inflows towards the coasts of Italy, by sea, from January 2014 to April 2017 could be described as chaotic.
Chaos concepts, control and constructive use
Bolotin, Yurii; Yanovsky, Vladimir
2017-01-01
This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interf...
Homoclinic chaos and energy condition violation
International Nuclear Information System (INIS)
Heinzle, J. Mark; Roehr, Niklas; Uggla, Claes
2006-01-01
In this letter we discuss the connection between so-called homoclinic chaos and the violation of energy conditions in locally rotationally symmetric Bianchi type IX models, where the matter is assumed to be nontilted dust and a positive cosmological constant. We show that homoclinic chaos in these models is an artifact of unphysical assumptions: it requires that there exist solutions with positive matter energy density ρ>0 that evolve through the singularity and beyond as solutions with negative matter energy density ρ<0. Homoclinic chaos is absent when it is assumed that the dust particles always retain their positive mass. In addition, we discuss more general models: for solutions that are not locally rotationally symmetric we demonstrate that the construction of extensions through the singularity, which is required for homoclinic chaos, is not possible in general
Searching for chaos on low frequency
Nicolas Wesner
2004-01-01
A new method for detecting low dimensional chaos in small sample sets is presented. The method is applied to financial data on low frequency (annual and monthly) for which few observations are available.
Coherence and chaos in condensed matter
International Nuclear Information System (INIS)
Bishop, A.R.
1989-01-01
This paper discusses the following topics: nonlinearity in condensed matter; coherence and chaos in spatially extended condensed matter systems; nonlinearity and magnetism; and solitons and conducting polymers. 52 refs., 7 figs
Semiconductor lasers stability, instability and chaos
Ohtsubo, Junji
2017-01-01
This book describes the fascinating recent advances made concerning the chaos, stability and instability of semiconductor lasers, and discusses their applications and future prospects in detail. It emphasizes the dynamics in semiconductor lasers by optical and electronic feedback, optical injection, and injection current modulation. Applications of semiconductor laser chaos, control and noise, and semiconductor lasers are also demonstrated. Semiconductor lasers with new structures, such as vertical-cavity surface-emitting lasers and broad-area semiconductor lasers, are intriguing and promising devices. Current topics include fast physical number generation using chaotic semiconductor lasers for secure communication, development of chaos, quantum-dot semiconductor lasers and quantum-cascade semiconductor lasers, and vertical-cavity surface-emitting lasers. This fourth edition has been significantly expanded to reflect the latest developments. The fundamental theory of laser chaos and the chaotic dynamics in se...
Nuclear physics and ideas of quantum chaos
International Nuclear Information System (INIS)
Zelevinsky, V.G.
2002-01-01
The field nowadays called 'many-body quantum chaos' was started in 1939 with the article by I.I. Gurevich studying the regularities of nuclear spectra. The field has been extensively developed recently, both mathematically and in application to mesoscopic systems and quantum fields. We argue that nuclear physics and the theory of quantum chaos are mutually beneficial. Many ideas of quantum chaos grew up from the factual material of nuclear physics; this enrichment still continues to take place. On the other hand, many phenomena in nuclear structure and reactions, as well as the general problem of statistical physics of finite strongly interacting systems, can be understood much deeper with the help of ideas and methods borrowed from the field of quantum chaos. A brief review of the selected topics related to the recent development is presented
From classical to quantum chaos
International Nuclear Information System (INIS)
Zaslavsky, G.M.
1991-01-01
The analysis is done for the quantum properties of systems that possess dynamical chaos in classical limit. Two main topics are considered: (i) the problem of quantum macroscopical description of the system and the Ehrenfest-Einstein problem of the validity of the classical approximation; and (ii) the problem of levels spacing distribution for the nonintegrable case. For the first topic the method of projecting on the coherent states base is considered and the ln 1/(h/2π) time for the quasiclassical approximation breaking is described. For the second topic the discussion of GOE and non-GOE distributions is done and estimations and simulations for the non-GOE case are reviewed. (author). 44 refs, 2 figs
Distributional chaos for triangular maps
International Nuclear Information System (INIS)
Smital, Jaroslav; Stefankova, Marta
2004-01-01
In this paper we exhibit a triangular map F of the square with the following properties: (i) F is of type 2 ∞ but has positive topological entropy; we recall that similar example was given by Kolyada in 1992, but our argument is much simpler. (ii) F is distributionally chaotic in the wider sense, but not distributionally chaotic in the sense introduced by Schweizer and Smital [Trans. Amer. Math. Soc. 344 (1994) 737]. In other words, there are lower and upper distribution functions PHI xy and PHI xy * generated by F such that PHI xy * ≡1 and PHI xy (0 + ) uv , and PHI uv * such that PHI uv * ≡1 and PHI uv (t)=0 whenever 0 0. We also show that the two notions of distributional chaos used in the paper, for continuous maps of a compact metric space, are invariants of topological conjugacy
Chaos, Fractals and Their Applications
Thompson, J. Michael T.
2016-12-01
This paper gives an up-to-date account of chaos and fractals, in a popular pictorial style for the general scientific reader. A brief historical account covers the development of the subject from Newton’s laws of motion to the astronomy of Poincaré and the weather forecasting of Lorenz. Emphasis is given to the important underlying concepts, embracing the fractal properties of coastlines and the logistics of population dynamics. A wide variety of applications include: NASA’s discovery and use of zero-fuel chaotic “superhighways” between the planets; erratic chaotic solutions generated by Euler’s method in mathematics; atomic force microscopy; spontaneous pattern formation in chemical and biological systems; impact mechanics in offshore engineering and the chatter of cutting tools; controlling chaotic heartbeats. Reference is made to a number of interactive simulations and movies accessible on the web.
International Nuclear Information System (INIS)
Luo Chuanwen; Wang Gang; Wang Chuncheng; Wei Junjie
2009-01-01
The concepts of uniform index and expectation uniform index are two mathematical descriptions of the uniformity and the mean uniformity of a finite set in a polyhedron. The concepts of instantaneous chaometry (ICM) and k step chaometry (k SCM) are introduced in order to apply the method in statistics for studying the nonlinear difference equations. It is found that k step chaometry is an indirect estimation of the expectation uniform index. The simulation illustrate that the expectation uniform index for the Lorenz System is increasing linearly, but increasing nonlinearly for the Chen's System with parameter b. In other words, the orbits for each system become more and more uniform with parameter b increasing. Finally, a conjecture is also brought forward, which implies that chaos can be interpreted by its orbit's mean uniformity described by the expectation uniform index and indirectly estimated by k SCM. The k SCM of the heart rate showes the feeble and old process of the heart.
Control of collective network chaos.
Wagemakers, Alexandre; Barreto, Ernest; Sanjuán, Miguel A F; So, Paul
2014-06-01
Under certain conditions, the collective behavior of a large globally-coupled heterogeneous network of coupled oscillators, as quantified by the macroscopic mean field or order parameter, can exhibit low-dimensional chaotic behavior. Recent advances describe how a small set of "reduced" ordinary differential equations can be derived that captures this mean field behavior. Here, we show that chaos control algorithms designed using the reduced equations can be successfully applied to imperfect realizations of the full network. To systematically study the effectiveness of this technique, we measure the quality of control as we relax conditions that are required for the strict accuracy of the reduced equations, and hence, the controller. Although the effects are network-dependent, we show that the method is effective for surprisingly small networks, for modest departures from global coupling, and even with mild inaccuracy in the estimate of network heterogeneity.
Quantum chaos on discrete graphs
International Nuclear Information System (INIS)
Smilansky, Uzy
2007-01-01
Adapting a method developed for the study of quantum chaos on quantum (metric) graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76), spectral ζ functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph and obtaining functions which belong to the class of ζ functions proposed originally by Ihara (1966 J. Mat. Soc. Japan 18 219) and expanded by subsequent authors (Stark and Terras 1996 Adv. Math. 121 124, Kotani and Sunada 2000 J. Math. Sci. Univ. Tokyo 7 7). Finally, a model of 'classical dynamics' on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76). (fast track communication)
Menstruation, perimenopause, and chaos theory.
Derry, Paula S; Derry, Gregory N
2012-01-01
This article argues that menstruation, including the transition to menopause, results from a specific kind of complex system, namely, one that is nonlinear, dynamical, and chaotic. A complexity-based perspective changes how we think about and research menstruation-related health problems and positive health. Chaotic systems are deterministic but not predictable, characterized by sensitivity to initial conditions and strange attractors. Chaos theory provides a coherent framework that qualitatively accounts for puzzling results from perimenopause research. It directs attention to variability within and between women, adaptation, lifespan development, and the need for complex explanations of disease. Whether the menstrual cycle is chaotic can be empirically tested, and a summary of our research on 20- to 40-year-old women is provided.
True quantum chaos? An instructive example
International Nuclear Information System (INIS)
Berry, M.V.
1992-01-01
Any chaotic classical system can be transformed into a quantum system that preserves the chaos, because the classical Liouville equation involving 2Ν phase-space variables q ,p has the form of a 'Schroedinger equation' with 'coordinates' Q=[q,p]. The feature of this quantum system that allows chaos to persist is linarity of the Hamiltonian' in the 2Ν 'momentum' operators conjugate to Q. (orig.)
Scaling properties of localized quantum chaos
International Nuclear Information System (INIS)
Izrailev, F.M.
1991-01-01
Statistical properties of spectra and eigenfunctions are studied for the model of quantum chaos in the presence of dynamical localization. The main attention is paid to the scaling properties of localization length and level spacing distribution in the intermediate region between Poissonian and Wigner-Dyson statistics. It is shown that main features of such localized quantum chaos are well described by the introduced ensemble of band random matrices. 28 refs.; 7 figs
Deterministic chaos in the processor load
International Nuclear Information System (INIS)
Halbiniak, Zbigniew; Jozwiak, Ireneusz J.
2007-01-01
In this article we present the results of research whose purpose was to identify the phenomenon of deterministic chaos in the processor load. We analysed the time series of the processor load during efficiency tests of database software. Our research was done on a Sparc Alpha processor working on the UNIX Sun Solaris 5.7 operating system. The conducted analyses proved the presence of the deterministic chaos phenomenon in the processor load in this particular case
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
Chaos control using sliding-mode theory
International Nuclear Information System (INIS)
Nazzal, Jamal M.; Natsheh, Ammar N.
2007-01-01
Chaos control means to design a controller that is able to mitigating or eliminating the chaos behavior of nonlinear systems that experiencing such phenomenon. In this paper, a nonlinear Sliding-Mode Controller (SMC) is presented. Two nonlinear chaotic systems are chosen to be our case study in this paper, the well known Chua's circuit and Lorenz system. The study shows the effectiveness of the designed nonlinear Sliding-Mode Controller
Indian Academy of Sciences (India)
K Krishan1 Manu2 R Ramaswamy2. Department of Physics, Indian Institute of Technology, Kanpur 208 016, India; School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067, India. Resonance – Journal of Science Education. Current Issue : Vol. 23, Issue 4 · Current Issue Volume 23 | Issue 4. April 2018.
Chaos in World Politics: A Reflection
Ferreira, Manuel Alberto Martins; Filipe, José António Candeias Bonito; Coelho, Manuel F. P.; Pedro, Isabel C.
Chaos theory results from natural scientists' findings in the area of non-linear dynamics. The importance of related models has increased in the last decades, by studying the temporal evolution of non-linear systems. In consequence, chaos is one of the concepts that most rapidly have been expanded in what research topics respects. Considering that relationships in non-linear systems are unstable, chaos theory aims to understand and to explain this kind of unpredictable aspects of nature, social life, the uncertainties, the nonlinearities, the disorders and confusion, scientifically it represents a disarray connection, but basically it involves much more than that. The existing close relationship between change and time seems essential to understand what happens in the basics of chaos theory. In fact, this theory got a crucial role in the explanation of many phenomena. The relevance of this kind of theories has been well recognized to explain social phenomena and has permitted new advances in the study of social systems. Chaos theory has also been applied, particularly in the context of politics, in this area. The goal of this chapter is to make a reflection on chaos theory - and dynamical systems such as the theories of complexity - in terms of the interpretation of political issues, considering some kind of events in the political context and also considering the macro-strategic ideas of states positioning in the international stage.
Spatiotemporal Modeling of Community Risk
2016-03-01
Ertugay, and Sebnem Duzgun, “Exploratory and Inferential Methods for Spatio-Temporal Analysis of Residential Fire Clustering in Urban Areas,” Fire ...response in communities.”26 In “Exploratory and Inferential Methods for Spatio-temporal Analysis of Residential Fire Clustering in Urban Areas,” Ceyhan...of fire resources spread across the community. Spatiotemporal modeling shows that actualized risk is dynamic and relatively patterned. Though
Intermittency in 197Au fragmentation
International Nuclear Information System (INIS)
Dabrowska, A.; Holynski, R.; Olszewski, A.; Szarska, M.; Wilczynska, B.; Wolter, W.; Wosiek, B.; Cherry, M.L.; Deines-Jones, P.; Jones, W.V.; Sengupta, K.; Wefel, B.
1995-07-01
The concept of factorial moments was applied to an analysis of the dynamical fluctuations in the charge distributions of the fragments emitted from gold nuclei with energies 10.6 and < 1.0 GeV/n interacting with emulsion nuclei. Clear evidence for intermittent fluctuations has been found in an analysis using all the particles released from the gold projectile, with a stronger effect observed below 1 GeV/n than at 10.6 GeV/n. For the full data sets, however, the intermittency effect was found to be very sensitive to the singly charged particles, and neglecting these particles strongly reduces the intermittency signal. When the analysis is restricted to the multiply charged fragments, an intermittency effect is revealed only for multifragmentation events, although one that is enhanced as compared to the analysis of all, singly and multiply charged, particles. The properties of the anomalous fractal dimensions suggest a sequential decay mechanism, rather than the existence of possible critical behaviour in the process of nuclear fragmentation. The likely influence of the charge conservation effects and the finite size of decaying systems on the observed intermittency signals was pointed out. (author). 37 refs, 9 figs, 5 tabs
Energy Technology Data Exchange (ETDEWEB)
Lafranceschina, Jacopo, E-mail: jlafranceschina@alaska.edu; Wackerbauer, Renate, E-mail: rawackerbauer@alaska.edu [Department of Physics, University of Alaska, Fairbanks, Alaska 99775-5920 (United States)
2015-01-15
Spatiotemporal chaos collapses to either a rest state or a propagating pulse solution in a ring network of diffusively coupled, excitable Morris-Lecar neurons. Weak excitatory synapses can increase the Lyapunov exponent, expedite the collapse, and promote the collapse to the rest state rather than the pulse state. A single traveling pulse solution may no longer be asymptotic for certain combinations of network topology and (weak) coupling strengths, and initiate spatiotemporal chaos. Multiple pulses can cause chaos initiation due to diffusive and synaptic pulse-pulse interaction. In the presence of chaos initiation, intermittent spatiotemporal chaos exists until typically a collapse to the rest state.
International Nuclear Information System (INIS)
Lafranceschina, Jacopo; Wackerbauer, Renate
2015-01-01
Spatiotemporal chaos collapses to either a rest state or a propagating pulse solution in a ring network of diffusively coupled, excitable Morris-Lecar neurons. Weak excitatory synapses can increase the Lyapunov exponent, expedite the collapse, and promote the collapse to the rest state rather than the pulse state. A single traveling pulse solution may no longer be asymptotic for certain combinations of network topology and (weak) coupling strengths, and initiate spatiotemporal chaos. Multiple pulses can cause chaos initiation due to diffusive and synaptic pulse-pulse interaction. In the presence of chaos initiation, intermittent spatiotemporal chaos exists until typically a collapse to the rest state
Genome chaos: survival strategy during crisis.
Liu, Guo; Stevens, Joshua B; Horne, Steven D; Abdallah, Batoul Y; Ye, Karen J; Bremer, Steven W; Ye, Christine J; Chen, David J; Heng, Henry H
2014-01-01
Genome chaos, a process of complex, rapid genome re-organization, results in the formation of chaotic genomes, which is followed by the potential to establish stable genomes. It was initially detected through cytogenetic analyses, and recently confirmed by whole-genome sequencing efforts which identified multiple subtypes including "chromothripsis", "chromoplexy", "chromoanasynthesis", and "chromoanagenesis". Although genome chaos occurs commonly in tumors, both the mechanism and detailed aspects of the process are unknown due to the inability of observing its evolution over time in clinical samples. Here, an experimental system to monitor the evolutionary process of genome chaos was developed to elucidate its mechanisms. Genome chaos occurs following exposure to chemotherapeutics with different mechanisms, which act collectively as stressors. Characterization of the karyotype and its dynamic changes prior to, during, and after induction of genome chaos demonstrates that chromosome fragmentation (C-Frag) occurs just prior to chaotic genome formation. Chaotic genomes seem to form by random rejoining of chromosomal fragments, in part through non-homologous end joining (NHEJ). Stress induced genome chaos results in increased karyotypic heterogeneity. Such increased evolutionary potential is demonstrated by the identification of increased transcriptome dynamics associated with high levels of karyotypic variance. In contrast to impacting on a limited number of cancer genes, re-organized genomes lead to new system dynamics essential for cancer evolution. Genome chaos acts as a mechanism of rapid, adaptive, genome-based evolution that plays an essential role in promoting rapid macroevolution of new genome-defined systems during crisis, which may explain some unwanted consequences of cancer treatment.
Particle ratios, quarks, and Chao-Yang statistics
Energy Technology Data Exchange (ETDEWEB)
Chew, C K; Low, G B; Lo, S Y [Nanyang Univ. (Singapore). Dept. of Physics; Phua, K K [Argonne National Lab., IL (USA)
1980-01-01
By introducing quarks into Chao-Yang statistics for 'violent' collisions, particle ratios are obtained which are consistent with the Chao-Yang results. The present method can also be extended to baryon-meson and baryon-antibaryon ratios.
Digital Communication Devices Based on Nonlinear Dynamics and Chaos
National Research Council Canada - National Science Library
Larson, Lawrence
2003-01-01
The final report of the ARO MURI "Digital Communications Based on Chaos and Nonlinear Dynamics" contains research results in the areas of chaos and nonlinear dynamics applied to wireless and optical communications...
International Nuclear Information System (INIS)
D'Arcy, Michael Brendan
2002-01-01
This thesis presents an account of experimental and numerical investigations of two quantum systems whose respective classical analogues are chaotic. These are the δ-kicked rotor, a paradigm in classical chaos theory, and the novel δ-kicked accelerator, created by application of a constant external acceleration or torque to the rotor. The experimental realisation of these systems has been achieved by the exposure of laser-cooled caesium atoms to approximate δ-kicks from a pulsed, high-intensity, vertical standing wave of laser light. Gravity's effect on the atoms can be controlled by appropriate shifting of the profile of the standing wave. Numerical simulations of the systems are based on a diffractive model of the potential's effect. Each system's dynamics are characterised by the final form of the momentum distribution and the dependence of the atoms' mean kinetic energy on the number and time period of the δ-kicks. The phenomena of dynamical localisation and quantum resonances in the δ-kicked rotor, which have no counterparts in the system's classical analogue, are observed and investigated. Similar experiments on the δ-kicked accelerator reveal the striking phenomenon of the quantum accelerator mode, in which a large momentum is transferred to a substantial fraction of the atomic ensemble. This feature, absent in the system's classical analogue, is characterised and an analytic explanation is presented. The effect on each quantum system of decoherence, introduced through spontaneous emission in the atoms, is examined and comparison is made with the results of classical simulations. While having little effect on the classical systems, the level of decoherence used is found to degrade quantum signatures of behaviour. Classical-like behaviour is, to some extent, restored, although significant quantum features remain. Possible applications of the quantum accelerator mode are discussed. These include use as a tool in atom optics and interferometry, a
2nd International Symposium on Chaos, Complexity and Leadership
Banerjee, Santo
2015-01-01
These proceedings from the 2013 symposium on "Chaos, complexity and leadership" reflect current research results from all branches of Chaos, Complex Systems and their applications in Management. Included are the diverse results in the fields of applied nonlinear methods, modeling of data and simulations, as well as theoretical achievements of Chaos and Complex Systems. Also highlighted are Leadership and Management applications of Chaos and Complexity Theory.
Chaos of discrete dynamical systems in complete metric spaces
International Nuclear Information System (INIS)
Shi Yuming; Chen Guanrong
2004-01-01
This paper is concerned with chaos of discrete dynamical systems in complete metric spaces. Discrete dynamical systems governed by continuous maps in general complete metric spaces are first discussed, and two criteria of chaos are then established. As a special case, two corresponding criteria of chaos for discrete dynamical systems in compact subsets of metric spaces are obtained. These results have extended and improved the existing relevant results of chaos in finite-dimensional Euclidean spaces
The three versions of distributional chaos
International Nuclear Information System (INIS)
Balibrea, F.; Smital, J.; Stefankova, M.
2005-01-01
The notion of distributional chaos was introduced by Schweizer and Smital [Trans. Amer. Math. Soc. 344 (1994) 737] for continuous maps of the interval. However, it turns out that, for continuous maps of a compact metric space three mutually nonequivalent versions of distributional chaos, DC1-DC3, can be considered. In this paper we consider the weakest one, DC3. We show that DC3 does not imply chaos in the sense of Li and Yorke. We also show that DC3 is not invariant with respect to topological conjugacy. In other words, there are lower and upper distribution functions Φ xy and Φxy* generated by a continuous map f of a compact metric space (M, ρ) such that Φxy*(t)>Φxy(t) for all t in an interval. However, f on the same space M, but with a metric ρ' generating the same topology as ρ is no more DC3.Recall that, contrary to this, either DC1 or DC2 is topological conjugacy invariant and implies Li and Yorke chaos (cf. [Chaos, Solitons and Fractals 21 (2004) 1125])
Generic superweak chaos induced by Hall effect
Ben-Harush, Moti; Dana, Itzhack
2016-05-01
We introduce and study the "kicked Hall system" (KHS), i.e., charged particles periodically kicked in the presence of uniform magnetic (B ) and electric (E ) fields that are perpendicular to each other and to the kicking direction. We show that for resonant values of B and E and in the weak-chaos regime of sufficiently small nonintegrability parameter κ (the kicking strength), there exists a generic family of periodic kicking potentials for which the Hall effect from B and E significantly suppresses the weak chaos, replacing it by "superweak" chaos (SWC). This means that the system behaves as if the kicking strength were κ2 rather than κ . For E =0 , SWC is known to be a classical fingerprint of quantum antiresonance, but it occurs under much less generic conditions, in particular only for very special kicking potentials. Manifestations of SWC are a decrease in the instability of periodic orbits and a narrowing of the chaotic layers, relative to the ordinary weak-chaos case. Also, for global SWC, taking place on an infinite "stochastic web" in phase space, the chaotic diffusion on the web is much slower than the weak-chaos one. Thus, the Hall effect can be relatively stabilizing for small κ . In some special cases, the effect is shown to cause ballistic motion for almost all parameter values. The generic global SWC on stochastic webs in the KHS appears to be the two-dimensional closest analog to the Arnol'd web in higher dimensional systems.
The Capabilities of Chaos and Complexity
Directory of Open Access Journals (Sweden)
David L. Abel
2009-01-01
Full Text Available To what degree could chaos and complexity have organized a Peptide or RNA World of crude yet necessarily integrated protometabolism? How far could such protolife evolve in the absence of a heritable linear digital symbol system that could mutate, instruct, regulate, optimize and maintain metabolic homeostasis? To address these questions, chaos, complexity, self-ordered states, and organization must all be carefully defined and distinguished. In addition their cause-and-effect relationships and mechanisms of action must be delineated. Are there any formal (non physical, abstract, conceptual, algorithmic components to chaos, complexity, self-ordering and organization, or are they entirely physicodynamic (physical, mass/energy interaction alone? Chaos and complexity can produce some fascinating self-ordered phenomena. But can spontaneous chaos and complexity steer events and processes toward pragmatic benefit, select function over non function, optimize algorithms, integrate circuits, produce computational halting, organize processes into formal systems, control and regulate existing systems toward greater efficiency? The question is pursued of whether there might be some yet-to-be discovered new law of biology that will elucidate the derivation of prescriptive information and control. Ã¢Â€ÂœSystemÃ¢Â€Â will be rigorously defined. Can a low-informational rapid succession of PrigogineÃ¢Â€Â™s dissipative structures self-order into bona fide organization?
International Nuclear Information System (INIS)
Dattani, Justine; Blake, Jack C.H.; Hilker, Frank M.
2011-01-01
Designing intervention methods to control chaotic behavior in dynamical systems remains a challenging problem, in particular for systems that are difficult to access or to measure. We propose a simple, intuitive technique that modifies the values of the state variables directly toward a certain target. The intervention takes into account the difference to the target value, and is a combination of traditional proportional feedback and constant feedback methods. It proves particularly useful when the target corresponds to the equilibrium of the uncontrolled system, and is available or can be estimated from expert knowledge (e.g. in biology and economy). -- Highlights: → We propose a chaos control method that forces the system to a certain target. → The intervention takes into account the difference to the target value. → It can be seen as a combination of proportional and constant feedback methods. → The method is very robust and highly efficient in the long-term. → It is particularly applicable when suitable target values are known or available.
Symbolic dynamics of noisy chaos
Energy Technology Data Exchange (ETDEWEB)
Crutchfield, J P; Packard, N H
1983-05-01
One model of randomness observed in physical systems is that low-dimensional deterministic chaotic attractors underly the observations. A phenomenological theory of chaotic dynamics requires an accounting of the information flow fromthe observed system to the observer, the amount of information available in observations, and just how this information affects predictions of the system's future behavior. In an effort to develop such a description, the information theory of highly discretized observations of random behavior is discussed. Metric entropy and topological entropy are well-defined invariant measures of such an attractor's level of chaos, and are computable using symbolic dynamics. Real physical systems that display low dimensional dynamics are, however, inevitably coupled to high-dimensional randomness, e.g. thermal noise. We investigate the effects of such fluctuations coupled to deterministic chaotic systems, in particular, the metric entropy's response to the fluctuations. It is found that the entropy increases with a power law in the noise level, and that the convergence of the entropy and the effect of fluctuations can be cast as a scaling theory. It is also argued that in addition to the metric entropy, there is a second scaling invariant quantity that characterizes a deterministic system with added fluctuations: I/sub 0/, the maximum average information obtainable about the initial condition that produces a particular sequence of measurements (or symbols). 46 references, 14 figures, 1 table.
Chaos and unpredictability in evolution.
Doebeli, Michael; Ispolatov, Iaroslav
2014-05-01
The possibility of complicated dynamic behavior driven by nonlinear feedbacks in dynamical systems has revolutionized science in the latter part of the last century. Yet despite examples of complicated frequency dynamics, the possibility of long-term evolutionary chaos is rarely considered. The concept of "survival of the fittest" is central to much evolutionary thinking and embodies a perspective of evolution as a directional optimization process exhibiting simple, predictable dynamics. This perspective is adequate for simple scenarios, when frequency-independent selection acts on scalar phenotypes. However, in most organisms many phenotypic properties combine in complicated ways to determine ecological interactions, and hence frequency-dependent selection. Therefore, it is natural to consider models for evolutionary dynamics generated by frequency-dependent selection acting simultaneously on many different phenotypes. Here we show that complicated, chaotic dynamics of long-term evolutionary trajectories in phenotype space is very common in a large class of such models when the dimension of phenotype space is large, and when there are selective interactions between the phenotypic components. Our results suggest that the perspective of evolution as a process with simple, predictable dynamics covers only a small fragment of long-term evolution. © 2014 The Author(s). Evolution © 2014 The Society for the Study of Evolution.
Chaos for induced hyperspace maps
International Nuclear Information System (INIS)
Banks, John
2005-01-01
For (X,d) be a metric space, f:X->X a continuous map and (K(X),H) the space of non-empty compact subsets of X with the Hausdorff metric, one may study the dynamical properties of the induced map (*)f-bar :K(X)->K(X):A-bar f(A).H. Roman-Flores [A note on in set-valued discrete systems. Chaos, Solitons and Fractals 2003;17:99-104] has shown that if f-bar is topologically transitive then so is f, but that the reverse implication does not hold. This paper shows that the topological transitivity of f-bar is in fact equivalent to weak topological mixing on the part of f. This is proved in the more general context of an induced map on some suitable hyperspace H of X with the Vietoris topology (which agrees with the topology of the Hausdorff metric in the case discussed by Roman-Flores
Deterministic Chaos - Complex Chance out of Simple Necessity ...
Indian Academy of Sciences (India)
This is a very lucid and lively book on deterministic chaos. Chaos is very common in nature. However, the understanding and realisation of its potential applications is very recent. Thus this book is a timely addition to the subject. There are several books on chaos and several more are being added every day. In spite of this ...
Chaos Theory as a Model for Managing Issues and Crises.
Murphy, Priscilla
1996-01-01
Uses chaos theory to model public relations situations in which the salient feature is volatility of public perceptions. Discusses the premises of chaos theory and applies them to issues management, the evolution of interest groups, crises, and rumors. Concludes that chaos theory is useful as an analogy to structure image problems and to raise…
God's Stuff: The Constructive Powers of Chaos for Teaching Religion
Willhauck, Susan
2010-01-01
Order and organization are valued in the classroom, and there is a prevailing understanding that chaos should be avoided. Yet chaos can also be potent space or a source from which new things spring forth. This article investigates biblical, scientific, and cultural understandings of chaos to discover how these contribute to a revelatory metaphor…
Chaos in the fractional order Chen system and its control
International Nuclear Information System (INIS)
Li Chunguang; Chen Guanrong
2004-01-01
In this letter, we study the chaotic behaviors in the fractional order Chen system. We found that chaos exists in the fractional order Chen system with order less than 3. The lowest order we found to have chaos in this system is 2.1. Linear feedback control of chaos in this system is also studied
The Nature (and Nurture) of Children's Perceptions of Family Chaos
Hanscombe, Ken B.; Haworth, Claire M. A.; Davis, Oliver S. P.; Jaffee, Sara R.; Plomin, Robert
2010-01-01
Chaos in the home is a key environment in cognitive and behavioural development. However, we show that children's experience of home chaos is partly genetically mediated. We assessed children's perceptions of household chaos at ages 9 and 12 in 2337 pairs of twins. Using child-specific reports allowed us to use structural equation modelling to…
International Nuclear Information System (INIS)
Ge Zhengming; Chang Chingming; Chen Yensheng
2006-01-01
Anti-control of chaos of single time scale brushless dc motors (BLDCM) and chaos synchronization of different order systems are studied in this paper. By addition of an external nonlinear term, we can obtain anti-control of chaos. Then, by addition of the coupling terms, by the use of Lyapunov stability theorem and by the linearization of the error dynamics, chaos synchronization between a third-order BLDCM and a second-order Duffing system are presented
International Nuclear Information System (INIS)
Li Qianshu; Zhu Rui
2004-01-01
A three-variable model of the Belousov-Zhabotinsky reaction system subject to external sinusoidal perturbations is investigated by means of frequency spectrum analysis. In the period-1 window of the model, the transitions from periodicity to chaos are observed; in the chaotic window, the transitions from chaos to periodicity are found. The former might be understood by the circle map of two coupled oscillators, and the latter is partly explained by the resonance between the main frequency of the chaos and the frequency of the external periodic perturbations
Hyperbolic Chaos A Physicist’s View
Kuznetsov, Sergey P
2012-01-01
"Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos. This book is designed as a reference work for university professors and researchers in the fields of physics, mechanics, and engineering. Dr. Sergey P. Kuznetsov is a professor at the Department of Nonlinear Processes, Saratov State University, Russia.
Nonlinear dynamics and quantum chaos an introduction
Wimberger, Sandro
2014-01-01
The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.
Improved particle swarm optimization combined with chaos
International Nuclear Information System (INIS)
Liu Bo; Wang Ling; Jin Yihui; Tang Fang; Huang Dexian
2005-01-01
As a novel optimization technique, chaos has gained much attention and some applications during the past decade. For a given energy or cost function, by following chaotic ergodic orbits, a chaotic dynamic system may eventually reach the global optimum or its good approximation with high probability. To enhance the performance of particle swarm optimization (PSO), which is an evolutionary computation technique through individual improvement plus population cooperation and competition, hybrid particle swarm optimization algorithm is proposed by incorporating chaos. Firstly, adaptive inertia weight factor (AIWF) is introduced in PSO to efficiently balance the exploration and exploitation abilities. Secondly, PSO with AIWF and chaos are hybridized to form a chaotic PSO (CPSO), which reasonably combines the population-based evolutionary searching ability of PSO and chaotic searching behavior. Simulation results and comparisons with the standard PSO and several meta-heuristics show that the CPSO can effectively enhance the searching efficiency and greatly improve the searching quality
Entanglement as a signature of quantum chaos.
Wang, Xiaoguang; Ghose, Shohini; Sanders, Barry C; Hu, Bambi
2004-01-01
We explore the dynamics of entanglement in classically chaotic systems by considering a multiqubit system that behaves collectively as a spin system obeying the dynamics of the quantum kicked top. In the classical limit, the kicked top exhibits both regular and chaotic dynamics depending on the strength of the chaoticity parameter kappa in the Hamiltonian. We show that the entanglement of the multiqubit system, considered for both the bipartite and the pairwise entanglement, yields a signature of quantum chaos. Whereas bipartite entanglement is enhanced in the chaotic region, pairwise entanglement is suppressed. Furthermore, we define a time-averaged entangling power and show that this entangling power changes markedly as kappa moves the system from being predominantly regular to being predominantly chaotic, thus sharply identifying the edge of chaos. When this entangling power is averaged over all states, it yields a signature of global chaos. The qualitative behavior of this global entangling power is similar to that of the classical Lyapunov exponent.
Chaos Concepts, Control and Constructive Use
Bolotin, Yurii; Yanovsky, Vladimir
2009-01-01
The study of chaotic behaviour in nonlinear, dynamical systems is now a well established research domain with ramifications into all fields of sciences, spanning a vast range of applications, from celestial mechanics, via climate change, to the functioning of brownian motors in cells. A more recent discovery is that chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter itself for the system under investigation, stochastic resonance being a prime example. The present work is putting emphasis on the latter aspects, and after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing relevant algorithms for both Hamiltonian and dissipative systems amongst others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance and a survey of ratchet models. This short and concise pr...
Polynomial chaos functions and stochastic differential equations
International Nuclear Information System (INIS)
Williams, M.M.R.
2006-01-01
The Karhunen-Loeve procedure and the associated polynomial chaos expansion have been employed to solve a simple first order stochastic differential equation which is typical of transport problems. Because the equation has an analytical solution, it provides a useful test of the efficacy of polynomial chaos. We find that the convergence is very rapid in some cases but that the increased complexity associated with many random variables can lead to very long computational times. The work is illustrated by exact and approximate solutions for the mean, variance and the probability distribution itself. The usefulness of a white noise approximation is also assessed. Extensive numerical results are given which highlight the weaknesses and strengths of polynomial chaos. The general conclusion is that the method is promising but requires further detailed study by application to a practical problem in transport theory
Bifurcation and chaos in neural excitable system
International Nuclear Information System (INIS)
Jing Zhujun; Yang Jianping; Feng Wei
2006-01-01
In this paper, we investigate the dynamical behaviors of neural excitable system without periodic external current (proposed by Chialvo [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] and with periodic external current as system's parameters vary. The existence and stability of three fixed points, bifurcation of fixed points, the conditions of existences of fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using bifurcation theory and center manifold theorem. The chaotic existence in the sense of Marotto's definition of chaos is proved. We then give the numerical simulated results (using bifurcation diagrams, computations of Maximum Lyapunov exponent and phase portraits), which not only show the consistence with the analytic results but also display new and interesting dynamical behaviors, including the complete period-doubling and inverse period-doubling bifurcation, symmetry period-doubling bifurcations of period-3 orbit, simultaneous occurrence of two different routes (invariant cycle and period-doubling bifurcations) to chaos for a given bifurcation parameter, sudden disappearance of chaos at one critical point, a great abundance of period windows (period 2 to 10, 12, 19, 20 orbits, and so on) in transient chaotic regions with interior crises, strange chaotic attractors and strange non-chaotic attractor. In particular, the parameter k plays a important role in the system, which can leave the chaotic behavior or the quasi-periodic behavior to period-1 orbit as k varies, and it can be considered as an control strategy of chaos by adjusting the parameter k. Combining the existing results in [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] with the new results reported in this paper, a more complete description of the system is now obtained
Harnessing quantum transport by transient chaos.
Yang, Rui; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso; Pecora, Louis M
2013-03-01
Chaos has long been recognized to be generally advantageous from the perspective of control. In particular, the infinite number of unstable periodic orbits embedded in a chaotic set and the intrinsically sensitive dependence on initial conditions imply that a chaotic system can be controlled to a desirable state by using small perturbations. Investigation of chaos control, however, was largely limited to nonlinear dynamical systems in the classical realm. In this paper, we show that chaos may be used to modulate or harness quantum mechanical systems. To be concrete, we focus on quantum transport through nanostructures, a problem of considerable interest in nanoscience, where a key feature is conductance fluctuations. We articulate and demonstrate that chaos, more specifically transient chaos, can be effective in modulating the conductance-fluctuation patterns. Experimentally, this can be achieved by applying an external gate voltage in a device of suitable geometry to generate classically inaccessible potential barriers. Adjusting the gate voltage allows the characteristics of the dynamical invariant set responsible for transient chaos to be varied in a desirable manner which, in turn, can induce continuous changes in the statistical characteristics of the quantum conductance-fluctuation pattern. To understand the physical mechanism of our scheme, we develop a theory based on analyzing the spectrum of the generalized non-Hermitian Hamiltonian that includes the effect of leads, or electronic waveguides, as self-energy terms. As the escape rate of the underlying non-attracting chaotic set is increased, the imaginary part of the complex eigenenergy becomes increasingly large so that pointer states are more difficult to form, making smoother the conductance-fluctuation pattern.
Chaos synchronization of coupled hyperchaotic system
International Nuclear Information System (INIS)
Yang Lixin; Chu Yandong; Zhang Jiangang; Li Xianfeng
2009-01-01
Chaos synchronization, as an important topic, has become an active research subject in nonlinear science. Over the past two decades, chaos synchronization between nonlinear systems has been extensively studied, and many types of synchronization have been announced. This paper introduces synchronization of coupled hyperchaotic system, based on the Lapunov stability theory, asymptotic stability of the system is guaranteed by means of Lapunov function. The numerical simulation was provided in order to show the effectiveness of this method for the synchronization of the chaotic hyperchaotic Chen system and Rossler system.
An introduction to chaos theory in CFD
Pulliam, Thomas H.
1990-01-01
The popular subject 'chaos theory' has captured the imagination of a wide variety of scientists and engineers. CFD has always been faced with nonlinear systems and it is natural to assume that nonlinear dynamics will play a role at sometime in such work. This paper will attempt to introduce some of the concepts and analysis procedures associated with nonlinear dynamics theory. In particular, results from computations of an airfoil at high angle of attack which exhibits a sequence of bifurcations for single frequency unsteady shedding through period doublings cascading into low dimensional chaos are used to present and demonstrate various aspects of nonlinear dynamics in CFD.
Chaos and random matrices in supersymmetric SYK
Hunter-Jones, Nicholas; Liu, Junyu
2018-05-01
We use random matrix theory to explore late-time chaos in supersymmetric quantum mechanical systems. Motivated by the recent study of supersymmetric SYK models and their random matrix classification, we consider the Wishart-Laguerre unitary ensemble and compute the spectral form factors and frame potentials to quantify chaos and randomness. Compared to the Gaussian ensembles, we observe the absence of a dip regime in the form factor and a slower approach to Haar-random dynamics. We find agreement between our random matrix analysis and predictions from the supersymmetric SYK model, and discuss the implications for supersymmetric chaotic systems.
Signatures of chaos in the Brillouin zone.
Barr, Aaron; Barr, Ariel; Porter, Max D; Reichl, Linda E
2017-10-01
When the classical dynamics of a particle in a finite two-dimensional billiard undergoes a transition to chaos, the quantum dynamics of the particle also shows manifestations of chaos in the form of scarring of wave functions and changes in energy level spacing distributions. If we "tile" an infinite plane with such billiards, we find that the Bloch states on the lattice undergo avoided crossings, energy level spacing statistics change from Poisson-like to Wigner-like, and energy sheets of the Brillouin zone begin to "mix" as the classical dynamics of the billiard changes from regular to chaotic behavior.
Chaos in an imperfectly premixed model combustor.
Kabiraj, Lipika; Saurabh, Aditya; Karimi, Nader; Sailor, Anna; Mastorakos, Epaminondas; Dowling, Ann P; Paschereit, Christian O
2015-02-01
This article reports nonlinear bifurcations observed in a laboratory scale, turbulent combustor operating under imperfectly premixed mode with global equivalence ratio as the control parameter. The results indicate that the dynamics of thermoacoustic instability correspond to quasi-periodic bifurcation to low-dimensional, deterministic chaos, a route that is common to a variety of dissipative nonlinear systems. The results support the recent identification of bifurcation scenarios in a laminar premixed flame combustor (Kabiraj et al., Chaos: Interdiscip. J. Nonlinear Sci. 22, 023129 (2012)) and extend the observation to a practically relevant combustor configuration.
Chaotic dynamics and chaos control in nonlinear laser systems
International Nuclear Information System (INIS)
Fang Jinqing; Yao Weiguang
2001-01-01
Chaotic dynamics and chaos control have become a great challenge in nonlinear laser systems and its advances are reviewed mainly based on the ring cavity laser systems. The principle and stability conditions for time-delay feedback control are analyzed and applied to chaos control in the laser systems. Other advanced methods of chaos control, such as weak spatial perturbation and occasional proportional feedback technique, are discussed. Prospects of chaos control for application (such as improvement of laser power and performance, synchronized chaos secure communication and information processing) are pointed out finally
One-way hash function construction based on the spatiotemporal chaotic system
International Nuclear Information System (INIS)
Luo Yu-Ling; Du Ming-Hui
2012-01-01
Based on the spatiotemporal chaotic system, a novel algorithm for constructing a one-way hash function is proposed and analysed. The message is divided into fixed length blocks. Each message block is processed by the hash compression function in parallel. The hash compression is constructed based on the spatiotemporal chaos. In each message block, the ASCII code and its position in the whole message block chain constitute the initial conditions and the key of the hash compression function. The final hash value is generated by further compressing the mixed result of all the hash compression values. Theoretic analyses and numerical simulations show that the proposed algorithm presents high sensitivity to the message and key, good statistical properties, and strong collision resistance. (general)
Chaos and routes to chaos in coupled Duffing oscillators with multiple degrees of freedom
International Nuclear Information System (INIS)
Musielak, D.E.; Musielak, Z.E.; Benner, J.W.
2005-01-01
New results are reported on the routes to chaos in increasingly complex Duffing oscillator systems, which are formed by coupling several oscillators, thereby increasing the number of degrees of freedom. Other forms of increasing system complexity through distributed excitation, different forcing function phasing, different excitation frequency ratios, and higher order coupling are also studied. Changes in the quantitative aspects of the chaotic regions and in the routes to chaos of complex Duffing systems are investigated by performing numerical simulations. It is shown that the number of chaotic regions in these systems is significantly reduced when compared to the original Duffing system, and that crisis replaces period doubling as the dominant route to chaos when the number of degrees of freedom is increased. A new discovered phenomenon is that chaos emerges in the symmetrically and asymmetrically coupled Duffing oscillators only after the quasi-periodic torus breaks down through a 3-periodic and 2-periodic window, respectively
Resurvey of order and chaos in spinning compact binaries
International Nuclear Information System (INIS)
Wu Xin; Xie Yi
2008-01-01
This paper is mainly devoted to applying the invariant, fast, Lyapunov indicator to clarify some doubt regarding the apparently conflicting results of chaos in spinning compact binaries at the second-order post-Newtonian approximation of general relativity from previous literatures. It is shown with a number of examples that no single physical parameter or initial condition can be described as responsible for causing chaos, but a complicated combination of all parameters and initial conditions is responsible. In other words, a universal rule for the dependence of chaos on each parameter or initial condition cannot be found in general. Chaos does not depend only on the mass ratio, and the maximal spins do not necessarily bring the strongest effect of chaos. Additionally, chaos does not always become drastic when the initial spin vectors are nearly perpendicular to the orbital plane, and the alignment of spins cannot trigger chaos by itself
Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos
Directory of Open Access Journals (Sweden)
Bin Wang
2015-01-01
Full Text Available This paper investigates fuzzy synchronization for fractional order chaos via linear matrix inequality. Based on generalized Takagi-Sugeno fuzzy model, one efficient stability condition for fractional order chaos synchronization or antisynchronization is given. The fractional order stability condition is transformed into a set of linear matrix inequalities and the rigorous proof details are presented. Furthermore, through fractional order linear time-invariant (LTI interval theory, the approach is developed for fractional order chaos synchronization regardless of the system with uncertain parameters. Three typical examples, including synchronization between an integer order three-dimensional (3D chaos and a fractional order 3D chaos, anti-synchronization of two fractional order hyperchaos, and the synchronization between an integer order 3D chaos and a fractional order 4D chaos, are employed to verify the theoretical results.
Spatiotemporal Data Organization and Application Research
Tan, C.; Yan, S.
2017-09-01
Organization and management of spatiotemporal data is a key support technology for intelligence in all fields of the smart city. The construction of a smart city cannot be realized without spatiotemporal data. Oriented to support intelligent applications this paper proposes an organizational model for spatiotemporal data, and details the construction of a spatiotemporal big data calculation, analysis, and service framework for highly efficient management and intelligent application of spatiotemporal data for the entire data life cycle.
Chaos, strange attractors, and fractal basin boundaries
International Nuclear Information System (INIS)
Grebogi, C.
1989-01-01
Even simple mathematical models of physical systems are often observed to exhibit rather complex time evolution. Upon observation, one often has the feeling that such complex time evolutions could, for most practical purposes, be best characterized by statistical properties rather than by detailed knowledge of the exact process. In such situations, the time evolution is often labeled chaotic or turbulent. The study of chaotic dynamics has recently undergone explosive growth. Motivation for this comes partly from the fact that chaotic dynamics is being found to be of fundamental importance in many branches of science and engineering. Examples illustrating the wide-ranging applications of chaotic dynamics to scientific and engineering problems are the following: fluid dynamics, biology, ecology, meteorology, optics, electronics, mechanical engineerings, physiology, economics, chemistry, accelerator technology, thermonuclear fusion, celestial mechanics, and oceanography. The common element in all of the above topics is that they involve nonlinearity in some way. Indeed chaos is expected to be common whenever nonlinearity plays a role. Since nonlinearity is inherent in so much of science and engineering, an understanding of chaos is essential. Given the varied nature of applications where chaos is important, it is natural that researchers in a broad range of fields have become interested in and have contributed to recent developments in chaos
Chaos control applied to heart rhythm dynamics
Energy Technology Data Exchange (ETDEWEB)
Borem Ferreira, Bianca, E-mail: biaborem@gmail.com [Universidade Federal do Rio de Janeiro, COPPE, Department of Mechanical Engineering, P.O. Box 68.503, 21.941.972 Rio de Janeiro, RJ (Brazil); Souza de Paula, Aline, E-mail: alinedepaula@unb.br [Universidade de Brasi' lia, Department of Mechanical Engineering, 70.910.900 Brasilia, DF (Brazil); Amorim Savi, Marcelo, E-mail: savi@mecanica.ufrj.br [Universidade Federal do Rio de Janeiro, COPPE, Department of Mechanical Engineering, P.O. Box 68.503, 21.941.972 Rio de Janeiro, RJ (Brazil)
2011-08-15
Highlights: > A natural cardiac pacemaker is modeled by a modified Van der Pol oscillator. > Responses related to normal and chaotic, pathological functioning of the heart are investigated. > Chaos control methods are applied to avoid pathological behaviors of heart dynamics. > Different approaches are treated: stabilization of unstable periodic orbits and chaos suppression. - Abstract: The dynamics of cardiovascular rhythms have been widely studied due to the key aspects of the heart in the physiology of living beings. Cardiac rhythms can be either periodic or chaotic, being respectively related to normal and pathological physiological functioning. In this regard, chaos control methods may be useful to promote the stabilization of unstable periodic orbits using small perturbations. In this article, the extended time-delayed feedback control method is applied to a natural cardiac pacemaker described by a mathematical model. The model consists of a modified Van der Pol equation that reproduces the behavior of this pacemaker. Results show the ability of the chaos control strategy to control the system response performing either the stabilization of unstable periodic orbits or the suppression of chaotic response, avoiding behaviors associated with critical cardiac pathologies.
Synchronization of chaos by nonlinear feedback
International Nuclear Information System (INIS)
Cheng Yanxiang
1995-01-01
The authors point out that synchronization of chaos may also be achieved by a nonlinear feedback without decomposing the original system. They apply the idea to the Lorentz system, and discuss several forms of nonlinear feedbacks by Lyapunov function and numerical method
Chaos synchronization based on contraction principle
International Nuclear Information System (INIS)
Wang Junwei; Zhou Tianshou
2007-01-01
This paper introduces contraction principle. Based on such a principle, a novel scheme is proposed to synchronize coupled systems with global diffusive coupling. A rigorous sufficient condition on chaos synchronization is derived. As an example, coupled Lorenz systems with nearest-neighbor diffusive coupling are investigated, and numerical simulations are given to validate the proposed synchronization approach
Importance of packing in spiral defect chaos
Indian Academy of Sciences (India)
We develop two measures to characterize the geometry of patterns exhibited by the state of spiral defect chaos, a weakly turbulent regime of Rayleigh-Bénard convection. These describe the packing of contiguous stripes within the pattern by quantifying their length and nearest-neighbor distributions. The distributions ...
Characterizing and quantifying quantum chaos with quantum ...
Indian Academy of Sciences (India)
We explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. The tomographic record consists of a time series of expectation values of a Hermitian operator evolving under the application of the Floquet operator of a quantum map that possesses (or lacks) time-reversal ...
Quantum Chaos via the Quantum Action
Kröger, H.
2002-01-01
We discuss the concept of the quantum action with the purpose to characterize and quantitatively compute quantum chaos. As an example we consider in quantum mechanics a 2-D Hamiltonian system - harmonic oscillators with anharmonic coupling - which is classically a chaotic system. We compare Poincar\\'e sections obtained from the quantum action with those from the classical action.
Chaos in schizophrenia associations, reality or metaphor?
Czech Academy of Sciences Publication Activity Database
Bob, P.; Šusta, M.; Chládek, Jan; Glaslová, K.; Paluš, Milan
2009-01-01
Roč. 73, č. 3 (2009), s. 179-185 ISSN 0167-8760 Institutional research plan: CEZ:AV0Z20650511; CEZ:AV0Z10300504 Keywords : Chaos * Schizophrenia * Associations * Electrodermal activity * Lyapunov exponent Subject RIV: FH - Neurology Impact factor: 3.045, year: 2009
Chaos synchronization of nonlinear Bloch equations
International Nuclear Information System (INIS)
Park, Ju H.
2006-01-01
In this paper, the problem of chaos synchronization of Bloch equations is considered. A novel nonlinear controller is designed based on the Lyapunov stability theory. The proposed controller ensures that the states of the controlled chaotic slave system asymptotically synchronizes the states of the master system. A numerical example is given to illuminate the design procedure and advantage of the result derived
Melnikov's vector - a 'measure of chaos'
International Nuclear Information System (INIS)
Haidegger, W.
1990-01-01
In this paper a method of global perturbation theory, the method of Melnikov, is introduced as a way of detecting Smale horseshoe chaos near homoclinic and heteroclinic orbits. Special emphasis is put on the point that Melnikov's method is of great practical value, as it yields computable, often even analytically solvable expressions. (Author) 18 refs
Order, chaos and nuclear dynamics: An introduction
International Nuclear Information System (INIS)
Swiatecki, W.J.
1990-08-01
This is an introductory lecture illustrating by simple examples the anticipated effect on collective nuclear dynamics of a transition from order to chaos in the motions of nucleons inside an idealized nucleus. The destruction of order is paralleled by a transition from a rubber-like to a honey-like behaviour of the independent-particle nuclear model. 10 refs., 6 figs
Chaos and fractals an elementary introduction
Feldman, David P
2012-01-01
For students with a background in elementary algebra, this text provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia sets and the Mandelbrot set, power laws, and cellular automata.
Chaos in Practice: Techniques for Career Counsellors
Pryor, Robert G. L.; Bright, Jim
2005-01-01
The chaos theory of careers emphasises continual change, the centrality and importance of chance events, the potential of minor events to have disproportionately large impacts on subsequent events, and the capacity for dramatic phase shifts in career behaviour. This approach challenges traditional approaches to career counselling, assumptions…
Controlling chaos in discontinuous dynamical systems
International Nuclear Information System (INIS)
Danca, Marius-F.
2004-01-01
In this paper we consider the possibility to implement the technique of changes in the system variables to control the chaos introduced by Gueemez and Matias for continuous dynamical systems to a class of discontinuous dynamical systems. The approach is realized via differential inclusions following the Filippov theory. Three practical examples are considered
[Chaos theory: a fascinating concept for oncologists].
Denis, F; Letellier, C
2012-05-01
The oncologist is confronted daily by questions related to the fact that any patient presents a specific evolution for his cancer: he is challenged by very different, unexpected and often unpredictable outcomes, in some of his patients. The mathematical approach used today to describe this evolution has recourse to statistics and probability laws: such an approach does not ultimately apply to one particular patient, but to a given more or less heterogeneous population. This approach therefore poorly characterizes the dynamics of this disease and does not allow to state whether a patient is cured, to predict if he will relapse and when this could occur, and in what form, nor to predict the response to treatment and, in particular, to radiation therapy. Chaos theory, not well known by oncologists, could allow a better understanding of these issues. Developed to investigate complex systems producing behaviours that cannot be predicted due to a great sensitivity to initial conditions, chaos theory is rich of suitable concepts for a new approach of cancer dynamics. This article is three-fold: to provide a brief introduction to chaos theory, to clarify the main connecting points between chaos and carcinogenesis and to point out few promising research perspectives, especially in radiotherapy. Copyright © 2012 Société française de radiothérapie oncologique (SFRO). Published by Elsevier SAS. All rights reserved.
Chaos in nuclei: Theory and experiment
Muñoz, L.; Molina, R. A.; Gómez, J. M. G.
2018-05-01
During the last three decades the quest for chaos in nuclei has been quite intensive, both with theoretical calculations using nuclear models and with detailed analyses of experimental data. In this paper we outline the concept and characteristics of quantum chaos in two different approaches, the random matrix theory fluctuations and the time series fluctuations. Then we discuss the theoretical and experimental evidence of chaos in nuclei. Theoretical calculations, especially shell-model calculations, have shown a strongly chaotic behavior of bound states in regions of high level density. The analysis of experimental data has shown a strongly chaotic behavior of nuclear resonances just above the one-nucleon emission threshold. For bound states, combining experimental data of a large number of nuclei, a tendency towards chaotic motion is observed in spherical nuclei, while deformed nuclei exhibit a more regular behavior associated to the collective motion. On the other hand, it had never been possible to observe chaos in the experimental bound energy levels of any single nucleus. However, the complete experimental spectrum of the first 151 states up to excitation energies of 6.20 MeV in the 208Pb nucleus have been recently identified and the analysis of its spectral fluctuations clearly shows the existence of chaotic motion.
Transient chaos in weakly coupled Josephson junctions
Energy Technology Data Exchange (ETDEWEB)
Koch, B P; Bruhn, B
1988-01-01
This paper considers periodic excitations and coupling of nonlinear Josephson oscillators. The Melnikov method is used to prove the existence of horseshoes in the dynamics. The coupling of two systems yields a reduction of the chaos threshold in comparison with the corresponding threshold of a single system. For some selected parameter values the theoretical predictions are checked by numerical methods.
Quantum chaos of the 2-level atom
Energy Technology Data Exchange (ETDEWEB)
Graham, R; Hoehnerbach, M [Essen Univ. (Germany, F.R.). Fachbereich Physik
1984-01-01
Recent work on the two-level atom coupled to a single mode of the electromagnetic field is reviewed from the point of view of 'quantum chaos', defined as the quantum behavior of a dynamical system which is non-integrable in the classical limit. Spectral properties and the dynamics of occupation probabilities including their revivals are obtained without making the rotating wave approximation.
A Framework for Chaos Theory Career Counselling
Pryor, Robert G. L.
2010-01-01
Theory in career development counselling provides a map that counsellors can use to understand and structure the career counselling process. It also provides a means to communicate this understanding and structuring to their clients as part of the counselling intervention. The chaos theory of careers draws attention to the complexity,…
Chaos theory: A fascinating concept for oncologists
International Nuclear Information System (INIS)
Denis, F.; Letellier, C.
2012-01-01
The oncologist is confronted daily by questions related to the fact that any patient presents a specific evolution for his cancer: he is challenged by very different, unexpected and often unpredictable outcomes, in some of his patients. The mathematical approach used today to describe this evolution has recourse to statistics and probability laws: such an approach does not ultimately apply to one particular patient, but to a given more or less heterogeneous population. This approach therefore poorly characterizes the dynamics of this disease and does not allow to state whether a patient is cured, to predict if he will relapse and when this could occur, and in what form, nor to predict the response to treatment and, in particular, to radiation therapy. Chaos theory, not well known by oncologists, could allow a better understanding of these issues. Developed to investigate complex systems producing behaviours that cannot be predicted due to a great sensitivity to initial conditions, chaos theory is rich of suitable concepts for a new approach of cancer dynamics. This article is three-fold: to provide a brief introduction to chaos theory, to clarify the main connecting points between chaos and carcinogenesis and to point out few promising research perspectives, especially in radiotherapy. (authors)
Meeting energy demands: chaos round the corner
Energy Technology Data Exchange (ETDEWEB)
Petrick, A J
1976-02-01
In this interview with Coal Gold and Base Minerals, Dr. Petrick talks about several aspects of his recent report and indicates that it will only be in the next 20 or 30 years that the real energy crisis will appear. He goes on to warn of possible chaos if energy is continually squandered throughout the world.
CHAOS-BASED ADVANCED ENCRYPTION STANDARD
Abdulwahed, Naif B.
2013-01-01
This thesis introduces a new chaos-based Advanced Encryption Standard (AES). The AES is a well-known encryption algorithm that was standardized by U.S National Institute of Standard and Technology (NIST) in 2001. The thesis investigates and explores
Analysis of chaos in plasma turbulence
DEFF Research Database (Denmark)
Pedersen, T.S.; Michelsen, Poul; Juul Rasmussen, J.
1996-01-01
-stationary turbulent state is reached in a finite time, independent of the initial conditions. Different regimes of the turbulent state can be obtained by varying the coupling parameter C, related to the parallel electron dynamics. The turbulence is described by using particle tracking and tools from chaos analysis...
Chaos in plasma simulation and experiment
International Nuclear Information System (INIS)
Watts, C.; Sprott, J.C.
1993-09-01
We investigate the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas using data from both numerical simulations and experiment. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos. These tools include phase portraits and Poincard sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulate the plasma dynamics. These are -the DEBS code, which models global RFP dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low,dimensional chaos and simple determinism. Experimental data were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or other simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system
Chaos in plasma simulation and experiment
Energy Technology Data Exchange (ETDEWEB)
Watts, C. [Texas Univ., Austin, TX (United States). Fusion Research Center; Newman, D.E. [Oak Ridge National Lab., TN (United States); Sprott, J.C. [Wisconsin Univ., Madison, WI (United States). Plasma Physics Research
1993-09-01
We investigate the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas using data from both numerical simulations and experiment. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos. These tools include phase portraits and Poincard sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulate the plasma dynamics. These are -the DEBS code, which models global RFP dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low,dimensional chaos and simple determinism. Experimental data were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or other simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system.
CHAOS-BASED ADVANCED ENCRYPTION STANDARD
Abdulwahed, Naif B.
2013-05-01
This thesis introduces a new chaos-based Advanced Encryption Standard (AES). The AES is a well-known encryption algorithm that was standardized by U.S National Institute of Standard and Technology (NIST) in 2001. The thesis investigates and explores the behavior of the AES algorithm by replacing two of its original modules, namely the S-Box and the Key Schedule, with two other chaos- based modules. Three chaos systems are considered in designing the new modules which are Lorenz system with multiplication nonlinearity, Chen system with sign modules nonlinearity, and 1D multiscroll system with stair case nonlinearity. The three systems are evaluated on their sensitivity to initial conditions and as Pseudo Random Number Generators (PRNG) after applying a post-processing technique to their output then performing NIST SP. 800-22 statistical tests. The thesis presents a hardware implementation of dynamic S-Boxes for AES that are populated using the three chaos systems. Moreover, a full MATLAB package to analyze the chaos generated S-Boxes based on graphical analysis, Walsh-Hadamard spectrum analysis, and image encryption analysis is developed. Although these S-Boxes are dynamic, meaning they are regenerated whenever the encryption key is changed, the analysis results show that such S-Boxes exhibit good properties like the Strict Avalanche Criterion (SAC) and the nonlinearity and in the application of image encryption. Furthermore, the thesis presents a new Lorenz-chaos-based key expansion for the AES. Many researchers have pointed out that there are some defects in the original key expansion of AES and thus have motivated such chaos-based key expansion proposal. The new proposed key schedule is analyzed and assessed in terms of confusion and diffusion by performing the frequency and SAC test respectively. The obtained results show that the new proposed design is more secure than the original AES key schedule and other proposed designs in the literature. The proposed
Chaos: A Very Short Introduction
Energy Technology Data Exchange (ETDEWEB)
Klages, R [School of Mathematical Sciences, Mile End Road, London, E1 4NS (United Kingdom)
2007-07-20
This book is a new volume of a series designed to introduce the curious reader to anything from ancient Egypt and Indian philosophy to conceptual art and cosmology. Very handy in pocket size, Chaos promises an introduction to fundamental concepts of nonlinear science by using mathematics that is 'no more complicated than X=2. Anyone who ever tried to give a popular science account of research knows that this is a more challenging task than writing an ordinary research article. Lenny Smith brilliantly succeeds to explain in words, in pictures and by using intuitive models the essence of mathematical dynamical systems theory and time series analysis as it applies to the modern world. In a more technical part he introduces the basic terms of nonlinear theory by means of simple mappings. He masterly embeds this analysis into the social, historical and cultural context by using numerous examples, from poems and paintings over chess and rabbits to Olbers' paradox, card games and 'phynance'. Fundamental problems of the modelling of nonlinear systems like the weather, sun spots or golf balls falling through an array of nails are discussed from the point of view of mathematics, physics and statistics by touching upon philosophical issues. At variance with Laplace's demon, Smith's 21st century demon makes 'real world' observations only with limited precision. This poses a severe problem to predictions derived from complex chaotic models, where small variations of initial conditions typically yield totally different outcomes. As Smith argues, this difficulty has direct implications on decision-making in everyday modern life. However, it also asks for an inherently probabilistic theory, which somewhat reminds us of what we are used to in the microworld. There is little to criticise in this nice little book except that some figures are of poor quality thus not really reflecting the beauty of fractals and other wonderful objects in this
Chaos: A Very Short Introduction
International Nuclear Information System (INIS)
Klages, R
2007-01-01
This book is a new volume of a series designed to introduce the curious reader to anything from ancient Egypt and Indian philosophy to conceptual art and cosmology. Very handy in pocket size, Chaos promises an introduction to fundamental concepts of nonlinear science by using mathematics that is 'no more complicated than X=2. Anyone who ever tried to give a popular science account of research knows that this is a more challenging task than writing an ordinary research article. Lenny Smith brilliantly succeeds to explain in words, in pictures and by using intuitive models the essence of mathematical dynamical systems theory and time series analysis as it applies to the modern world. In a more technical part he introduces the basic terms of nonlinear theory by means of simple mappings. He masterly embeds this analysis into the social, historical and cultural context by using numerous examples, from poems and paintings over chess and rabbits to Olbers' paradox, card games and 'phynance'. Fundamental problems of the modelling of nonlinear systems like the weather, sun spots or golf balls falling through an array of nails are discussed from the point of view of mathematics, physics and statistics by touching upon philosophical issues. At variance with Laplace's demon, Smith's 21st century demon makes 'real world' observations only with limited precision. This poses a severe problem to predictions derived from complex chaotic models, where small variations of initial conditions typically yield totally different outcomes. As Smith argues, this difficulty has direct implications on decision-making in everyday modern life. However, it also asks for an inherently probabilistic theory, which somewhat reminds us of what we are used to in the microworld. There is little to criticise in this nice little book except that some figures are of poor quality thus not really reflecting the beauty of fractals and other wonderful objects in this field. I feel that occasionally the book
THEORY OF SECULAR CHAOS AND MERCURY'S ORBIT
International Nuclear Information System (INIS)
Lithwick, Yoram; Wu Yanqin
2011-01-01
We study the chaotic orbital evolution of planetary systems, focusing on secular (i.e., orbit-averaged) interactions, which dominate on long timescales. We first focus on the evolution of a test particle that is forced by multiple planets. To linear order in eccentricity and inclination, its orbit precesses with constant frequencies. But nonlinearities modify the frequencies, and can shift them into and out of resonance with either the planets' eigenfrequencies (forming eccentricity or inclination secular resonances), or with linear combinations of those frequencies (forming mixed high-order secular resonances). The overlap of these nonlinear secular resonances drives secular chaos. We calculate the locations and widths of nonlinear secular resonances, display them together on a newly developed map (the 'map of the mean momenta'), and find good agreement between analytical and numerical results. This map also graphically demonstrates how chaos emerges from overlapping secular resonances. We then apply this newfound understanding to Mercury to elucidate the origin of its orbital chaos. We find that since Mercury's two free precession frequencies (in eccentricity and inclination) lie within ∼25% of two other eigenfrequencies in the solar system (those of the Jupiter-dominated eccentricity mode and the Venus-dominated inclination mode), secular resonances involving these four modes overlap and cause Mercury's chaos. We confirm this with N-body integrations by showing that a slew of these resonant angles alternately librate and circulate. Our new analytical understanding allows us to calculate the criterion for Mercury to become chaotic: Jupiter and Venus must have eccentricity and inclination of a few percent. The timescale for Mercury's chaotic diffusion depends sensitively on the forcing. As it is, Mercury appears to be perched on the threshold for chaos, with an instability timescale comparable to the lifetime of the solar system.
Energy Technology Data Exchange (ETDEWEB)
Lopez de Bertodano, Martín, E-mail: bertodan@purdue.edu [School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907 (United States); Fullmer, William D. [Department of Chemical and Biological Engineering, U. of Colorado, Boulder, CO 80309 (United States); Clausse, Alejandro [CNEA-CONICET and Universidad Nacional del Centro, 7000 Tandil (Argentina)
2016-12-15
A 1D TFM numerical simulation of near horizontal stratified two-phase flow is performed where the TFM, including surface tension and viscous stresses, is simplified to a two-equation model using the fixed-flux approximation. As the angle of inclination of the channel increases so does the driving body force, so the flow becomes KH unstable, and waves grow and develop nonlinearities. It is shown that these waves grow until they reach a limit cycle due to viscous dissipation at wave fronts. Upon further inclination of the channel, chaos is observed. The appearance of chaos in a 1D TFM implies a nonlinear process that transfers energy intermittently from long wavelengths where energy is produced to short wavelengths where energy is dissipated by viscosity, so that an averaged energy equilibrium in frequency space is attained. This is comparable to the well-known turbulent stability mechanism of the multi-dimensional Navier–Stokes equations, i.e., chaos implies Lyapunov stability, but in this case it is strictly a two-phase phenomenon.
Mondal, S; Pawar, S A; Sujith, R I
2017-10-01
Thermoacoustic instability, caused by a positive feedback between the unsteady heat release and the acoustic field in a combustor, is a major challenge faced in most practical combustors such as those used in rockets and gas turbines. We employ the synchronization theory for understanding the coupling between the unsteady heat release and the acoustic field of a thermoacoustic system. Interactions between coupled subsystems exhibiting different collective dynamics such as periodic, quasiperiodic, and chaotic oscillations are addressed. Even though synchronization studies have focused on different dynamical states separately, synchronous behaviour of two coupled systems exhibiting a quasiperiodic route to chaos has not been studied. In this study, we report the first experimental observation of different synchronous behaviours between two subsystems of a thermoacoustic system exhibiting such a transition as reported in Kabiraj et al. [Chaos 22, 023129 (2012)]. A rich variety of synchronous behaviours such as phase locking, intermittent phase locking, and phase drifting are observed as the dynamics of such subsystem change. The observed synchronization behaviour is further characterized using phase locking value, correlation coefficient, and relative mean frequency. These measures clearly reveal the boundaries between different states of synchronization.
Defects and spatiotemporal disorder in a pattern of falling liquid columns
Brunet, Philippe; Limat, Laurent
2004-10-01
Disordered regimes of a one-dimensional pattern of liquid columns hanging below an overflowing circular dish are investigated experimentally. The interaction of two basic dynamical modes (oscillations and drift) combined with the occurrence of defects (birth of new columns, disappearances by coalescences of two columns) leads to spatiotemporal chaos. When the flow rate is progressively increased, a continuous transition between transient and permanent chaos is pointed into evidence. We introduce the rate of defects as the sole relevant quantity to quantify this “turbulence” without ambiguity. Statistics on both transient and endlessly chaotic regimes enable to define a critical flow rate around which exponents are extracted. Comparisons are drawn with other interfacial pattern-forming systems, where transition towards chaos follows similar steps. Qualitatively, careful examinations of the global dynamics show that the contamination processes are nonlocal and involve the propagation of blocks of elementary laminar states (such as propagative domains or local oscillations), emitted near the defects, which turn out to be essential ingredients of this self-sustained disorder.
Phase Chaos and Multistability in the Discrete Kuramoto Model
DEFF Research Database (Denmark)
Maistrenko, V. L.; Vasylenko, A. A.; Maistrenko, Y. L.
2008-01-01
The paper describes the appearance of a novel high-dimensional chaotic regime, called phase chaos, in the discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It is caused by the nonlinear interact......The paper describes the appearance of a novel high-dimensional chaotic regime, called phase chaos, in the discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It is caused by the nonlinear...... interaction of the oscillators, while the individual oscillators behave periodically when left uncoupled. For the four-dimensional discrete Kuramoto model, we outline the region of phase chaos in the parameter plane, distinguish the region where the phase chaos coexists with other periodic attractors...
Chaos in electric drive systems analysis control and application
Chau, K T
2011-01-01
In Chaos in Electric Drive Systems: Analysis, Control and Application authors Chau and Wang systematically introduce an emerging technology of electrical engineering that bridges abstract chaos theory and practical electric drives. The authors consolidate all important information in this interdisciplinary technology, including the fundamental concepts, mathematical modeling, theoretical analysis, computer simulation, and hardware implementation. The book provides comprehensive coverage of chaos in electric drive systems with three main parts: analysis, control and application. Corresponding drive systems range from the simplest to the latest types: DC, induction, synchronous reluctance, switched reluctance, and permanent magnet brushless drives.The first book to comprehensively treat chaos in electric drive systemsReviews chaos in various electrical engineering technologies and drive systemsPresents innovative approaches to stabilize and stimulate chaos in typical drivesDiscusses practical application of cha...
Lü, Hua-Ping; Wang, Shi-Hong; Li, Xiao-Wen; Tang, Guo-Ning; Kuang, Jin-Yu; Ye, Wei-Ping; Hu, Gang
2004-06-01
Two-dimensional one-way coupled map lattices are used for cryptography where multiple space units produce chaotic outputs in parallel. One of the outputs plays the role of driving for synchronization of the decryption system while the others perform the function of information encoding. With this separation of functions the receiver can establish a self-checking and self-correction mechanism, and enjoys the advantages of both synchronous and self-synchronizing schemes. A comparison between the present system with the system of advanced encryption standard (AES) is presented in the aspect of channel noise influence. Numerical investigations show that our system is much stronger than AES against channel noise perturbations, and thus can be better used for secure communications with large channel noise.
Suppression of spatio-temporal chaos in simple models of re-entrant fibrillations
Energy Technology Data Exchange (ETDEWEB)
Vysotsky, Semion A [Student, Faculty of Physics, M.V.Lomonosov Moscow State Universitry, Leninskie Gory, 119992 Moscow (Russian Federation); Cheremin, Ruslan V [Research Scientist, Faculty of Physics, M.V.Lomonosov Moscow State Universitry, Leninskie Gory, 119992 Moscow (Russian Federation); Loskutov, Alexander [Professor, Faculty of Physics, M.V.Lomonosov Moscow State Universitry, Leninskie Gory, 119992 Moscow (Russian Federation)
2005-01-01
On the basis of the FitzHugh-Nagumo-type model we investigate the possibility of suppression of the spiral wave turbulence by weak pacemaker excitations. We consider different ways of media stabilization and study the dependence of the suppression efficiency on the excitation shape and the media parameters. Also, we analyze the frequency of target waves in the unperturbed media as a function of the external force frequency. Applications of the obtained results to cardiac rhythm pathologies are considered.
Synchronizing spatio-temporal chaos with imperfect models: A stochastic surface growth picture
International Nuclear Information System (INIS)
Pazó, Diego; López, Juan M.; Rodríguez, Miguel A.; Gallego, Rafael
2014-01-01
We study the synchronization of two spatially extended dynamical systems where the models have imperfections. We show that the synchronization error across space can be visualized as a rough surface governed by the Kardar-Parisi-Zhang equation with both upper and lower bounding walls corresponding to nonlinearities and model discrepancies, respectively. Two types of model imperfections are considered: parameter mismatch and unresolved fast scales, finding in both cases the same qualitative results. The consistency between different setups and systems indicates that the results are generic for a wide family of spatially extended systems
Influence of solitons on the transition to spatiotemporal chaos in coupled map lattices
DEFF Research Database (Denmark)
Mikkelsen, R.; van Hecke, M.; Bohr, Tomas
2003-01-01
We study the transition from laminar to chaotic behavior in deterministic chaotic coupled map lattices and in an extension of the stochastic Domany-Kinzel cellular automaton [E. Domany and W. Kinzel, Phys. Rev. Lett. 53, 311 (1984)]. For the deterministic coupled map lattices, we find evidence th...
Synchronization of discrete-time spatiotemporal chaos via adaptive fuzzy control
International Nuclear Information System (INIS)
Xue Yueju; Yang Shiyuan
2003-01-01
A discrete-time adaptive fuzzy control scheme is presented to synchronize model-unknown coupled Henon-map lattices (CHMLs). The proposed method is robust to approximate errors, parameter mismatches and disturbances, because it integrates the merits of the adaptive fuzzy systems and the variable structure control with a sector. The simulation results of synchronization of CHMLs show that it not only can synchronize model-unknown CHMLs but also is robust against parameter mismatches and noise of the systems. These merits are advantageous for engineering realization
Synchronization of discrete-time spatiotemporal chaos via adaptive fuzzy control
Energy Technology Data Exchange (ETDEWEB)
Xue Yueju E-mail: xueyj@mail.tsinghua.edu.cn; Yang Shiyuan E-mail: ysy-dau@tsinghua.edu.cn
2003-08-01
A discrete-time adaptive fuzzy control scheme is presented to synchronize model-unknown coupled Henon-map lattices (CHMLs). The proposed method is robust to approximate errors, parameter mismatches and disturbances, because it integrates the merits of the adaptive fuzzy systems and the variable structure control with a sector. The simulation results of synchronization of CHMLs show that it not only can synchronize model-unknown CHMLs but also is robust against parameter mismatches and noise of the systems. These merits are advantageous for engineering realization.
Spatiotemporal chaos in the dynamics of buoyantly and diffusively unstable chemical fronts
Baroni, M. P. M. A.; Guéron, E.; De Wit, A.
2012-03-01
Nonlinear dynamics resulting from the interplay between diffusive and buoyancy-driven Rayleigh-Taylor (RT) instabilities of autocatalytic traveling fronts are analyzed numerically for various values of the relevant parameters. These are the Rayleigh numbers of the reactant A and autocatalytic product B solutions as well as the ratio D =DB/DA between the diffusion coefficients of the two key chemical species. The interplay between the coarsening dynamics characteristic of the RT instability and the constant short wavelength modulation of the diffusive instability can lead in some regimes to complex dynamics dominated by irregular succession of birth and death of fingers. By using spectral entropy measurements, we characterize the transition between order and spatial disorder in this system. The analysis of the power spectrum and autocorrelation function, moreover, identifies similarities between the various spatial patterns. The contribution of the diffusive instability to the complex dynamics is discussed.
Spatiotemporal Data Mining: A Computational Perspective
Directory of Open Access Journals (Sweden)
Shashi Shekhar
2015-10-01
Full Text Available Explosive growth in geospatial and temporal data as well as the emergence of new technologies emphasize the need for automated discovery of spatiotemporal knowledge. Spatiotemporal data mining studies the process of discovering interesting and previously unknown, but potentially useful patterns from large spatiotemporal databases. It has broad application domains including ecology and environmental management, public safety, transportation, earth science, epidemiology, and climatology. The complexity of spatiotemporal data and intrinsic relationships limits the usefulness of conventional data science techniques for extracting spatiotemporal patterns. In this survey, we review recent computational techniques and tools in spatiotemporal data mining, focusing on several major pattern families: spatiotemporal outlier, spatiotemporal coupling and tele-coupling, spatiotemporal prediction, spatiotemporal partitioning and summarization, spatiotemporal hotspots, and change detection. Compared with other surveys in the literature, this paper emphasizes the statistical foundations of spatiotemporal data mining and provides comprehensive coverage of computational approaches for various pattern families. ISPRS Int. J. Geo-Inf. 2015, 4 2307 We also list popular software tools for spatiotemporal data analysis. The survey concludes with a look at future research needs.
Approximate motion integrals and the quantum chaos problem
International Nuclear Information System (INIS)
Bunakov, V.E.; Ivanov, I.B.
2001-01-01
One discusses the problem of occurrence and seek for the motion integrals in the stationary quantum mechanics and its relation to the quantum chaos. One studies decomposition of quantum numbers and derives the criterion of chaos. To seek the motion integrals one applies the convergence method. One derived the approximate integrals in the Hennone-Hales problem. One discusses the problem of compatibility of chaos and integrability [ru
Nonlinear physics: Catastrophe, chaos and complexity
International Nuclear Information System (INIS)
Arecchi, F.T.
1992-01-01
Currently in the world of physics, there is open debate on the role of the three C's - catastrophe, chaos and complexity. Seen as new ideas or paradigms, incapable of being harmonized within the realm of traditional physics, these terms seem to be creating turmoil in the classical physics establishment whose foundations date back to the early seventeenth century. This paper first defines catastrophe, chaos and complexity and shows how these terms are all connected to nonlinear dynamics and how they have long since been present within scientific treatises. It also evidences the relationship of the three C's with the concept of organization, inappropriately called self-organization, and with recognition and decisional strategies of cognitive systems. Relevant to natural science, the development of these considerations is necessitating the re-examination of the role and capabilities of human knowledge and a return to inter-disciplinary scientific-philosophical debate
Communication with spatial periodic chaos synchronization
International Nuclear Information System (INIS)
Zhou, J.; Huang, H.B.; Qi, G.X.; Yang, P.; Xie, X.
2005-01-01
Based on the spatial periodic chaos synchronization in coupled ring and linear arrays, we proposed a random high-dimensional chaotic encryption scheme. The transmitter can choose hyperchaotic signals randomly from the ring at any different time and simultaneously transmit the information of chaotic oscillators in the ring to receiver through public channel, so that the message can be masked by different hyperchaotic signals in different time intervals during communication, and the receiver can decode the message based on chaos synchronization but the attacker does not know the random hyperchaotic dynamics and cannot decode the message. Furthermore, the high sensitivity to the symmetry of the coupling structure makes the attacker very difficult to obtain any useful message from the channel
An exploration of dynamical systems and chaos
Argyris, John H; Haase, Maria; Friedrich, Rudolf
2015-01-01
This book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems with particular emphasis on the exploration of chaotic phenomena. The self-contained introductory presentation is addressed both to those who wish to study the physics of chaotic systems and non-linear dynamics intensively as well as those who are curious to learn more about the fascinating world of chaotic phenomena. Basic concepts like Poincaré section, iterated mappings, Hamiltonian chaos and KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity and renormalisation and transitions to chaos are thoroughly explained. To facilitate comprehension, mathematical concepts and tools are introduced in short sub-sections. The text is supported by numerous computer experiments and a multitude of graphical illustrations and colour plates emphasising the geometrical and topological characteristics of the underlying dynamics. This volume is a completely revised and enlar...
Inequivalent topologies of chaos in simple equations
International Nuclear Information System (INIS)
Letellier, Christophe; Roulin, Elise; Roessler, Otto E.
2006-01-01
In the 1970, one of us introduced a few simple sets of ordinary differential equations as examples showing different types of chaos. Most of them are now more or less forgotten with the exception of the so-called Roessler system published in [Roessler OE. An equation for continuous chaos. Phys Lett A 1976;57(5):397-8]. In the present paper, we review most of the original systems and classify them using the tools of modern topological analysis, that is, using the templates and the bounding tori recently introduced by Tsankov and Gilmore in [Tsankov TD, Gilmore R. Strange attractors are classified by bounding tori. Phys Rev Lett 2003;91(13):134104]. Thus, examples of inequivalent topologies of chaotic attractors are provided in modern spirit
Order in nuclei and transition to chaos
International Nuclear Information System (INIS)
Soloviev, V.G.
1995-01-01
Based on the statement that there is order in the large and chaos in the small components of nuclear wave functions, the order-to-chaos transition is treated as a transition from the large to small components of wave functions. Therefore, experimental investigation of fragmentation of the many-quasiparticle and quasiparticle-phonon states plays a decisive role. The mixing of closely-spaced states having the same K π in the doubly even well-deformed nuclei is investigated. The quasiparticle-phonon interaction is responsible for fragmentation of the quasiparticle and phonon states and therefore for their mixing. Experimental investigation of the strength distribution of the many-quasiparticle and quasiparticle-phonon states should discover a new region of regularity in nuclei at intermediate excitation energies. A chaotic behaviour of nuclear states can be shifted to higher excitation energies. (author). 21 refs., 1 fig., 1 tab
Order in nuclei and transition to chaos
International Nuclear Information System (INIS)
Soloviev, V.G.
1995-01-01
Based on the statement that there is order in the large and chaos in the small components of nuclear wave functions, the order-to-chaos transition is treated as a transition from the large to small components of wave functions. Therefore, experimental investigation of fragmentation of the many-quasiparticle and quasiparticle-phonon states a decisive role. The mixing of closely-spaced states having the same K π in the doubly even well-deformed nuclei is investigated. The quasiparticle-phonon interaction is responsible for fragmentation of the quasiparticle and phonon states and therefore for their mixing. Experimental investigation of the strength distribution of the many-quasiparticle and quasiparticle-phonon states should discover a new region of regularity in nuclei at intermediate excitation energies. A chaotic behaviour of nuclear states can be shifted to higher excitation energies. (author). 21 refs., 1 fig., 1 tab
Tuning quantum measurements to control chaos.
Eastman, Jessica K; Hope, Joseph J; Carvalho, André R R
2017-03-20
Environment-induced decoherence has long been recognised as being of crucial importance in the study of chaos in quantum systems. In particular, the exact form and strength of the system-environment interaction play a major role in the quantum-to-classical transition of chaotic systems. In this work we focus on the effect of varying monitoring strategies, i.e. for a given decoherence model and a fixed environmental coupling, there is still freedom on how to monitor a quantum system. We show here that there is a region between the deep quantum regime and the classical limit where the choice of the monitoring parameter allows one to control the complex behaviour of the system, leading to either the emergence or suppression of chaos. Our work shows that this is a result from the interplay between quantum interference effects induced by the nonlinear dynamics and the effectiveness of the decoherence for different measurement schemes.
Kac-Moody algebras and controlled chaos
International Nuclear Information System (INIS)
Wesley, Daniel H
2007-01-01
Compactification can control chaotic Mixmaster behaviour in gravitational systems with p-form matter: we consider this in light of the connection between supergravity models and Kac-Moody algebras. We show that different compactifications define 'mutations' of the algebras associated with the noncompact theories. We list the algebras obtained in this way, and find novel examples of wall systems determined by Lorentzian (but not hyperbolic) algebras. Cosmological models with a smooth pre-big bang phase require that chaos is absent: we show that compactification alone cannot eliminate chaos in the simplest compactifications of the heterotic string on a Calabi-Yau, or M theory on a manifold of G 2 holonomy. (fast track communication)
Chaos theory perspective for industry clusters development
Yu, Haiying; Jiang, Minghui; Li, Chengzhang
2016-03-01
Industry clusters have outperformed in economic development in most developing countries. The contributions of industrial clusters have been recognized as promotion of regional business and the alleviation of economic and social costs. It is no doubt globalization is rendering clusters in accelerating the competitiveness of economic activities. In accordance, many ideas and concepts involve in illustrating evolution tendency, stimulating the clusters development, meanwhile, avoiding industrial clusters recession. The term chaos theory is introduced to explain inherent relationship of features within industry clusters. A preferred life cycle approach is proposed for industrial cluster recessive theory analysis. Lyapunov exponents and Wolf model are presented for chaotic identification and examination. A case study of Tianjin, China has verified the model effectiveness. The investigations indicate that the approaches outperform in explaining chaos properties in industrial clusters, which demonstrates industrial clusters evolution, solves empirical issues and generates corresponding strategies.
Polynomial chaos representation of databases on manifolds
Energy Technology Data Exchange (ETDEWEB)
Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-La-Vallée, Cedex 2 (France); Ghanem, R., E-mail: ghanem@usc.edu [University of Southern California, 210 KAP Hall, Los Angeles, CA 90089 (United States)
2017-04-15
Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. The method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.
Poincaré chaos and unpredictable functions
Akhmet, Marat; Fen, Mehmet Onur
2017-07-01
The results of this study are continuation of the research of Poincaré chaos initiated in the papers (M. Akhmet and M.O. Fen, Commun Nonlinear Sci Numer Simulat 40 (2016) 1-5; M. Akhmet and M.O. Fen, Turk J Math, doi:10.3906/mat-1603-51, in press). We focus on the construction of an unpredictable function, continuous on the real axis. As auxiliary results, unpredictable orbits for the symbolic dynamics and the logistic map are obtained. By shaping the unpredictable function as well as Poisson function we have performed the first step in the development of the theory of unpredictable solutions for differential and discrete equations. The results are preliminary ones for deep analysis of chaos existence in differential and hybrid systems. Illustrative examples concerning unpredictable solutions of differential equations are provided.
Controllable chaos in hybrid electro-optomechanical systems
Wang, Mei; Lü, Xin-You; Ma, Jin-Yong; Xiong, Hao; Si, Liu-Gang; Wu, Ying
2016-01-01
We investigate the nonlinear dynamics of a hybrid electro-optomechanical system (EOMS) that allows us to realize the controllable opto-mechanical nonlinearity by driving the microwave LC resonator with a tunable electric field. A controllable optical chaos is realized even without changing the optical pumping. The threshold and lifetime of the chaos could be optimized by adjusting the strength, frequency, or phase of the electric field. This study provides a method of manipulating optical chaos with an electric field. It may offer the prospect of exploring the controllable chaos in on-chip optoelectronic devices and its applications in secret communication. PMID:26948505
Controllable chaos in hybrid electro-optomechanical systems.
Wang, Mei; Lü, Xin-You; Ma, Jin-Yong; Xiong, Hao; Si, Liu-Gang; Wu, Ying
2016-03-07
We investigate the nonlinear dynamics of a hybrid electro-optomechanical system (EOMS) that allows us to realize the controllable opto-mechanical nonlinearity by driving the microwave LC resonator with a tunable electric field. A controllable optical chaos is realized even without changing the optical pumping. The threshold and lifetime of the chaos could be optimized by adjusting the strength, frequency, or phase of the electric field. This study provides a method of manipulating optical chaos with an electric field. It may offer the prospect of exploring the controllable chaos in on-chip optoelectronic devices and its applications in secret communication.
Congenital high airway obstruction syndrome (CHAOS) associated with cervical myelomeningocele.
Adin, Mehmet Emin
2017-10-01
Congenital high airway obstruction syndrome (CHAOS) is a rare and potentially fatal entity resulting from complete or near complete developmental airway obstruction. Although most reported cases of CHAOS are sporadic, the condition may also be associated with certain syndromes and a variety of cervical masses. Meningocele and myelomeningocele have not yet been reported in association with CHAOS. We describe the typical constellation of sonographic findings in a case of early diagnosis of CHAOS associated with cervical myelomeningocele. © 2016 Wiley Periodicals, Inc. J Clin Ultrasound 45:507-510, 2017. © 2016 Wiley Periodicals, Inc.
Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons
Kröger, H.
2003-01-01
We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.
Robinson's chaos in set-valued discrete systems
International Nuclear Information System (INIS)
Roman-Flores, Heriberto; Chalco-Cano, Y.
2005-01-01
Let (X,d) be a compact metric space and f:X->X a continuous function. If we consider the space (K(X),H) of all non-empty compact subsets of X endowed with the Hausdorff metric induced by d and f-bar :K(X)->K(X), f-bar (A)={f(a)/a-bar A}, then the aim of this work is to show that Robinson's chaos in f-bar implies Robinson's chaos in f. Also, we give an example showing that R-chaos in f does not implies R-chaos in f-bar
Chaos theory in geophysics: past, present and future
International Nuclear Information System (INIS)
Sivakumar, B.
2004-01-01
The past two decades of research on chaos theory in geophysics has brought about a significant shift in the way we view geophysical phenomena. Research on chaos theory in geophysics continues to grow at a much faster pace, with applications to a wide variety of geophysical phenomena and geophysical problems. In spite of our success in understanding geophysical phenomena also from a different (i.e. chaotic) perspective, there still seems to be lingering suspicions on the scope of chaos theory in geophysics. The goal of this paper is to present a comprehensive account of the achievements and status of chaos theory in geophysics, and to disseminate the hope and scope for the future. A systematic review of chaos theory in geophysics, covering a wide spectrum of geophysical phenomena studied (e.g. rainfall, river flow, sediment transport, temperature, pressure, tree ring series, etc.), is presented to narrate our past achievements not only in understanding and predicting geophysical phenomena but also in improving the chaos identification and prediction techniques. The present state of chaos research in geophysics (in terms of geophysical phenomena, problems, and chaos methods) and potential for future improvements (in terms of where, why and possibly how) are also highlighted. Our popular views of nature (i.e. stochastic and deterministic), and of geophysical phenomena in particular, are discussed, and the usefulness of chaos theory as a bridge between such views is also put forth
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
Chaos and creation in Fernando Pessoa
Directory of Open Access Journals (Sweden)
José Nuno Gil
2016-07-01
Full Text Available Fernando Pessoa's poem "A Múmia" describes a sort of psychotic experience, which shows the condition of the literary creation by itself. The poem springs from – and describes – the experience of psychic and existential chaos: criticism and clinic overlap in the making and analysis of "A Múmia" This critical reading aims at bringing some intelligibility to the creative processes and, in particular, to Pessoa's heteronyms.
Bifurcations and chaos of DNA solitonic dynamics
International Nuclear Information System (INIS)
Gonzalez, J.A.; Martin-Landrove, M.; Carbo, J.R.; Chacon, M.
1994-09-01
We investigated the nonlinear DNA torsional equations proposed by Yakushevich in the presence of damping and external torques. Analytical expressions for some solutions are obtained in the case of the isolated chain. Special attention is paid to the stability of the solutions and the range of soliton interaction in the general case. The bifurcation analysis is performed and prediction of chaos is obtained for some set of parameters. Some biological implications are suggested. (author). 11 refs, 13 figs
Li-Yorke chaos in linear dynamics
Czech Academy of Sciences Publication Activity Database
Bernardes Jr., N.C.; Bonilla, A.; Müller, Vladimír; Peris, A.
2015-01-01
Roč. 35, č. 6 (2015), s. 1723-1745 ISSN 0143-3857 R&D Projects: GA ČR GA201/09/0473; GA AV ČR IAA100190903 Institutional support: RVO:67985840 Keywords : Li-York chaos * Banach space * Fréchet space Subject RIV: BA - General Mathematics Impact factor: 0.983, year: 2015 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9884748&fileId=S0143385714000200
The chaos theory and the quality assurance
International Nuclear Information System (INIS)
Aguilar, Omar; Domech More, Jesus
1999-01-01
In the present paper we suggest the importance that the new science of chaos offers in the analysis,design and improvement processes in the production of gamma shielding devices as part of the quality assurance system. A brief analysis of the influence of the errors of measures, the interactions between the process and its environment in determining of the basic behaviour of the process and its stability is done.(author)
Coherence and chaos in extended dynamical systems
International Nuclear Information System (INIS)
Bishop, A.R.
1994-01-01
Coherence, chaos, and pattern formation are characteristic elements of the nonequilibrium statistical mechanics controlling mesoscopic order and disorder in many-degree-of-freedom nonlinear dynamical systems. Competing length scales and/or time scales are the underlying microscopic driving forces for many of these aspects of ''complexity.'' We illustrate the basic concepts with some model examples of classical and quantum, ordered and disordered, nonlinear systems
Classical and Quantum Chaos in Atom Optics
Saif, Farhan
2006-01-01
The interaction of an atom with an electromagnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electromagnetic fields helps to design the quantum analog of classical optical systems. In these atom optical systems chaos may appear at the onset of external fields. The classical and quantum chaotic dynamics is discussed, in particular in an atom optics Fermi accelerator. It is found that the quantum dynamics exhibits ...
Wave Chaos and Coupling to EM Structures
2006-07-01
Antonsen, E. Ott and S. Anlage, Aspects of the Scattering and Impedance Properties of Chaotic Microwave Cavities, Acta Physica Polonica A 109, 65...other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a ...currently valid OMB control number. 1. REPORT DATE JUL 2006 2. REPORT TYPE N/ A 3. DATES COVERED - 4. TITLE AND SUBTITLE Wave Chaos and Coupling
Complex motions and chaos in nonlinear systems
Machado, José; Zhang, Jiazhong
2016-01-01
This book brings together 10 chapters on a new stream of research examining complex phenomena in nonlinear systems—including engineering, physics, and social science. Complex Motions and Chaos in Nonlinear Systems provides readers a particular vantage of the nature and nonlinear phenomena in nonlinear dynamics that can develop the corresponding mathematical theory and apply nonlinear design to practical engineering as well as the study of other complex phenomena including those investigated within social science.
Effect of smoothing on robust chaos.
Deshpande, Amogh; Chen, Qingfei; Wang, Yan; Lai, Ying-Cheng; Do, Younghae
2010-08-01
In piecewise-smooth dynamical systems, situations can arise where the asymptotic attractors of the system in an open parameter interval are all chaotic (e.g., no periodic windows). This is the phenomenon of robust chaos. Previous works have established that robust chaos can occur through the mechanism of border-collision bifurcation, where border is the phase-space region where discontinuities in the derivatives of the dynamical equations occur. We investigate the effect of smoothing on robust chaos and find that periodic windows can arise when a small amount of smoothness is present. We introduce a parameter of smoothing and find that the measure of the periodic windows in the parameter space scales linearly with the parameter, regardless of the details of the smoothing function. Numerical support and a heuristic theory are provided to establish the scaling relation. Experimental evidence of periodic windows in a supposedly piecewise linear dynamical system, which has been implemented as an electronic circuit, is also provided.
Dynamics and chaos control of gyrostat satellite
International Nuclear Information System (INIS)
Aslanov, Vladimir; Yudintsev, Vadim
2012-01-01
Highlights: ► Free dual-spin gyrostat with a small rotor asymmetry is considered. ► Equations in Andoyer-Deprit canonical dimensionless variables are obtained. ► Phase space heteroclinic and homoclinic trajectories are written in closed form. ► Modified Melnikov function is used to construct the control that eliminates chaos. - Abstract: We consider the chaotic motion of the free gyrostat consisting of a platform with a triaxial inertia ellipsoid and a rotor with a small asymmetry with respect to the axis of rotation. Dimensionless equations of motion of the system with perturbations caused by small asymmetries of the rotor are written in Andoyer-Deprit variables. These perturbations lead to separatrix chaos. For gyrostats with different ratios of moments of inertia heteroclinic and homoclinic trajectories are written in closed-form. These trajectories are used for constructing modified Melnikov function, which is used for determine the control that eliminates separatrix chaos. Melnikov function and phase space trajectory are built to show the effectiveness of the control.
Chaos and Structures in Nonlinear Plasmas
Chen, James
In recent decades, the concepts and applications of chaos, complexity, and nonlinear dynamics have profoundly influenced scientific as well as literary thinking. Some aspects of these concepts are used in almost all of the geophysical disciplines. Chaos and Structures in Nonlinear Plasmas, written by two respected plasma physicists, focuses on nonlinear phenomena in laboratory and space plasmas, which are rich in nonlinear and complex collective effects. Chaos is treated only insofar as it relates to some aspects of nonlinear plasma physics.At the outset, the authors note that plasma physics research has made fundamental contributions to modern nonlinear sciences. For example, the Poincare surface of section technique was extensively used in studies of stochastic field lines in magnetically confined plasmas and turbulence. More generally, nonlinearity in plasma waves and wave-wave and wave-particle interactions critically determines the propagation of energy through a plasma medium. The book also makes it clear that the importance of understanding nonlinear waves goes beyond plasma physics, extending to such diverse fields as solid state physics, fluid dynamics, atmospheric physics, and optics. In space physics, non-linear plasma physics is essential for interpreting in situ as well as remote-sensing data.
Dynamical chaos: systems of classical mechanics
International Nuclear Information System (INIS)
Loskutov, A Yu
2007-01-01
This article is a methodological manual for those who are interested in chaotic dynamics. An exposition is given on the foundations of the theory of deterministic chaos that originates in classical mechanics systems. Fundamental results obtained in this area are presented, such as elements of the theory of nonlinear resonance and the Kolmogorov-Arnol'd-Moser theory, the Poincare-Birkhoff fixed-point theorem, and the Mel'nikov method. Particular attention is given to the analysis of the phenomena underlying the self-similarity and nature of chaos: splitting of separatrices and homoclinic and heteroclinic tangles. Important properties of chaotic systems - unpredictability, irreversibility, and decay of temporal correlations - are described. Models of classical statistical mechanics with chaotic properties, which have become popular in recent years - billiards with oscillating boundaries - are considered. It is shown that if a billiard has the property of well-developed chaos, then perturbations of its boundaries result in Fermi acceleration. But in nearly-integrable billiard systems, excitations of the boundaries lead to a new phenomenon in the ensemble of particles, separation of particles in accordance their velocities. If the initial velocity of the particles exceeds a certain critical value characteristic of the given billiard geometry, the particles accelerate; otherwise, they decelerate. (methodological notes)
Detecting chaos in irregularly sampled time series.
Kulp, C W
2013-09-01
Recently, Wiebe and Virgin [Chaos 22, 013136 (2012)] developed an algorithm which detects chaos by analyzing a time series' power spectrum which is computed using the Discrete Fourier Transform (DFT). Their algorithm, like other time series characterization algorithms, requires that the time series be regularly sampled. Real-world data, however, are often irregularly sampled, thus, making the detection of chaotic behavior difficult or impossible with those methods. In this paper, a characterization algorithm is presented, which effectively detects chaos in irregularly sampled time series. The work presented here is a modification of Wiebe and Virgin's algorithm and uses the Lomb-Scargle Periodogram (LSP) to compute a series' power spectrum instead of the DFT. The DFT is not appropriate for irregularly sampled time series. However, the LSP is capable of computing the frequency content of irregularly sampled data. Furthermore, a new method of analyzing the power spectrum is developed, which can be useful for differentiating between chaotic and non-chaotic behavior. The new characterization algorithm is successfully applied to irregularly sampled data generated by a model as well as data consisting of observations of variable stars.
Chaos, dynamical structure and climate variability
Energy Technology Data Exchange (ETDEWEB)
Stewart, H.B. [Brookhaven National Lab., Upton, NY (United States). Dept. of Applied Science
1995-09-01
Deterministic chaos in dynamical systems offers a new paradigm for understanding irregular fluctuations. Techniques for identifying deterministic chaos from observed data, without recourse to mathematical models, are being developed. Powerful methods exist for reconstructing multidimensional phase space from an observed time series of a single scalar variable; these methods are invaluable when only a single scalar record of the dynamics is available. However, in some applications multiple concurrent time series may be available for consideration as phase space coordinates. Here the authors propose some basic analytical tools for such multichannel time series data, and illustrate them by applications to a simple synthetic model of chaos, to a low-order model of atmospheric circulation, and to two high-resolution paleoclimate proxy data series. The atmospheric circulation model, originally proposed by Lorenz, has 27 principal unknowns; they establish that the chaotic attractor can be embedded in a subspace of eight dimensions by exhibiting a specific subset of eight unknowns which pass multichannel tests for false nearest neighbors. They also show that one of the principal unknowns in the 27-variable model--the global mean sea surface temperature--is of no discernible usefulness in making short-term forecasts.
The Yo-Yo intermittent recovery test
DEFF Research Database (Denmark)
Bangsbo, Jens; Iaia, F. Marcello; Krustrup, Peter
2008-01-01
The two Yo-Yo intermittent recovery (IR) tests evaluate an individual's ability to repeatedly perform intense exercise. The Yo-Yo IR level 1 (Yo-Yo IR1) test focuses on the capacity to carry out intermittent exercise leading to a maximal activation of the aerobic system, whereas Yo-Yo IR level 2...
Intermittent behavior of the logistic system
Mayer-Kress, G.; Haken, H.
1981-03-01
In the discrete logistic model a transition to chaotic behavior via intermittency occurs in a neighborhood of periodic bands. Intermittent behavior is also induced if a stable periodic orbit is perturbed by low-level external noise, whereas alterations due to computer digitalisation produce remarkable periodicities. We compare our numerical results with the predictions of Pomeau and Manneville for the Lorenz system.
The chaos and order in nuclear molecular dynamics; Chaos i porzadek w jadrowej dynamice molekularnej
Energy Technology Data Exchange (ETDEWEB)
Srokowski, T. [Institute of Nuclear Physics, Cracow (Poland)
1995-12-31
The subject of the presented report is role of chaos in scattering processes in the frame of molecular dynamics. In this model, it is assumed that scattering particles (nuclei) consist of not-interacted components as alpha particles or {sup 12}C, {sup 16}O and {sup 20}Ne clusters. The results show such effects as dynamical in stabilities and fractal structure as well as compound nuclei decay and heavy-ion fusion. The goal of the report is to make the reader more familiar with the chaos model and its application to nuclear phenomena. 157 refs, 40 figs.
International Nuclear Information System (INIS)
Chen, H Y; Lv, J T; Zhang, S Q; Zhang, L G; Li, J
2005-01-01
At the present time, the ultrasonic Doppler measuring means has been extensively used in the human body's bloodstream speed measuring. The ultrasonic Doppler measuring means can achieve the measuring of liquid flux by detecting Doppler frequency shift of ultrasonic in the process of liquid spread. However, the detected sound wave is a weak signal that is flooded in the strong noise signal. The traditional measuring method depends on signal-to-noise ratio. Under the very low signal-to-noise ratio or the strong noise signal background, the signal frequency is not measured. This article studied on chaotic movement of Duffing oscillator and intermittent chaotic characteristic on chaotic oscillator of Duffing equation. In the light of the range of the bloodstream speed of human body and the principle of Doppler shift, the paper determines the frequency shift range. An oscillator array including many oscillators is designed according to it. The reflected ultrasonic frequency information can be ascertained accurately by the intermittent chaos quality of the oscillator. The signal-to-noise ratio of -26.5 dB is obtained by the result of the experiment. Compared with the tradition the frequency method compare, the dependence to signal-to-noise ratio is lowered consumedly. The measuring precision of the bloodstream speed is heightened
Cosmic Rays in Intermittent Magnetic Fields
International Nuclear Information System (INIS)
Shukurov, Anvar; Seta, Amit; Bushby, Paul J.; Wood, Toby S.; Snodin, Andrew P.
2017-01-01
The propagation of cosmic rays in turbulent magnetic fields is a diffusive process driven by the scattering of the charged particles by random magnetic fluctuations. Such fields are usually highly intermittent, consisting of intense magnetic filaments and ribbons surrounded by weaker, unstructured fluctuations. Studies of cosmic-ray propagation have largely overlooked intermittency, instead adopting Gaussian random magnetic fields. Using test particle simulations, we calculate cosmic-ray diffusivity in intermittent, dynamo-generated magnetic fields. The results are compared with those obtained from non-intermittent magnetic fields having identical power spectra. The presence of magnetic intermittency significantly enhances cosmic-ray diffusion over a wide range of particle energies. We demonstrate that the results can be interpreted in terms of a correlated random walk.
Cosmic Rays in Intermittent Magnetic Fields
Energy Technology Data Exchange (ETDEWEB)
Shukurov, Anvar; Seta, Amit; Bushby, Paul J.; Wood, Toby S. [School of Mathematics and Statistics, Newcastle University, Newcastle Upon Tyne NE1 7RU (United Kingdom); Snodin, Andrew P., E-mail: a.seta1@ncl.ac.uk, E-mail: amitseta90@gmail.com [Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800 (Thailand)
2017-04-10
The propagation of cosmic rays in turbulent magnetic fields is a diffusive process driven by the scattering of the charged particles by random magnetic fluctuations. Such fields are usually highly intermittent, consisting of intense magnetic filaments and ribbons surrounded by weaker, unstructured fluctuations. Studies of cosmic-ray propagation have largely overlooked intermittency, instead adopting Gaussian random magnetic fields. Using test particle simulations, we calculate cosmic-ray diffusivity in intermittent, dynamo-generated magnetic fields. The results are compared with those obtained from non-intermittent magnetic fields having identical power spectra. The presence of magnetic intermittency significantly enhances cosmic-ray diffusion over a wide range of particle energies. We demonstrate that the results can be interpreted in terms of a correlated random walk.
Application of Chaos Theory to Psychological Models
Blackerby, Rae Fortunato
This dissertation shows that an alternative theoretical approach from physics--chaos theory--offers a viable basis for improved understanding of human beings and their behavior. Chaos theory provides achievable frameworks for potential identification, assessment, and adjustment of human behavior patterns. Most current psychological models fail to address the metaphysical conditions inherent in the human system, thus bringing deep errors to psychological practice and empirical research. Freudian, Jungian and behavioristic perspectives are inadequate psychological models because they assume, either implicitly or explicitly, that the human psychological system is a closed, linear system. On the other hand, Adlerian models that require open systems are likely to be empirically tenable. Logically, models will hold only if the model's assumptions hold. The innovative application of chaotic dynamics to psychological behavior is a promising theoretical development because the application asserts that human systems are open, nonlinear and self-organizing. Chaotic dynamics use nonlinear mathematical relationships among factors that influence human systems. This dissertation explores these mathematical relationships in the context of a sample model of moral behavior using simulated data. Mathematical equations with nonlinear feedback loops describe chaotic systems. Feedback loops govern the equations' value in subsequent calculation iterations. For example, changes in moral behavior are affected by an individual's own self-centeredness, family and community influences, and previous moral behavior choices that feed back to influence future choices. When applying these factors to the chaos equations, the model behaves like other chaotic systems. For example, changes in moral behavior fluctuate in regular patterns, as determined by the values of the individual, family and community factors. In some cases, these fluctuations converge to one value; in other cases, they diverge in
Household chaos and family sleep during infants' first year.
Whitesell, Corey J; Crosby, Brian; Anders, Thomas F; Teti, Douglas M
2018-05-21
Household chaos has been linked with dysregulated family and individual processes. The present study investigated linkages between household chaos and infant and parent sleep, a self-regulated process impacted by individual, social, and environmental factors. Studies of relations between household chaos and child sleep have focused on older children and teenagers, with little attention given to infants or parent sleep. This study examines these relationships using objective measures of household chaos and sleep while controlling for, respectively, maternal emotional availability at bedtime and martial adjustment, in infant and parent sleep. Multilevel modeling examined mean and variability of sleep duration and fragmentation for infants, mothers, and fathers when infants were 1, 3, 6, 9, and 12 months (N = 167). Results indicated infants in higher chaos homes experienced delays in sleep consolidation patterns, with longer and more variable sleep duration, and greater fragmentation. Parent sleep was also associated with household chaos such that in higher chaos homes, mothers and fathers experienced greater variability in sleep duration, which paralleled infant findings. In lower chaos homes, parents' sleep fragmentation mirrored infants' decreasingly fragmented sleep across the first year and remained lower at all timepoints compared to parents and infants in high chaos homes. Collectively, these findings indicate that after controlling for maternal emotional availability and marital adjustment (respectively) household chaos has a dysregulatory impact on infant and parent sleep. Results are discussed in terms of the potential for chaos-induced poor sleep to dysregulate daytime functioning and, in turn, place parent-infant relationships at risk. (PsycINFO Database Record (c) 2018 APA, all rights reserved).
Spatiotemporal throughfall patterns beneath an urban tree row
Bogeholz, P.; Van Stan, J. T., II; Hildebrandt, A.; Friesen, J.; Dibble, M.; Norman, Z.
2016-12-01
Much recent research has focused on throughfall patterns in natural forests as they can influence the heterogeneity of surface ecohydrological and biogeochemical processes. However, to the knowledge of the authors, no work has assessed how urban forest structures affect the spatiotemporal variability of throughfall water flux. Urbanization greatly alters not only a significant portion of the land surface, but canopy structure, with the most typical urban forest configuration being landscaped tree rows along streets, swales, parking lot medians, etc. This study examines throughfall spatiotemporal patterns for a landscaped tree row of Pinus elliottii (Engelm., slash pine) on Georgia Southern University's campus (southeastern, USA) using 150 individual observations per storm. Throughfall correlation lengths beneath this tree row were similar to, but appeared to be more stable across storm size than, observations in past studies on natural forests. Individual tree overlap and the planting interval also may more strongly drive throughfall patterns in tree rows. Meteorological influences beyond storm magnitude (intensity, intermittency, wind conditions, and atmospheric moisture demand) are also examined.
ANISOTROPIC INTERMITTENCY OF MAGNETOHYDRODYNAMIC TURBULENCE
International Nuclear Information System (INIS)
Osman, K. T.; Kiyani, K. H.; Chapman, S. C.; Hnat, B.
2014-01-01
A higher-order multiscale analysis of spatial anisotropy in inertial range magnetohydrodynamic turbulence is presented using measurements from the STEREO spacecraft in fast ambient solar wind. We show for the first time that, when measuring parallel to the local magnetic field direction, the full statistical signature of the magnetic and Elsässer field fluctuations is that of a non-Gaussian globally scale-invariant process. This is distinct from the classic multiexponent statistics observed when the local magnetic field is perpendicular to the flow direction. These observations are interpreted as evidence for the weakness, or absence, of a parallel magnetofluid turbulence energy cascade. As such, these results present strong observational constraints on the statistical nature of intermittency in turbulent plasmas
Prolonged Intermittent Renal Replacement Therapy.
Edrees, Fahad; Li, Tingting; Vijayan, Anitha
2016-05-01
Prolonged intermittent renal replacement therapy (PIRRT) is becoming an increasingly popular alternative to continuous renal replacement therapy in critically ill patients with acute kidney injury. There are significant practice variations in the provision of PIRRT across institutions, with respect to prescription, technology, and delivery of therapy. Clinical trials have generally demonstrated that PIRRT is non-inferior to continuous renal replacement therapy regarding patient outcomes. PIRRT offers cost-effective renal replacement therapy along with other advantages such as early patient mobilization and decreased nursing time. However, due to lack of standardization of the procedure, PIRRT still poses significant challenges, especially pertaining to appropriate drug dosing. Future guidelines and clinical trials should work toward developing consensus definitions for PIRRT and ensure optimal delivery of therapy. Copyright © 2016 National Kidney Foundation, Inc. Published by Elsevier Inc. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Guszejnov, Dávid; Lazányi, Nóra [Department of Nuclear Techniques, Budapest University of Technology and Economics, Association EURATOM, Műegyetem rkp. 9., H-1111 Budapest (Hungary); Bencze, Attila; Zoletnik, Sándor [MTA Wigner RCP, EURATOM Association, PO Box 49, H-1525 Budapest (Hungary)
2013-11-15
This paper is aimed to contribute to the scientific discussions that have been triggered by the experimental observation of a quadratic relation between the kurtosis and skewness of turbulent fluctuations present in fusion plasmas and other nonlinear physical systems. In this paper, we offer a general statistical model which attributes the observed K=aS{sup 2}+b relation to the varying intermittency of the experimental signals. The model is a two random variable model constructed to catch the essential intermittent feature of the real signal. One of the variables is the amplitude of the underlying intermittent event (e.g., turbulent structure) while the other is connected to the intermittency level of the system. This simple model can attribute physical meaning to the a and b coefficients, as they characterize the spatio-temporal statistics of intermittent events. By constructing a particle-conserving Gaussian model for the underlying coherent structures, the experimentally measured a and b coefficients could be adequately reproduced.
Spatiotemporal Wave Patterns: Information Dynamics
Energy Technology Data Exchange (ETDEWEB)
Mikhail Rabinovich; Lev Tsimring
2006-01-20
Pattern formation has traditionally been studied in non-equilibrium physics from the viewpoint of describing the basic structures and their interactions. While this is still an important area of research, the emphasis in the last few years has shifted towards analysis of specific properties of patterns in various complex media. For example, diverse and unexpected phenomena occur in neuro-like media that are characterized by highly non-trivial local dynamics. We carried out an active research program on analysis of spatio-temporal patterns in various physical systems (convection, oscillating fluid layer, soap film), as well as in neuro-like media, with an emphasis on informational aspects of the dynamics. Nonlinear nonequilibrium media and their discrete analogs have a unique ability to represent, memorize, and process the information contained in spatio-temporal patterns. Recent neurophysiological experiments demonstrated a certain universality of spatio-temporal representation of information by neural ensembles. Information processing is also revealed in the spatio-temporal dynamics of cellular patterns in nonequilibrium media. It is extremely important for many applications to study the informational aspects of these dynamics, including the origins and mechanisms of information generation, propagation and storage. Some of our results are: the discovery of self-organization of periodically oscillatory patterns in chaotic heterogeneous media; the analysis of the propagation of the information along a chaotic media as function of the entropy of the signal; the analysis of wave propagation in discrete non-equilibrium media with autocatalytic properties, which simulates the calcium dynamics in cellular membranes. Based on biological experiments we suggest the mechanism by which the spatial sensory information is transferred into the spatio-temporal code in the neural media. We also found a new mechanism of self-pinning in cellular structures and the related phenomenon
Chaos controlling problems for circuit systems with Josephson junction
International Nuclear Information System (INIS)
Gou, X-F; Wang, X; Xie, J-L
2008-01-01
The complex dynamical characters of the Josephson junction circuit system are studied and the tunnel effect is considered. The dynamical equation of the system is established. The route from periodic motion to chaos is illustrated using bifurcation diagram. An adscititious coupling controller is constructed to control the chaos
On the efficiency of chaos optimization algorithms for global optimization
International Nuclear Information System (INIS)
Yang Dixiong; Li Gang; Cheng Gengdong
2007-01-01
Chaos optimization algorithms as a novel method of global optimization have attracted much attention, which were all based on Logistic map. However, we have noticed that the probability density function of the chaotic sequences derived from Logistic map is a Chebyshev-type one, which may affect the global searching capacity and computational efficiency of chaos optimization algorithms considerably. Considering the statistical property of the chaotic sequences of Logistic map and Kent map, the improved hybrid chaos-BFGS optimization algorithm and the Kent map based hybrid chaos-BFGS algorithm are proposed. Five typical nonlinear functions with multimodal characteristic are tested to compare the performance of five hybrid optimization algorithms, which are the conventional Logistic map based chaos-BFGS algorithm, improved Logistic map based chaos-BFGS algorithm, Kent map based chaos-BFGS algorithm, Monte Carlo-BFGS algorithm, mesh-BFGS algorithm. The computational performance of the five algorithms is compared, and the numerical results make us question the high efficiency of the chaos optimization algorithms claimed in some references. It is concluded that the efficiency of the hybrid optimization algorithms is influenced by the statistical property of chaotic/stochastic sequences generated from chaotic/stochastic algorithms, and the location of the global optimum of nonlinear functions. In addition, it is inappropriate to advocate the high efficiency of the global optimization algorithms only depending on several numerical examples of low-dimensional functions
Research on a family of n-scroll chaos generators
International Nuclear Information System (INIS)
Zhang, G; Yang, S-Z; He, L-F
2008-01-01
This paper studies a family of n-scroll chaos generators using a modified Chua's circuit. A mathematic model of the generators is established, the relationship between equilibrium points and scrolls is also analyzed, and a general theorem for generation of n-scroll chaos attractors is given. Numerical simulation is illustrated, showing excellent agreement with our theoretical predictions
On the suppression of chaos in quantum and classical physics
International Nuclear Information System (INIS)
Fried, H.M.; Gabellini, Y.
1997-01-01
A brief outline is presented of an example of potential-theory quantum chaos, which is suppressed by the full radiative corrections of quantum field theory. A similar mechanism may be devised and applied to classically chaotic systems, and provides an example in which an explicit diminution of the original chaos becomes apparent. (author)
Applying Chaos Theory to Lesson Planning and Delivery
Cvetek, Slavko
2008-01-01
In this article, some of the ways in which thinking about chaos theory can help teachers and student-teachers to accept uncertainty and randomness as natural conditions in the classroom are considered. Building on some key features of complex systems commonly attributed to chaos theory (e.g. complexity, nonlinearity, sensitivity to initial…
The Chaos Theory of Careers: A User's Guide
Bright, Jim E. H.; Pryor, Robert G. L.
2005-01-01
The purpose of this article is to set out the key elements of the Chaos Theory of Careers. The complexity of influences on career development presents a significant challenge to traditional predictive models of career counseling. Chaos theory can provide a more appropriate description of career behavior, and the theory can be applied with clients…
Switching control of linear systems for generating chaos
International Nuclear Information System (INIS)
Liu Xinzhi; Teo, Kok-Lay; Zhang Hongtao; Chen Guanrong
2006-01-01
In this paper, a new switching method is developed, which can be applied to generating different types of chaos or chaos-like dynamics from two or more linear systems. A numerical simulation is given to illustrate the generated chaotic dynamic behavior of the systems with some variable parameters. Finally, a circuit is built to realize various chaotic dynamical behaviors
Chaos: A Topic for Interdisciplinary Education in Physics
Bae, Saebyok
2009-01-01
Since society and science need interdisciplinary works, the interesting topic of chaos is chosen for interdisciplinary education in physics. The educational programme contains various university-level activities such as computer simulations, chaos experiment and team projects besides ordinary teaching. According to the participants, the programme…
Chaos and the classical limit of quantum systems
Energy Technology Data Exchange (ETDEWEB)
Hogg, T; Huberman, B A [Xerox Palo Alto Research Center, CA (USA)
1984-10-01
The authors discuss the question of whether experiments can be designed to test the existence of quantum chaos. In particular, they show that high energies are not sufficient to guarantee that an initially localized wave packet will behave classically for long times. Computer simulations illustrating these ideas are presented and the question whether experiments can be designed to observe quantum chaos is commented on.
Specifying the Links between Household Chaos and Preschool Children's Development
Martin, Anne; Razza, Rachel A.; Brooks-Gunn, Jeanne
2012-01-01
Household chaos has been linked to poorer cognitive, behavioural, and self-regulatory outcomes in young children, but the mechanisms responsible remain largely unknown. Using a diverse sample of families in Chicago, the present study tests for the independent contributions made by five indicators of household chaos: noise, crowding, family…
Cornick, Matthew; Hunt, Brian; Ott, Edward; Kurtuldu, Huseyin; Schatz, Michael F
2009-03-01
Data assimilation refers to the process of estimating a system's state from a time series of measurements (which may be noisy or incomplete) in conjunction with a model for the system's time evolution. Here we demonstrate the applicability of a recently developed data assimilation method, the local ensemble transform Kalman filter, to nonlinear, high-dimensional, spatiotemporally chaotic flows in Rayleigh-Bénard convection experiments. Using this technique we are able to extract the full temperature and velocity fields from a time series of shadowgraph measurements. In addition, we describe extensions of the algorithm for estimating model parameters. Our results suggest the potential usefulness of our data assimilation technique to a broad class of experimental situations exhibiting spatiotemporal chaos.
Random matrices and chaos in nuclear physics: Nuclear structure
International Nuclear Information System (INIS)
Weidenmueller, H. A.; Mitchell, G. E.
2009-01-01
Evidence for the applicability of random-matrix theory to nuclear spectra is reviewed. In analogy to systems with few degrees of freedom, one speaks of chaos (more accurately, quantum chaos) in nuclei whenever random-matrix predictions are fulfilled. An introduction into the basic concepts of random-matrix theory is followed by a survey over the extant experimental information on spectral fluctuations, including a discussion of the violation of a symmetry or invariance property. Chaos in nuclear models is discussed for the spherical shell model, for the deformed shell model, and for the interacting boson model. Evidence for chaos also comes from random-matrix ensembles patterned after the shell model such as the embedded two-body ensemble, the two-body random ensemble, and the constrained ensembles. All this evidence points to the fact that chaos is a generic property of nuclear spectra, except for the ground-state regions of strongly deformed nuclei.
Replication of chaos in neural networks, economics and physics
Akhmet, Marat
2016-01-01
This book presents detailed descriptions of chaos for continuous-time systems. It is the first-ever book to consider chaos as an input for differential and hybrid equations. Chaotic sets and chaotic functions are used as inputs for systems with attractors: equilibrium points, cycles and tori. The findings strongly suggest that chaos theory can proceed from the theory of differential equations to a higher level than previously thought. The approach selected is conducive to the in-depth analysis of different types of chaos. The appearance of deterministic chaos in neural networks, economics and mechanical systems is discussed theoretically and supported by simulations. As such, the book offers a valuable resource for mathematicians, physicists, engineers and economists studying nonlinear chaotic dynamics.
Strong chaos in one-dimensional quantum system
International Nuclear Information System (INIS)
Yang, C.-D.; Wei, C.-H.
2008-01-01
According to the Poincare-Bendixson theorem, a minimum of three autonomous equations is required to exhibit deterministic chaos. Because a one-dimensional quantum system is described by only two autonomous equations using de Broglie-Bohm's trajectory interpretation, chaos in one-dimensional quantum systems has long been considered impossible. We will prove in this paper that chaos phenomenon does exist in one-dimensional quantum systems, if the domain of quantum motions is extended to complex space by noting that the quantum world is actually characterized by a four-dimensional complex spacetime according to the E (∞) theory. Furthermore, we point out that the interaction between the real and imaginary parts of complex trajectories produces a new chaos phenomenon unique to quantum systems, called strong chaos, which describes the situation that quantum trajectories may emerge and diverge spontaneously without any perturbation in the initial position
Relativistic quantum chaos-An emergent interdisciplinary field.
Lai, Ying-Cheng; Xu, Hong-Ya; Huang, Liang; Grebogi, Celso
2018-05-01
Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics-all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.
A new approach for realizing electronic chaos generators
International Nuclear Information System (INIS)
Elwakeel, A.E.
1997-01-01
A dictionary definition of chaos is a 'formless primordial matter, utter confusion' [1]. The study of chaos is part of a larger program of study of so-called strongly nonlinear systems. No strict definition of chaos yet exists, however, nonrandom complicated motions that exhibit a very rapid growth of errors and that, despite perfect determinism, inhibit any ability to render accurate long-term prediction are usually termed chaotic. In other words, chaos may be referred to as deterministic randomness since it is the phenomenon where deterministic laws, are sometimes extremely simple, show random (or random-like) behaviours while random (or random-like) motions happen to follow strict deterministic laws. The sense of order in chaos can be usually observed in the space of dimensions where time is not a dimension, while the sense of randomness is usually evident when time is incorporated. 10 refs., 29 figs
Elimination of spiral chaos by periodic force for the Aliev-Panfilov model
Sakaguchi, Hidetsugu; Fujimoto, Takefumi
2003-01-01
Spiral chaos appears in the two dimensional Aliev-Panfilov model. The generation mechanism of the spiral chaos is related to the breathing instability of pulse trains. The spiral chaos can be eliminated by applying periodic force uniformly. The elimination of spiral chaos is most effective, when the frequency of the periodic force is close to that of the breathing motion.
Intermittent cranial lung herniation in two dogs.
Guglielmini, Carlo; De Simone, Antonio; Valbonetti, Luca; Diana, Alessia
2007-01-01
Two aged dogs with chronic obstructive airway disease were evaluated because of intermittent swelling of the ventral cervical region. Radiographs made at expiration and caudal positioning of the forelimbs allowed identification of intermittent cervical lung herniation of the left and right cranial lung lobe in both dogs. Pulmonary hyperinflation, increased expiratory effort, and chronic coughing were considered responsible for the lung herniation. Cervical lung hernia should be included in the differential diagnoses of intermittent cervical swelling in dogs with chronic respiratory disorders associated with increased expiratory effort and chronic coughing.
Chaos and its Role in Design and Simulation of Railway Vehicles
DEFF Research Database (Denmark)
True, Hans
1996-01-01
First certain important properties of nonlinear problems are discussed. Thenthe concept of chaos is described. It can only appear in nonlinear systemsand it is very common in the real world. Certain characteristic features ofdeterministic chaos and in relation hereto tests for the existence...... of chaos indynamical systems are presented.\\ Next the relevance of chaos for railwaydynamics is discussed and examples of chaotic oscillations in railwaydynamical model are shown, whereby the distinction between a chaoticattractor and transient chaos is introduces. Some causes of chaos in railwaytechnology...... are discussed. Finally the effects of chaos on field tests andnumerical simulations are discussed....
Method of controlling chaos in laser equations
International Nuclear Information System (INIS)
Duong-van, M.
1993-01-01
A method of controlling chaotic to laminar flows in the Lorenz equations using fixed points dictated by minimizing the Lyapunov functional was proposed by Singer, Wang, and Bau [Phys. Rev. Lett. 66, 1123 (1991)]. Using different fixed points, we find that the solutions in a chaotic regime can also be periodic. Since the laser equations are isomorphic to the Lorenz equations we use this method to control chaos when the laser is operated over the pump threshold. Furthermore, by solving the laser equations with an occasional proportional feedback mechanism, we recover the essential laser controlling features experimentally discovered by Roy, Murphy, Jr., Maier, Gills, and Hunt [Phys. Rev. Lett. 68, 1259 (1992)
Chaos of several typical asymmetric systems
International Nuclear Information System (INIS)
Feng Jingjing; Zhang Qichang; Wang Wei
2012-01-01
The threshold for the onset of chaos in asymmetric nonlinear dynamic systems can be determined using an extended Padé method. In this paper, a double-well asymmetric potential system with damping under external periodic excitation is investigated, as well as an asymmetric triple-well potential system under external and parametric excitation. The integrals of Melnikov functions are established to demonstrate that the motion is chaotic. Threshold values are acquired when homoclinic and heteroclinic bifurcations occur. The results of analytical and numerical integration are compared to verify the effectiveness and feasibility of the analytical method.
Method of controlling chaos in laser equations
Duong-van, Minh
1993-01-01
A method of controlling chaotic to laminar flows in the Lorenz equations using fixed points dictated by minimizing the Lyapunov functional was proposed by Singer, Wang, and Bau [Phys. Rev. Lett. 66, 1123 (1991)]. Using different fixed points, we find that the solutions in a chaotic regime can also be periodic. Since the laser equations are isomorphic to the Lorenz equations we use this method to control chaos when the laser is operated over the pump threshold. Furthermore, by solving the laser equations with an occasional proportional feedback mechanism, we recover the essential laser controlling features experimentally discovered by Roy, Murphy, Jr., Maier, Gills, and Hunt [Phys. Rev. Lett. 68, 1259 (1992)].
Controlling chaos in Internet congestion control model
International Nuclear Information System (INIS)
Chen Liang; Wang Xiaofan; Han Zhengzhi
2004-01-01
The TCP end-to-end congestion control plus RED router queue management can be modeled as a discrete-time dynamical system, which may create complex bifurcating and chaotic behavior. Based on the basic features of the TCP-RED model, we propose a time-dependent delayed feedback control algorithm to control chaos in the system by perturbing the accessible RED parameter p max . This method is able to stabilized a router queue occupancy at a level without knowing the exact knowledge of the network. Further, we study the situation of the presence of the UDP traffic
Experimental chaos in nonlinear vibration isolation system
International Nuclear Information System (INIS)
Lou Jingjun; Zhu Shijian; He Lin; He Qiwei
2009-01-01
The chaotic vibration isolation method was studied thoroughly from an experimental perspective. The nonlinear load-deflection characteristic of the conical coil spring used in the experiment was surveyed. Chaos and subharmonic responses including period-2 and period-6 motions were observed. The line spectrum reduction and the drop of the acceleration vibration level in chaotic state and that in non-chaotic state were compared, respectively. It was concluded from the experiment that the nonlinear vibration isolation system in chaotic state has strong ability in line spectrum reduction.