WorldWideScience

Sample records for archaic chaos intrinsically

  1. 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....

  2. Some chaotic features of intrinsically coupled Josephson junctions

    International Nuclear Information System (INIS)

    Kolahchi, M.R.; Shukrinov, Yu.M.; Hamdipour, M.; Botha, A.E.; Suzuki, M.

    2013-01-01

    Highlights: ► Intrinsically coupled Josephson junctions model a high-T c superconductor. ► Intrinsically coupled Josephson junctions can act as a chaotic nonlinear system. ► Chaos could be due to resonance overlap. ► Avoiding parameters that lead to chaos is important for the design of resonators. -- Abstract: We look for chaos in an intrinsically coupled system of Josephson junctions. This study has direct applications for the high-T c resonators which require coherence amongst the junctions

  3. [Shedding light on chaos theory].

    Science.gov (United States)

    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.

  4. Archaic admixture in human history.

    Science.gov (United States)

    Wall, Jeffrey D; Yoshihara Caldeira Brandt, Debora

    2016-12-01

    Modern humans evolved in Southern or Eastern Africa, and spread from there across the rest of the world. As they expanded across Africa and Eurasia, they encountered other hominin groups. The extent to which modern and 'archaic' human groups interbred is an area of active research, and while we know that modern humans interbred with Neanderthals and Denisovans, there is not yet agreement on how many admixture events there were or on how much Neanderthal or Denisovan DNA can be found in contemporary genomes. Here we review what is known about archaic admixture in human history, with a focus on what has been discovered in the past 2 years. Copyright © 2016 Elsevier Ltd. All rights reserved.

  5. High-dimensional chaos from self-sustained collisions of solitons

    Energy Technology Data Exchange (ETDEWEB)

    Yildirim, O. Ozgur, E-mail: donhee@seas.harvard.edu, E-mail: oozgury@gmail.com [Cavium, Inc., 600 Nickerson Rd., Marlborough, Massachusetts 01752 (United States); Ham, Donhee, E-mail: donhee@seas.harvard.edu, E-mail: oozgury@gmail.com [Harvard University, 33 Oxford St., Cambridge, Massachusetts 02138 (United States)

    2014-06-16

    We experimentally demonstrate chaos generation based on collisions of electrical solitons on a nonlinear transmission line. The nonlinear line creates solitons, and an amplifier connected to it provides gain to these solitons for their self-excitation and self-sustenance. Critically, the amplifier also provides a mechanism to enable and intensify collisions among solitons. These collisional interactions are of intrinsically nonlinear nature, modulating the phase and amplitude of solitons, thus causing chaos. This chaos generated by the exploitation of the nonlinear wave phenomena is inherently high-dimensional, which we also demonstrate.

  6. Morphological comparison of archaic Homo sapiens crania from China and Africa.

    Science.gov (United States)

    Wu, X; Bräuer, G

    1993-12-01

    Regional features play a great role in the analysis of the differentiations of Homo erectus and Homo sapiens. However, this poses the question how widespread and variable these features are. In order to examine this with regard to the features commonly seen in China their occurrence and variability were determined in Chinese as well as in African crania of archaic and late Pleistocene/Holocene modern Homo sapiens. Furthermore, some features known from Africa were examined with regard to their occurrence and variability in China. Although the variability might change due to new finds, the present results for some features point to larger morphological spectra in the African than in the Chinese archaic Homo sapiens. It is furthermore remarkable that the early modern Chinese in many features show deviations from the pattern of archaic Homo sapiens of this region and exhibit broader spectra similar to those seen in African archaic and early modern Homo sapiens.

  7. The shaping of modern human immune systems by multiregional admixture with archaic humans.

    Science.gov (United States)

    Abi-Rached, Laurent; Jobin, Matthew J; Kulkarni, Subhash; McWhinnie, Alasdair; Dalva, Klara; Gragert, Loren; Babrzadeh, Farbod; Gharizadeh, Baback; Luo, Ma; Plummer, Francis A; Kimani, Joshua; Carrington, Mary; Middleton, Derek; Rajalingam, Raja; Beksac, Meral; Marsh, Steven G E; Maiers, Martin; Guethlein, Lisbeth A; Tavoularis, Sofia; Little, Ann-Margaret; Green, Richard E; Norman, Paul J; Parham, Peter

    2011-10-07

    Whole genome comparisons identified introgression from archaic to modern humans. Our analysis of highly polymorphic human leukocyte antigen (HLA) class I, vital immune system components subject to strong balancing selection, shows how modern humans acquired the HLA-B*73 allele in west Asia through admixture with archaic humans called Denisovans, a likely sister group to the Neandertals. Virtual genotyping of Denisovan and Neandertal genomes identified archaic HLA haplotypes carrying functionally distinctive alleles that have introgressed into modern Eurasian and Oceanian populations. These alleles, of which several encode unique or strong ligands for natural killer cell receptors, now represent more than half the HLA alleles of modern Eurasians and also appear to have been later introduced into Africans. Thus, adaptive introgression of archaic alleles has significantly shaped modern human immune systems.

  8. [Archaic stereotypies and modern approaches for understanding of ageing].

    Science.gov (United States)

    Grigoryeva, I A; Kelasev, V N

    2017-01-01

    In the article we discussed the processes of awareness of the place of elderly people in modern society, elaboration of adequate relation to global aging and elderly themselves are still going in social sciences. These processes are expressed in a clash of archaic stereotypes and new approaches which changed social and age structure requires. Not only elderly people are providers of archaic stereotypes, but scientific institutions and practices as well. Reorientation of science, media and social policy towards study and realization of «postponed aging» opportunities is needed.

  9. Chaos and non-linear phenomena in renal vascular control

    DEFF Research Database (Denmark)

    Yip, K P; Holstein-Rathlou, N H

    1996-01-01

    are an example of deterministic chaos. Experimental studies show that the development of hypertension is associated with an increase in strength of the interaction between nephrons. Mathematical models suggest that an increased nephron-nephron interaction could cause a bifurcation in the dynamics of TGF from...... periodic oscillations to deterministic chaos. In addition to the TGF mediated oscillation, experimental studies have also demonstrated the presence of a faster oscillation, this having a frequency of 120-160 mHz. This is caused by a mechanism intrinsic to the vascular wall, and presumably represents...

  10. Harnessing quantum transport by transient chaos.

    Science.gov (United States)

    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.

  11. Chaos, complexity, and random matrices

    Science.gov (United States)

    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.

  12. Palaeo-philosophy: Complex and Concept in Archaic Patterns of Thought

    Directory of Open Access Journals (Sweden)

    Paul S. MacDonald

    2005-01-01

    Full Text Available This paper argues that efforts to understand historically remote patterns of thought are driven away from their original meaning if the investigation focuses on reconstruction of concepts. It is simply not appropriate to be looking for an archaic concept of soul, name or dream, for example, when considering the earliest documents which attest to their writers’ (and others’ beliefs about certain types of phenomena. Instead, we propose to employ the notion of cognitive complex (as elaborated in the work of Piaget, Vygotsky, and Hallpike in order to investigate some important philosophical themes in Ancient Egyptian, Ancient Iranian, and Ancient Near Eastern documents. Our principal theoretical claim is that archaic thought does not work with concepts but with complexes whose salient features are an over-abundance of properties, an over-production of connections, and weakness in abstraction. The basic level of complex formation may be the most inclusive level at which it is possible to form a mental image. Specific studies are focused on ancient texts which exhibit archaic patterns of thought. In Egyptian texts, “manifestation” (kheperu seems to convey something which all categories of beings are capable of becoming, being and having, assuming and leaving; the “name” (ren was considered to be an essential component of the individual’s survival; symbolic representations, such as images and words, are causally connected to the ‘objects’ the image or word signifies. In ANE records the human etemmu was plainly the corpse or skeleton of the dead person; on the other hand it was also the shadowy, volatile image of what he was during life. In ANE records the baffling idea of the divine me referred to an entire cultural area, an acquisition of civilized life; but at the same time it is also the result of an invention, a divine decision. The complexes involved in these archaic ideas about soul, name and dream are ideas fused with their

  13. 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.

  14. 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.

  15. The intrinsic stochasticity of near-integrable Hamiltonian systems

    Energy Technology Data Exchange (ETDEWEB)

    Krlin, L [Ceskoslovenska Akademie Ved, Prague (Czechoslovakia). Ustav Fyziky Plazmatu

    1989-09-01

    Under certain conditions, the dynamics of near-integrable Hamiltonian systems appears to be stochastic. This stochasticity (intrinsic stochasticity, or deterministic chaos) is closely related to the Kolmogorov-Arnold-Moser (KAM) theorem of the stability of near-integrable multiperiodic Hamiltonian systems. The effect of the intrinsic stochasticity attracts still growing attention both in theory and in various applications in contemporary physics. The paper discusses the relation of the intrinsic stochasticity to the modern ergodic theory and to the KAM theorem, and describes some numerical experiments on related astrophysical and high-temperature plasma problems. Some open questions are mentioned in conclusion. (author).

  16. Space in Archaic Greek Lyric : City, Countryside and Sea

    NARCIS (Netherlands)

    Heirman, Jo

    2012-01-01

    From the end of the twentieth century onwards space has become a 'hot topic' in literary studies. This thesis contributes to the spatial turn by focusing on space in archaic Greek lyric (7th-5th c bc). A theoretical framework inspired by narratology, phenomenology and metaphor theory is applied to

  17. Silver sources of archaic Greek coinage

    International Nuclear Information System (INIS)

    Gentner, W.; Mueller, O.; Wagner, G.A.; Gale, N.H.

    1978-01-01

    The authors report on new chemical and lead isotopic results and interpretations of archaic Greek silver coins from the Asyut hoard which was buried around 475 B.C. Aeginetan coins were of central interest in this study. Possible ancient silver mines were explored in the Aegean region in the course of several geologic expeditions, and chemically and isotopically investigated. Some of the silver sources in Greece were traced by combination of the analytical methods and questions of provenance were solved. In addition, processes of silver smelting and refining were studied. Results and implications of this work are summarized in the final section on Conclusions. (orig.) [de

  18. Granular chaos and mixing: Whirled in a grain of sand

    Energy Technology Data Exchange (ETDEWEB)

    Shinbrot, Troy, E-mail: shinbrot@rutgers.edu [Department of Biomedical Engineering, Rutgers University, Piscataway, New Jersey 08854 (United States)

    2015-09-15

    In this paper, we overview examples of chaos in granular flows. We begin by reviewing several remarkable behaviors that have intrigued researchers over the past few decades, and we then focus on three areas in which chaos plays an intrinsic role in granular behavior. First, we discuss pattern formation in vibrated beds, which we show is a direct result of chaotic scattering combined with dynamical dissipation. Next, we consider stick-slip motion, which involves chaotic scattering on the micro-scale, and which results in complex and as yet unexplained peculiarities on the macro-scale. Finally, we examine granular mixing, which we show combines micro-scale chaotic scattering and macro-scale stick-slip motion into behaviors that are well described by dynamical systems tools, such as iterative mappings.

  19. Granular chaos and mixing: Whirled in a grain of sand.

    Science.gov (United States)

    Shinbrot, Troy

    2015-09-01

    In this paper, we overview examples of chaos in granular flows. We begin by reviewing several remarkable behaviors that have intrigued researchers over the past few decades, and we then focus on three areas in which chaos plays an intrinsic role in granular behavior. First, we discuss pattern formation in vibrated beds, which we show is a direct result of chaotic scattering combined with dynamical dissipation. Next, we consider stick-slip motion, which involves chaotic scattering on the micro-scale, and which results in complex and as yet unexplained peculiarities on the macro-scale. Finally, we examine granular mixing, which we show combines micro-scale chaotic scattering and macro-scale stick-slip motion into behaviors that are well described by dynamical systems tools, such as iterative mappings.

  20. Stimulus-dependent suppression of chaos in recurrent neural networks

    International Nuclear Information System (INIS)

    Rajan, Kanaka; Abbott, L. F.; Sompolinsky, Haim

    2010-01-01

    Neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli. Using mean-field analysis, we ask how a neural network that intrinsically generates chaotic patterns of activity can remain sensitive to extrinsic input. We find that inputs not only drive network responses, but they also actively suppress ongoing activity, ultimately leading to a phase transition in which chaos is completely eliminated. The critical input intensity at the phase transition is a nonmonotonic function of stimulus frequency, revealing a 'resonant' frequency at which the input is most effective at suppressing chaos even though the power spectrum of the spontaneous activity peaks at zero and falls exponentially. A prediction of our analysis is that the variance of neural responses should be most strongly suppressed at frequencies matching the range over which many sensory systems operate.

  1. Quantum chaos

    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.)

  2. Archaic artifacts resembling celestial spheres

    Science.gov (United States)

    Dimitrakoudis, S.; Papaspyrou, P.; Petoussis, V.; Moussas, X.

    We present several bronze artifacts from the Archaic Age in Greece (750-480 BC) that resemble celestial spheres or forms of other astronomical significance. They are studied in the context of the Dark Age transition from Mycenaean Age astronomical themes to the philosophical and practical revival of astronomy in the Classical Age with its plethora of astronomical devices. These artifacts, mostly votive in nature are spherical in shape and appear in a variety of forms their most striking characteristic being the depiction of meridians and/or an equator. Most of those artifacts come from Thessaly, and more specifically from the temple of Itonia Athena at Philia, a religious center of pan-Hellenic significance. Celestial spheres, similar in form to the small artifacts presented in this study, could be used to measure latitudes, or estimate the time at a known place, and were thus very useful in navigation.

  3. Pausanias and the Archaic Agora at Athens

    DEFF Research Database (Denmark)

    Dickenson, Christopher Paul

    2015-01-01

    This article challenges the increasingly popular view that Pausanias’s description of Athens in the 2nd century A.D. contains a reference to the Agora of the city in the Archaic period. Consideration of Pausanias’s methods and his attitude toward the agoras of other Greek cities described in his...... work suggests that the “agora” mentioned in his description of Athens is most likely the so-called Roman Agora, paid for by Julius Caesar and Augustus. The discussion also casts light on the function and meaning of the agora in Greek cities of the Roman period, and on the ways in which Pausanias should...

  4. Embrace the Chaos

    Science.gov (United States)

    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…

  5. Chaos in neurons and its application: perspective of chaos engineering.

    Science.gov (United States)

    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.

  6. A 400,000-year-old mitochondrial genome questions phylogenetic relationships amongst archaic hominins

    DEFF Research Database (Denmark)

    Orlando, Ludovic Antoine Alexandre

    2014-01-01

    By combining state-of-the-art approaches in ancient genomics, Meyer and co-workers have reconstructed the mitochondrial sequence of an archaic hominin that lived at Sierra de Atapuerca, Spain about 400,000 years ago. This achievement follows recent advances in molecular anthropology that delivere...

  7. Spatial interaction creates period-doubling bifurcation and chaos of urbanization

    International Nuclear Information System (INIS)

    Chen Yanguang

    2009-01-01

    This paper provides a new way of looking at complicated dynamics of simple mathematical models. The complicated behavior of simple equations is one of the headstreams of chaos theory. However, a recent study based on dynamical equations of urbanization shows that there are still some undiscovered secrets behind the simple mathematical models such as logistic equation. The rural-urban interaction model can also display varied kinds of complicated dynamics, including period-doubling bifurcation and chaos. The two-dimension map of urbanization presents the same dynamics as that from the one-dimension logistic map. In theory, the logistic equation can be derived from the two-population interaction model. This seems to suggest that the complicated behavior of simple models results from interaction rather than pure intrinsic randomicity. In light of this idea, the classical predator-prey interaction model can be revised to explain the complex dynamics of logistic equation in physical and social sciences.

  8. Defining chaos.

    Science.gov (United States)

    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.

  9. 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.

  10. Quantum chaos

    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)

  11. Paths to 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)

  12. Model for Shock Wave Chaos

    KAUST Repository

    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

  13. Does chaos assist localization or delocalization?

    Science.gov (United States)

    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.

  14. Death and revival of chaos.

    Science.gov (United States)

    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.

  15. Colpitts and Chaos

    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...

  16. Noise tolerant spatiotemporal chaos computing.

    Science.gov (United States)

    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.

  17. 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.

  18. Chaos Criminology: A critical analysis

    Science.gov (United States)

    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.

  19. Chaos excited chaos synchronizations of integral and fractional order generalized van der Pol systems

    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

  20. Chaos theory in politics

    CERN Document Server

    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.

  1. Stochastic Estimation via Polynomial Chaos

    Science.gov (United States)

    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

  2. Frequency and developmental timing of linear enamel hypoplasia defects in Early Archaic Texan hunter-gatherers

    Directory of Open Access Journals (Sweden)

    J. Colette Berbesque

    2018-02-01

    Full Text Available Digital photographs taken under controlled conditions were used to examine the incidence of linear enamel hypoplasia defects (LEHs in burials from the Buckeye Knoll archaeological site (41VT98 Victoria county, Texas, which spans the Early to Late Archaic Period (ca. 2,500–6,500 BP uncorrected radiocarbon. The majority (68 of 74 burials date to the Texas Early Archaic, including one extremely early burial dated to 8,500 BP. The photogrammetric data collection method also results in an archive for Buckeye Knoll, a significant rare Archaic period collection that has been repatriated and reinterred. We analyzed the incidence and developmental timing of LEHs in permanent canines. Fifty-nine percent of permanent canines (n = 54 had at least one defect. There were no significant differences in LEH frequency between the maxillary and mandibular canines (U = 640.5, n1 = 37, n2 = 43, p = .110. The sample studied (n = 92 permanent canines had an overall mean of 0.93 LEH defect per tooth, with a median of one defect, and a mode of zero defects. Average age at first insult was 3.92 (median = 4.00, range = 2.5–5.4 and the mean age of all insults per individual was 4.18 years old (range = 2.5–5.67. Age at first insult is consistent with onset of weaning stress—the weaning age range for hunter-gatherer societies is 1–4.5. Having an earlier age of first insult was associated with having more LEHs (n = 54, rho = −0.381, p = 0.005.

  3. Chaos and noise.

    Science.gov (United States)

    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.

  4. "Chaos Rules" Revisited

    Science.gov (United States)

    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…

  5. Chaos applications in telecommunications

    CERN Document Server

    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

  6. A bound on chaos

    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.

  7. Application of Chaos Theory to Engine Systems

    OpenAIRE

    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...

  8. Hastily Formed Networks-Chaos to Recovery

    Science.gov (United States)

    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

  9. 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

  10. 3D pulsed chaos lidar system.

    Science.gov (United States)

    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.

  11. Archaic adaptive introgression in TBX15/WARS2

    DEFF Research Database (Denmark)

    Racimo, Fernando; Gokhman, David; Fumagalli, Matteo

    2017-01-01

    A recent study conducted the first genome-wide scan for selection in Inuit from Greenland using SNP chip data. Here, we report that selection in the region with the second most extreme signal of positive selection in Greenlandic Inuit favored a deeply divergent haplotype that is closely related...... to the sequence in the Denisovan genome, and was likely introgressed from an archaic population. The region contains two genes, WARS2 and TBX15, and has previously been associated with adipose tissue differentiation and body-fat distribution in humans. We show that the adaptively introgressed allele has been...... under selection in a much larger geographic region than just Greenland. Furthermore, it is associated with changes in expression of WARS2 and TBX15 in multiple tissues including the adrenal gland and subcutaneous adipose tissue, and with regional DNA methylation changes in TBX15....

  12. Recent development of chaos theory in topological dynamics

    OpenAIRE

    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.

  13. Chaos at High School

    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.

  14. Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems

    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

  15. The joy of transient chaos

    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.

  16. The joy of transient chaos.

    Science.gov (United States)

    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.

  17. 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))

  18. 2012 Symposium on Chaos, Complexity and Leadership

    CERN Document Server

    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.

  19. 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...

  20. Nonlinear chaos control and synchronization

    NARCIS (Netherlands)

    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

  1. 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.

  2. Experimental Induction of Genome Chaos.

    Science.gov (United States)

    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.

  3. 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.

  4. Using chaos theory: the implications for nursing.

    Science.gov (United States)

    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.

  5. 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

  6. 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....

  7. 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 ...

  8. 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

  9. Towards chaos criterion in quantum field theory

    OpenAIRE

    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.

  10. Semiconductor Lasers Stability, Instability and Chaos

    CERN Document Server

    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...

  11. Advances in chaos theory and intelligent control

    CERN Document Server

    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...

  12. 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...

  13. Encounters with chaos and fractals

    CERN Document Server

    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.

  14. Treponemal disease in the middle Archaic to early Woodland periods of the western Tennessee River Valley.

    Science.gov (United States)

    Smith, Maria Ostendorf

    2006-10-01

    The high frequency of late prehistoric New World treponemal disease is attributable to the demographic changes concomitant with the adoption of agriculture. However, these demographic changes in group mobility and site density episodically preceded intensive plant domestication, suggesting possible staggered temporal change in observed treponemal disease case frequency. Thirteen convincing and an additional two probable (N = 581) cases of treponemal disease were identified in an eight-site skeletal sample spanning the Middle (6,000-3,000 BCE) to Late (2,500-ca. 1,000 to 500 BCE) Archaic and Early Woodland (500 BCE-0 CE) periods from the western Tennessee River Valley. Treponemal disease cases are infrequent in both the Middle (3/115, 2.6%) and Late (2 to 4 cases, subsistence economy across the Archaic-Woodland temporal boundary in the western Tennessee River Valley remained, as elsewhere, based on intensive hunting and collecting, the demographic corollaries of treponemal disease would apparently not be met. However, the traditional horizon marker of the Woodland period is the adoption of pottery, an activity associated with sedentism.

  15. 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

  16. 4th international interdisciplinary chaos symposium

    CERN Document Server

    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...

  17. Chaos to periodicity and periodicity to chaos by periodic perturbations in the Belousov-Zhabotinsky reaction

    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

  18. Fractals and chaos

    CERN Document Server

    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...

  19. 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

  20. Scaling of chaos in strongly nonlinear lattices.

    Science.gov (United States)

    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.

  1. 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.

  2. Colored chaos

    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

  3. Colored chaos

    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.

  4. Survival and weak chaos.

    Science.gov (United States)

    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.

  5. 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....

  6. 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...

  7. 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

  8. 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

  9. The chaos cookbook a practical programming guide

    CERN Document Server

    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

  10. Genome chaos: survival strategy during crisis.

    Science.gov (United States)

    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.

  11. 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

  12. How to test for partially predictable chaos.

    Science.gov (United States)

    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.

  13. The archaic concept of the universe and its echo in Russian traditional embroidery

    Science.gov (United States)

    Denisova, I.

    2001-12-01

    This paper is a brief account of the hypothetical concept of the stages of development of ancient cosmology. An attempt to interpret the original semantics of Russian folk embroidery has led the author to a reconstruction of archaic cosmology, based upon the idea of the Universe as a live autoreproductive organism/being. This approach allows to clear up some 'dark spots' in mythology and to consider separate cults as elements of the whole system. The rudiments of such system manifest themselves in different cultures of the world.

  14. Channeling and dynamic chaos

    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.

  15. 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

  16. Chaos in periodically forced Holling type IV predator-prey system with impulsive perturbations

    International Nuclear Information System (INIS)

    Zhang Shuwen; Tan Dejun; Chen Lansun

    2006-01-01

    The effect of periodic forcing and impulsive perturbations on predator-prey model with Holling type IV functional response is investigated. The periodic forcing is affected by assuming a periodic variation in the intrinsic growth rate of the prey. The impulsive perturbations are affected by introducing periodic constant impulsive immigration of predator. The dynamical behavior of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that periodic forcing and impulsive perturbation can easily give rise to complex dynamics, including (1) quasi-periodic oscillating, (2) period doubling cascade, (3) chaos, (4) period halfing cascade

  17. Chaos in periodically forced Holling type II predator-prey system with impulsive perturbations

    International Nuclear Information System (INIS)

    Zhang Shuwen; Tan Dejun; Chen Lansun

    2006-01-01

    The effect of periodic forcing and impulsive perturbations on predator-prey model with Holling type II functional response is investigated. The periodic forcing is affected by assuming a periodic variation in the intrinsic growth rate of prey. The impulsive perturbation is affected by introducing periodic constant impulsive immigration of predator. The dynamical behavior of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that periodic forcing and impulsive perturbation can very easily give rise to complex dynamics, including (1) quasi-periodic oscillating, (2) period doubling cascade, (3) chaos, (4) period halfing cascade, (5) non-unique dynamics

  18. 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.

  19. 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.

  20. 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.)

  1. Chaos in collective nuclei

    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

  2. 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.

  3. Meaning Finds a Way: Chaos (Theory) and Composition

    Science.gov (United States)

    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.

  4. 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

  5. Interplay of Determinism and Randomness: From Irreversibility to Chaos, Fractals, and Stochasticity

    Science.gov (United States)

    Tsonis, A.

    2017-12-01

    We will start our discussion into randomness by looking exclusively at our formal mathematical system to show that even in this pure and strictly logical system one cannot do away with randomness. By employing simple mathematical models, we will identify the three possible sources of randomness: randomness due to inability to find the rules (irreversibility), randomness due to inability to have infinite power (chaos), and randomness due to stochastic processes. Subsequently we will move from the mathematical system to our physical world to show that randomness, through the quantum mechanical character of small scales, through chaos, and because of the second law of thermodynamics, is an intrinsic property of nature as well. We will subsequently argue that the randomness in the physical world is consistent with the three sources of randomness suggested from the study of simple mathematical systems. Many examples ranging from purely mathematical to natural processes will be presented, which clearly demonstrate how the combination of rules and randomness produces the world we live in. Finally, the principle of least effort or the principle of minimum energy consumption will be suggested as the underlying principle behind this symbiosis between determinism and randomness.

  6. Chaos in World Politics: A Reflection

    Science.gov (United States)

    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.

  7. Controllable chaos in hybrid electro-optomechanical systems

    Science.gov (United States)

    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

  8. Controllable chaos in hybrid electro-optomechanical systems.

    Science.gov (United States)

    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.

  9. 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

  10. Relativistic quantum chaos-An emergent interdisciplinary field.

    Science.gov (United States)

    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.

  11. 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

  12. Order against chaos in nuclei

    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.))

  13. Effects of maturation and acidosis on the chaos-like complexity of the neural respiratory output in the isolated brainstem of the tadpole, Rana esculenta

    Science.gov (United States)

    Samara, Ziyad; Fiamma, Marie-Noëlle; Bautin, Nathalie; Ranohavimparany, Anja; Le Coz, Patrick; Golmard, Jean-Louis; Darré, Pierre; Zelter, Marc; Poon, Chi-Sang; Similowski, Thomas

    2011-01-01

    Human ventilation at rest exhibits mathematical chaos-like complexity that can be described as long-term unpredictability mediated (in whole or in part) by some low-dimensional nonlinear deterministic process. Although various physiological and pathological situations can affect respiratory complexity, the underlying mechanisms remain incompletely elucidated. If such chaos-like complexity is an intrinsic property of central respiratory generators, it should appear or increase when these structures mature or are stimulated. To test this hypothesis, we employed the isolated tadpole brainstem model [Rana (Pelophylax) esculenta] and recorded the neural respiratory output (buccal and lung rhythms) of pre- (n = 8) and postmetamorphic tadpoles (n = 8), at physiologic (7.8) and acidic pH (7.4). We analyzed the root mean square of the cranial nerve V or VII neurograms. Development and acidosis had no effect on buccal period. Lung frequency increased with development (P Chaos-like complexity, assessed through the noise limit, increased from pH 7.8 to pH 7.4 (P chaos-like complexity, especially in the postmetamorphic stage and at low pH. According to the ventilatory generators homology theory, this may also be the case in mammals. PMID:21325645

  14. 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.)

  15. Chaos in hadrons

    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.

  16. Household chaos and family sleep during infants' first year.

    Science.gov (United States)

    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).

  17. 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

  18. Chaos the science of predictable random motion

    CERN Document Server

    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.

  19. Using largest Lyapunov exponent to confirm the intrinsic stability of boiling water reactors

    International Nuclear Information System (INIS)

    Gavilian-Moreno, Carlos; Espinosa-Paredes, Gilberto

    2016-01-01

    The aim of this paper is the study of instability state of boiling water reactors with a method based in largest Lyapunov exponents (LLEs). Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the LLE. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. This method was applied to a set of signals from several nuclear power plant (NPP) reactors under commercial operating conditions that experienced instabilities events, apparently each of a different nature. Laguna Verde and Forsmark NPPs with in-phase instabilities, and Cofrentes NPP with out-of-phases instability. This study presents the results of intrinsic instability in the boiling water reactors of three NPPs. In the analyzed cases the limit cycle was not reached, which implies that the point of equilibrium exerts influence and attraction on system evolution

  20. Using largest Lyapunov exponent to confirm the intrinsic stability of boiling water reactors

    Energy Technology Data Exchange (ETDEWEB)

    Gavilian-Moreno, Carlos [Iberdrola Generacion, S.A., Cofrentes Nuclear Power Plant, Project Engineering Department, Paraje le Plano S/N, Valencia (Spain); Espinosa-Paredes, Gilberto [Area de ingeniera en Recursos Energeticos, Universidad Autonoma Metropolitana-Iztapalapa, Mexico city (Mexico)

    2016-04-15

    The aim of this paper is the study of instability state of boiling water reactors with a method based in largest Lyapunov exponents (LLEs). Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the LLE. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. This method was applied to a set of signals from several nuclear power plant (NPP) reactors under commercial operating conditions that experienced instabilities events, apparently each of a different nature. Laguna Verde and Forsmark NPPs with in-phase instabilities, and Cofrentes NPP with out-of-phases instability. This study presents the results of intrinsic instability in the boiling water reactors of three NPPs. In the analyzed cases the limit cycle was not reached, which implies that the point of equilibrium exerts influence and attraction on system evolution.

  1. Using Largest Lyapunov Exponent to Confirm the Intrinsic Stability of Boiling Water Reactors

    Directory of Open Access Journals (Sweden)

    Carlos J. Gavilán-Moreno

    2016-04-01

    Full Text Available The aim of this paper is the study of instability state of boiling water reactors with a method based in largest Lyapunov exponents (LLEs. Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the LLE. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. This method was applied to a set of signals from several nuclear power plant (NPP reactors under commercial operating conditions that experienced instabilities events, apparently each of a different nature. Laguna Verde and Forsmark NPPs with in-phase instabilities, and Cofrentes NPP with out-of-phases instability. This study presents the results of intrinsic instability in the boiling water reactors of three NPPs. In the analyzed cases the limit cycle was not reached, which implies that the point of equilibrium exerts influence and attraction on system evolution.

  2. 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

  3. Chaos Theory and Post Modernism

    Science.gov (United States)

    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…

  4. 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])

  5. 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

  6. !CHAOS: A cloud of controls

    Science.gov (United States)

    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.

  7. !CHAOS: A cloud of controls

    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.

  8. On CFT and quantum chaos

    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.

  9. 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)

  10. 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)

  11. On CFT and quantum chaos

    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.

  12. Semiconductor lasers stability, instability and chaos

    CERN Document Server

    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...

  13. 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

  14. Iani Chaos

    Science.gov (United States)

    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.

  15. Semiconductor Lasers Stability, Instability and Chaos

    CERN Document Server

    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.

  16. Chua's circuit a paradigm for chaos

    CERN Document Server

    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

  17. The Strength of Chaos: Accurate Simulation of Resonant Electron Scattering by Many-Electron Ions and Atoms in the Presence of Quantum Chaos

    Science.gov (United States)

    2017-01-20

    AFRL-AFOSR-JP-TR-2017-0012 The Strength of Chaos : accurate simulation of resonant electron scattering by many-electron ions and atoms in the presence...of quantum chaos Igor Bray CURTIN UNIVERSITY OF TECHNOLOGY Final Report 01/20/2017 DISTRIBUTION A: Distribution approved for public release. AF...SUBTITLE The Strength of Chaos : accurate simulation of resonant electron scattering by many- electron ions and atoms in the presence of quantum chaos

  18. CHAOS-BASED ADVANCED ENCRYPTION STANDARD

    KAUST Repository

    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

  19. 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.

  20. 2nd International Symposium on Chaos, Complexity and Leadership

    CERN Document Server

    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.

  1. 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

  2. Chaos in electric drive systems analysis control and application

    CERN Document Server

    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...

  3. Discursive Maps at the Edge of Chaos

    Science.gov (United States)

    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

  4. Exploiting chaos for applications.

    Science.gov (United States)

    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.

  5. 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.

  6. 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)

  7. 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.

  8. Chaos, Chaos Control and Synchronization of a Gyrostat System

    Science.gov (United States)

    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.

  9. 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....

  10. 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

  11. Chaos on the interval

    CERN Document Server

    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...

  12. 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...

  13. 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 ...

  14. 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

  15. Chaos concepts, control and constructive use

    CERN Document Server

    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...

  16. An archaic ionian inscription in Huelva | Una inscripción jonia arcaica en Huelva

    OpenAIRE

    Jesús Fernández Jurado; Ricardo Olmos Romera

    1985-01-01

    We analyse in this paper a bowl fragment, probably Milesian, which comes from the excavations of Calle del Puerto, in the Tartessian settlement of Huelva. Along the outside lip runs an archaic Ionian inscription —middle of the 6th c. B .C.— whose interpretation is particularly difficult. It may be a dedication or offering made by a Greek for a local chief. But nothing can be said about it with certainty. | Se estudia en este artículo un fragmento de cuenco, probablemente milesio, que procede ...

  17. Global chaos synchronization with channel time-delay

    International Nuclear Information System (INIS)

    Jiang Guoping; Zheng Weixing; Chen Guanrong

    2004-01-01

    This paper addresses a practical issue in chaos synchronization where there is a time-delay in the receiver as compared with the transmitter. A new synchronization scheme and a general criterion for global chaos synchronization are proposed and developed from the approach of unidirectional linear error feedback coupling with time-delay. The chaotic Chua's circuit is used for illustration, where the coupling parameters are determined according to the criterion under which the global chaos synchronization of the time-delay coupled systems is achieved

  18. 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)

  19. 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

  20. L'ordre du chaos

    CERN Document Server

    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.

  1. 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

  2. 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. “System” will be rigorously defined. Can a low-informational rapid succession of Prigogine’s dissipative structures self-order into bona fide organization?

  3. The Six Fundamental Characteristics of Chaos and Their Clinical Relevance to Psychiatry: a New Hypothesis for the Origin of Psychosis

    Science.gov (United States)

    Schmid, Gary Bruno

    Underlying idea: A new hypothesis about how the mental state of psychosis may arise in the brain as a "linear" information processing pathology is briefly introduced. This hypothesis is proposed in the context of a complementary approach to psychiatry founded in the logical paradigm of chaos theory. To best understand the relation between chaos theory and psychiatry, the semantic structure of chaos theory is analyzed with the help of six general, and six specific, fundamental characteristics which can be directly inferred from empirical observations on chaotic systems. This enables a mathematically and physically stringent perspective on psychological phenomena which until now could only be grasped intuitively: Chaotic systems are in a general sense dynamic, intrinsically coherent, deterministic, recursive, reactive and structured: in a specific sense, self-organizing, unpredictable, nonreproducible, triadic, unstable and self-similar. To a great extent, certain concepts of chaos theory can be associated with corresponding concepts in psychiatry, psychology and psychotherapy, thus enabling an understanding of the human psyche in general as a (fractal) chaotic system and an explanation of certain mental developments, such as the course of schizophrenia, the course of psychosis and psychotherapy as chaotic processes. General overview: A short comparison and contrast of classical and chaotic physical theory leads to four postulates and one hypothesis motivating a new, dynamic, nonlinear approach to classical, causal psychiatry: Process-Oriented PSYchiatry or "POPSY", for short. Four aspects of the relationship between chaos theory and POPSY are discussed: (1) The first of these, namely, Identification of Chaos / Picture of Illness involves a definition of Chaos / Psychosis and a discussion of the 6 logical characteristics of each. This leads to the concept of dynamical disease (definition, characteristics and examples) and to the idea of "psychological disturbance as

  4. 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.

  5. 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

  6. Replication of chaos in neural networks, economics and physics

    CERN Document Server

    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.

  7. Observation of Hamiltonian chaos and its control in wave-particle interaction

    International Nuclear Information System (INIS)

    Doveil, F; Macor, A; Aissi, A

    2007-01-01

    Wave-particle interactions are central in plasma physics. They can be studied in a traveling wave tube (TWT) to avoid intrinsic plasma noise. This led to detailed experimental analysis of the self-consistent interaction between unstable waves and an either cold or warm beam. More recently a test cold electron beam has been used to observe its non-self-consistent interaction with externally excited wave(s). The velocity distribution function of the electron beam is recorded with a trochoidal energy analyzer at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the slow wave structure (a 4 m long helix) of the TWT. The nonlinear synchronization of particles by a single wave responsible for Landau damping is observed. The resonant velocity domain associated with a single wave is also observed, as well as the transition to large scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a 'devil's staircase' behavior when increasing the excitation amplitude in agreement with numerical simulation. A new strategy for control of chaos by building barriers of transport which prevent electrons from escaping from a given velocity region as well as its robustness are successfully tested. The underlying concepts extend far beyond the field of electron devices and plasma physics

  8. 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

  9. Chaos based encryption system for encrypting electroencephalogram signals.

    Science.gov (United States)

    Lin, Chin-Feng; Shih, Shun-Han; Zhu, Jin-De

    2014-05-01

    In the paper, we use the Microsoft Visual Studio Development Kit and C# programming language to implement a chaos-based electroencephalogram (EEG) encryption system involving three encryption levels. A chaos logic map, initial value, and bifurcation parameter for the map were used to generate Level I chaos-based EEG encryption bit streams. Two encryption-level parameters were added to these elements to generate Level II chaos-based EEG encryption bit streams. An additional chaotic map and chaotic address index assignment process was used to implement the Level III chaos-based EEG encryption system. Eight 16-channel EEG Vue signals were tested using the encryption system. The encryption was the most rapid and robust in the Level III system. The test yielded superior encryption results, and when the correct deciphering parameter was applied, the EEG signals were completely recovered. However, an input parameter error (e.g., a 0.00001 % initial point error) causes chaotic encryption bit streams, preventing the recovery of 16-channel EEG Vue signals.

  10. Chaos from simple models to complex systems

    CERN Document Server

    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

  11. 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...

  12. Controlling chaos in a pendulum equation with ultra-subharmonic resonances

    International Nuclear Information System (INIS)

    Yang Jianping; Jing Zhujun

    2009-01-01

    Analytical and numerical results concerning control of chaos in a pendulum equation with parametric and external excitations are given by using Melnikov methods. We give the necessary conditions of chaos control with ultra-subharmonic resonances (i.e. Ω/ω=p/q,q>1,p,q are prime), where homoclinic chaos or heteroclinic chaos can be inhibited. Numerical simulations show that chaotic behavior can be converted to period-nq (n element of Z + ) orbits by adjusting amplitude and phase-difference of parametric excitation, and the distribution of maximum Lyapunov exponents in parameter-plane (Ψ,β) gives the regions in which chaos can be controlled.

  13. Ray and wave chaos in underwater acoustic waveguides

    International Nuclear Information System (INIS)

    Virovlyansky, Anatolii L; Makarov, Denis V; Prants, Sergei V

    2012-01-01

    In the 1990s, the study of the chaotic behavior of ray trajectories in inhomogeneous waveguides emerged as a new field in ocean acoustics. It turned out that at ranges on the order of or larger than 1000 km ray chaos is well developed and should be taken into account when describing long-range sound propagation in the ocean. The theoretical analysis of ray chaos and of its finite-wavelength manifestation, wave chaos, is to a large extent based on well-known methods and ideas from the theory of dynamical and quantum chaos. Concrete examples are used to review the results obtained in this field over the last two decades. (reviews of topical problems)

  14. 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

  15. Galloping instability to chaos of cables

    CERN Document Server

    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.

  16. Control of chaos in a three-well duffing system

    International Nuclear Information System (INIS)

    Yang Jianping; Jing Zhujun

    2009-01-01

    Analytical and numerical results concerning control of chaos in a three-well duffing system with two external excitations are given by using the Melnikov methods proposed by Chacon et al. [Chacon R. General results on chaos suppression for biharmonically driven dissipative systems. Phys Lett A 1999;257:293-300, Chacon R, Palmero F, Balibrea F. Taming chaos in a driven Josephson Junction. Int J Bifurc Chaos 2001;11(7):1897-909, Chacon R. Role of ultrasubharmonic resonances in taming chaos by weak harmonic perturbations. Europhys Lett 2001;54(2):148C153]. We theoretically give the parameter-space region and intervals of initial phase difference for primary and subharmonic resonance and the necessary condition for the superharmonic and supersubharmonic resonance, where homoclinic chaos or heteroclinic chaos can be suppressed. Numerical simulations show the consistency and difference with theoretical analysis and the chaotic behavior can be converted to periodic orbits by adjusting amplitude and phase-difference of inhibiting excitation. Moreover, we consider the influence of parametric frequency on maximum Lyapunov exponent (LE) for different phase-differences, and give the distribution of maximum Lyapunov exponents in parameter-plane, which indicates the regions of non-chaotic states (non-positive LE) and chaotic states (positive LE).

  17. CHAOS: An SDN-Based Moving Target Defense System

    Directory of Open Access Journals (Sweden)

    Yuan Shi

    2017-01-01

    Full Text Available Moving target defense (MTD has provided a dynamic and proactive network defense to reduce or move the attack surface that is available for exploitation. However, traditional network is difficult to realize dynamic and active security defense effectively and comprehensively. Software-defined networking (SDN points out a brand-new path for building dynamic and proactive defense system. In this paper, we propose CHAOS, an SDN-based MTD system. Utilizing the programmability and flexibility of SDN, CHAOS obfuscates the attack surface including host mutation obfuscation, ports obfuscation, and obfuscation based on decoy servers, thereby enhancing the unpredictability of the networking environment. We propose the Chaos Tower Obfuscation (CTO method, which uses the Chaos Tower Structure (CTS to depict the hierarchy of all the hosts in an intranet and define expected connection and unexpected connection. Moreover, we develop fast CTO algorithms to achieve a different degree of obfuscation for the hosts in each layer. We design and implement CHAOS as an application of SDN controller. Our approach makes it very easy to realize moving target defense in networks. Our experimental results show that a network protected by CHAOS is capable of decreasing the percentage of information disclosure effectively to guarantee the normal flow of traffic.

  18. Spin squeezing as an indicator of quantum chaos in the Dicke model.

    Science.gov (United States)

    Song, Lijun; Yan, Dong; Ma, Jian; Wang, Xiaoguang

    2009-04-01

    We study spin squeezing, an intrinsic quantum property, in the Dicke model without the rotating-wave approximation. We show that the spin squeezing can reveal the underlying chaotic and regular structures in phase space given by a Poincaré section, namely, it acts as an indicator of quantum chaos. Spin squeezing vanishes after a very short time for an initial coherent state centered in a chaotic region, whereas it persists over a longer time for the coherent state centered in a regular region of the phase space. We also study the distribution of the mean spin directions when quantum dynamics takes place. Finally, we discuss relations among spin squeezing, bosonic quadrature squeezing, and two-qubit entanglement in the dynamical processes.

  19. Neutron activation analysis of bird bowls and related archaic ceramics from Miletus

    International Nuclear Information System (INIS)

    Kerschner, M.; Mommsen, H.; Beier, T.; Heimermann, D.; Hein, A.

    1993-01-01

    In this paper we present the results of a chemical investigation by neutron activation analysis of sherds of different kinds of bird kotylai, bird bowls and related wares excavated in Kalabaktepe, a hill of the ancient city of Miletus. A new archaeological classification of this well-known group of Archaic ceramics of eastern Greece is presented. A number of kiln wasters of misfired vessels from Kalabaktepe revealed a characteristic local pattern. This pattern helped to clarify the provenance of some of the bird bowls classified archaeologically as of orientalizing type: they have been made in Miletus. But bird kotylai and bird bowls in the ''standard fabric'' as well as other archaeologically related vessels show a different chemical pattern of unknown provenance. (author)

  20. Neutron activation analysis of bird bowls and related archaic ceramics from Miletus

    International Nuclear Information System (INIS)

    Kerschner, M.; Mommsen, H.; Beier, T.; Heimermann, D.; Hein, A.

    1993-01-01

    In this paper we present the results of a chemical investigation by neutron activation analysis of sherds of different kinds of bird kotylai, bird bowls and related wares excavated in Kalabaktepe, a hill of the ancient city of Miletus. A new archaeological classification of this well-known group of Archaic ceramics of eastern Greece is represented. A number of kiln wasters of misfired vessels from Kalabaktepe revealed a characteristic local pattern. This pattern helped to clarify the provenance of some of the bird bowls classified archaeologically as of orientalizing type: they have been made in Miletus. But bird kotylai and bird bowls in the 'standard fabric' as well as other archaeologically related vessels show a different chemical pattern of unknown provenance. (author)

  1. 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...

  2. Controlling beam halo-chaos via backstepping design

    International Nuclear Information System (INIS)

    Gao Yuan; Kong Feng

    2008-01-01

    A backstepping control method is proposed for controlling beam halo-chaos in the periodic focusing channels (PFCs) of high-current ion accelerator. The analysis and numerical results show that the method, via adjusting an exterior magnetic field, is effective to control beam halo chaos with five types of initial distribution ion beams, all statistical quantities of the beam halo-chaos are largely reduced, and the uniformity of ion beam is improved. This control method has an important value of application, for the exterior magnetic field can be easily adjusted in the periodical magnetic focusing channels in experiment

  3. Chaos in the Solar System

    Science.gov (United States)

    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!

  4. Hyperbolic Chaos A Physicist’s View

    CERN Document Server

    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.  

  5. Effortful control and school adjustment: The moderating role of classroom chaos.

    Science.gov (United States)

    Berger, Rebecca H; Valiente, Carlos; Eisenberg, Nancy; Hernandez, Maciel M; Thompson, Marilyn; Spinrad, Tracy; VanSchyndel, Sarah; Silva, Kassondra; Southworth, Jody

    2017-11-01

    Guided by the person by environment framework, the primary goal of this study was to determine whether classroom chaos moderated the relation between effortful control and kindergarteners' school adjustment. Classroom observers reported on children's ( N = 301) effortful control in the fall. In the spring, teachers reported on classroom chaos and school adjustment outcomes (teacher-student relationship closeness and conflict, and school liking and avoidance). Cross-level interactions between effortful control and classroom chaos predicting school adjustment outcomes were assessed. A consistent pattern of interactions between effortful control and classroom chaos indicated that the relations between effortful control and the school adjustment outcomes were strongest in high chaos classrooms. Post-hoc analyses indicated that classroom chaos was associated with poor school adjustment when effortful control was low, suggesting that the combination of high chaos and low effortful control was associated with the poorest school outcomes.

  6. Chaos as a Social Determinant of Child Health: Reciprocal Associations?

    Science.gov (United States)

    Schmeer, Kammi K.; Taylor, Miles

    2013-01-01

    This study informs the social determinants of child health by exploring an understudied aspect of children’s social contexts: chaos. Chaos has been conceptualized as crowded, noisy, disorganized, unpredictable settings for child development (Evans et al., 2010). We measure chaos at two levels of children’s ecological environment - the microsystem (household) and the mesosystem (work-family-child care nexus) – and at two points in early childhood (ages 3 and 5). Using data from the Fragile Families and Child Wellbeing Study (N=3288), a study of predominantly low-income women and their partners in large US cities, we develop structural equation models that assess how maternal-rated child health (also assessed at ages 3 and 5) is associated with latent constructs of chaos, and whether there are important reciprocal effects. Autoregressive crosslagged path analysis suggest that increasing chaos (at both the household and maternal work levels) is associated with worse child health, controlling for key confounders like household economic status, family structure, and maternal health status. Child health has little effect on chaos, providing further support for the hypothesis that chaos is an important social determinant of child health in this sample of relatively disadvantaged children. This suggests child health may be improved by supporting families in ways that reduce chaos in their home and work/family environments, and that as researchers move beyond SES, race, and family structure to explore other sources of health inequalities, chaos and its proximate determinants may be a promising avenue for future research. PMID:23541250

  7. Chaos: Choto delat?

    Science.gov (United 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.

  8. 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

  9. 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.

  10. 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

  11. Model for Shock Wave Chaos

    KAUST Repository

    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.

  12. From chaos to order methodologies, perspectives and applications

    CERN Document Server

    Chen Guan Rong

    1998-01-01

    Chaos control has become a fast-developing interdisciplinary research field in recent years. This book is for engineers and applied scientists who want to have a broad understanding of the emerging field of chaos control. It describes fundamental concepts, outlines representative techniques, provides case studies, and highlights recent developments, putting the reader at the forefront of current research.Important topics presented in the book include: Fundamentals of nonlinear dynamical systems, essential for understanding and developing chaos control methods.; Parametric variation and paramet

  13. Philosophical perspectives on quantum chaos: Models and interpretations

    Science.gov (United States)

    Bokulich, Alisa Nicole

    2001-09-01

    The problem of quantum chaos is a special case of the larger problem of understanding how the classical world emerges from quantum mechanics. While we have learned that chaos is pervasive in classical systems, it appears to be almost entirely absent in quantum systems. The aim of this dissertation is to determine what implications the interpretation of quantum mechanics has for attempts to explain the emergence of classical chaos. There are three interpretations of quantum mechanics that have set out programs for solving the problem of quantum chaos: the standard interpretation, the statistical interpretation, and the deBroglie-Bohm causal interpretation. One of the main conclusions of this dissertation is that an interpretation alone is insufficient for solving the problem of quantum chaos and that the phenomenon of decoherence must be taken into account. Although a completely satisfactory solution of the problem of quantum chaos is still outstanding, I argue that the deBroglie-Bohm interpretation with the help of decoherence outlines the most promising research program to pursue. In addition to making a contribution to the debate in the philosophy of physics concerning the interpretation of quantum mechanics, this dissertation reveals two important methodological lessons for the philosophy of science. First, issues of reductionism and intertheoretic relations cannot be divorced from questions concerning the interpretation of the theories involved. Not only is the exploration of intertheoretic relations a central part of the articulation and interpretation of an individual theory, but the very terms used to discuss intertheoretic relations, such as `state' and `classical limit', are themselves defined by particular interpretations of the theory. The second lesson that emerges is that, when it comes to characterizing the relationship between classical chaos and quantum mechanics, the traditional approaches to intertheoretic relations, namely reductionism and

  14. 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.)

  15. Discrete chaos with applications in science and engineering

    CERN Document Server

    Elaydi, Saber N

    2007-01-01

    PREFACE FOREWORD The Stability of One-Dimensional Maps Introduction Maps vs. Difference Equations Maps vs. Differential Equations Linear Maps/Difference Equations Fixed (Equilibrium) Points Graphical Iteration and Stability Criteria for Stability Periodic Points and Their Stability The Period-Doubling Route to Chaos Applications Attraction and Bifurcation Introduction Basin of Attraction of Fixed Points Basin of Attraction of Periodic Orbits Singer's Theorem Bifurcation Sharkovsky's Theorem The Lorenz Map Period-Doubling in the Real World Poincaré Section/Map Appendix Chaos in One Dimension Introduction Density of the Set of Periodic Points Transitivity Sensitive Dependence Definition of Chaos Cantor Sets Symbolic Dynamics Conjugacy Other Notions of Chaos Rössler's Attractor Saturn's Rings Stability of Two-Dimensional Maps Linear Maps vs. Linear Systems Computing An Fundamental Set of Solutions Second-Order Difference Equations Phase Space ...

  16. 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.

  17. Gullies of Gorgonus Chaos

    Science.gov (United States)

    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

  18. 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.

  19. Quantum chaos induced by nonadiabatic coupling in wave-packet dynamics

    International Nuclear Information System (INIS)

    Higuchi, Hisashi; Takatsuka, Kazuo

    2002-01-01

    The effect of nonadiabatic coupling due to breakdown of the Born-Oppenheimer approximation on chaos is investigated. A couple of measures (indicators) that detect the extent of chaos in wave-packet dynamics on coupled potential functions are devised. Using them, we show that chaos is indeed induced by a nonadiabatic coupling in individual time-dependent wave-packet dynamics. This chaos is genuinely of quantum nature, since it arises from bifurcation and merging of a wave packet at the quasicrossing region of two coupled potential functions

  20. 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

  1. Polynomiography and Chaos

    Science.gov (United States)

    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.

  2. Collision analysis of one kind of chaos-based hash function

    International Nuclear Information System (INIS)

    Xiao Di; Peng Wenbing; Liao Xiaofeng; Xiang Tao

    2010-01-01

    In the last decade, various chaos-based hash functions have been proposed. Nevertheless, the corresponding analyses of them lag far behind. In this Letter, we firstly take a chaos-based hash function proposed very recently in Amin, Faragallah and Abd El-Latif (2009) as a sample to analyze its computational collision problem, and then generalize the construction method of one kind of chaos-based hash function and summarize some attentions to avoid the collision problem. It is beneficial to the hash function design based on chaos in the future.

  3. Congenital high airway obstruction syndrome (CHAOS) associated with cervical myelomeningocele.

    Science.gov (United States)

    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.

  4. Chaos analysis and chaotic EMI suppression of DC-DC converters

    CERN Document Server

    Zhang, Bo

    2014-01-01

    Introduces chaos theory, its analytical methods and the means to apply chaos to the switching power supply design DC-DC converters are typical switching systems which have plenty of nonlinear behaviors, such as bifurcation and chaos. The nonlinear behaviors of DC-DC converters have been studied heavily over the past 20 years, yet researchers are still unsure of the practical application of bifurcations and chaos in switching converters. The electromagnetic interference (EMI), which resulted from the high rates of changes of voltage and current, has become a major design criterion in DC-DC co

  5. Colloquium: Random matrices and chaos in nuclear spectra

    International Nuclear Information System (INIS)

    Papenbrock, T.; Weidenmueller, H. A.

    2007-01-01

    Chaos occurs in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the existence of chaos be reconciled with the known dynamical features of spherical nuclei? Such nuclei are described by the shell model (a mean-field theory) plus a residual interaction. The question is answered using a statistical approach (the two-body random ensemble): The matrix elements of the residual interaction are taken to be random variables. Chaos is shown to be a generic feature of the ensemble and some of its properties are displayed, emphasizing those which differ from standard random-matrix theory. In particular, the existence of correlations among spectra carrying different quantum numbers is demonstrated. These are subject to experimental verification

  6. Effects of maturation and acidosis on the chaos-like complexity of the neural respiratory output in the isolated brainstem of the tadpole, Rana esculenta.

    Science.gov (United States)

    Straus, Christian; Samara, Ziyad; Fiamma, Marie-Noëlle; Bautin, Nathalie; Ranohavimparany, Anja; Le Coz, Patrick; Golmard, Jean-Louis; Darré, Pierre; Zelter, Marc; Poon, Chi-Sang; Similowski, Thomas

    2011-05-01

    Human ventilation at rest exhibits mathematical chaos-like complexity that can be described as long-term unpredictability mediated (in whole or in part) by some low-dimensional nonlinear deterministic process. Although various physiological and pathological situations can affect respiratory complexity, the underlying mechanisms remain incompletely elucidated. If such chaos-like complexity is an intrinsic property of central respiratory generators, it should appear or increase when these structures mature or are stimulated. To test this hypothesis, we employed the isolated tadpole brainstem model [Rana (Pelophylax) esculenta] and recorded the neural respiratory output (buccal and lung rhythms) of pre- (n = 8) and postmetamorphic tadpoles (n = 8), at physiologic (7.8) and acidic pH (7.4). We analyzed the root mean square of the cranial nerve V or VII neurograms. Development and acidosis had no effect on buccal period. Lung frequency increased with development (P acidosis, but in postmetamorphic tadpoles only (P respiratory central rhythm generator accounts for ventilatory chaos-like complexity, especially in the postmetamorphic stage and at low pH. According to the ventilatory generators homology theory, this may also be the case in mammals.

  7. 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

  8. 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

  9. Chaos in nuclei: Theory and experiment

    Science.gov (United States)

    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.

  10. Stochastic chaos in a Duffing oscillator and its control

    International Nuclear Information System (INIS)

    Wu Cunli; Lei Youming; Fang Tong

    2006-01-01

    Stochastic chaos discussed here means a kind of chaotic responses in a Duffing oscillator with bounded random parameters under harmonic excitations. A system with random parameters is usually called a stochastic system. The modifier 'stochastic' here implies dependent on some random parameter. As the system itself is stochastic, so is the response, even under harmonic excitations alone. In this paper stochastic chaos and its control are verified by the top Lyapunov exponent of the system. A non-feedback control strategy is adopted here by adding an adjustable noisy phase to the harmonic excitation, so that the control can be realized by adjusting the noise level. It is found that by this control strategy stochastic chaos can be tamed down to the small neighborhood of a periodic trajectory or an equilibrium state. In the analysis the stochastic Duffing oscillator is first transformed into an equivalent deterministic nonlinear system by the Gegenbauer polynomial approximation, so that the problem of controlling stochastic chaos can be reduced into the problem of controlling deterministic chaos in the equivalent system. Then the top Lyapunov exponent of the equivalent system is obtained by Wolf's method to examine the chaotic behavior of the response. Numerical simulations show that the random phase control strategy is an effective way to control stochastic chaos

  11. Handbook of Chaos Control

    CERN Document Server

    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

  12. Chaos Theory as a Model for Managing Issues and Crises.

    Science.gov (United States)

    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…

  13. God's Stuff: The Constructive Powers of Chaos for Teaching Religion

    Science.gov (United States)

    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…

  14. 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

  15. The Nature (and Nurture) of Children's Perceptions of Family Chaos

    Science.gov (United States)

    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…

  16. Experimental study of chaos synchronization in the Belousov-Zhabotinsky chemical system

    International Nuclear Information System (INIS)

    Li Yanni; Chen Lan; Cai Zunsheng; Zhao Xuezhuang

    2004-01-01

    Employing self-adaptive parameter regulation scheme, chaos synchronization in the Belousov-Zhabotinsky-CSTR chemical system has been studied experimentally. By optimizing the combination of regulation parameters, the trend of chaos synchronization is observed and the prediction of chaos synchronization from numerical simulation is thus verified by the experiment. In addition, the difference of sensitivity to noise with the mass coupling scheme and the self-adaptive parameter regulation scheme in chaos synchronization has also been discussed

  17. 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

  18. Individual chaos implies collective chaos for weakly mixing discrete dynamical systems

    International Nuclear Information System (INIS)

    Liao Gongfu; Ma Xianfeng; Wang Lidong

    2007-01-01

    Let X be a metric space (X,f) a discrete dynamical system, where f:X->X is a continuous function. Let f-bar denote the natural extension of f to the space of all non-empty compact subsets of X endowed with Hausdorff metric induced by d. In this paper we investigate some dynamical properties of f and f-bar . It is proved that f is weakly mixing (mixing) if and only if f-bar is weakly mixing (mixing, respectively). From this, we deduce that weak-mixing of f implies transitivity of f-bar , further, if f is mixing or weakly mixing, then chaoticity of f (individual chaos) implies chaoticity of f-bar (collective chaos) and if X is a closed interval then f-bar is chaotic (in the sense of Devaney) if and only if f is weakly mixing

  19. 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

  20. Calculating topological entropy for transient chaos with an application to communicating with chaos

    International Nuclear Information System (INIS)

    Jacobs, J.; Ott, E.; Hunt, B.R.

    1998-01-01

    Recent work on communicating with chaos provides a practical motivation for being able to determine numerically the topological entropy for chaotic invariant sets. In this paper we discuss numerical methods for evaluating topological entropy. To assess the accuracy and convergence of the methods, we test them in situations where the topological entropy is known independently. We also discuss the entropy of invariant chaotic saddles formed by those points in a given attractor that never visit some forbidden 'gap' region. Such gaps have been proposed as a means of providing noise immunity in schemes for communication with chaos, and we discuss the dependence of the topological entropy on the size of the gap. copyright 1998 The American Physical Society

  1. The Chaos of Katrina

    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...

  2. Generic superweak chaos induced by Hall effect

    Science.gov (United States)

    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.

  3. Editor's intervention in the register of compounds in archaic Portuguese texts: some reflections on the use of hyphen

    Directory of Open Access Journals (Sweden)

    Antonia Vieira dos Santos

    2014-07-01

    Full Text Available The use of hyphen within compounds was not built up before the nineteenth century. Thus, compounds spelled with hyphen in archaic Portuguese texts are a result of editing criteria adopted by editors. From this type of intervention, the relationship between hyphen use – result of a spelling convention – and the definition of compound adopted by the editor are discussed. Its absence is significant to the history of the language.

  4. 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.

  5. Design of High-Security USB Flash Drives Based on Chaos Authentication

    Directory of Open Access Journals (Sweden)

    Teh-Lu Liao

    2018-05-01

    Full Text Available This paper aims to propose a novel design of high-security USB flash drives with the chaos authentication. A chaos authentication approach with the non-linear encryption and decryption function design is newly proposed and realized based on the controller design of chaos synchronization. To complete the design of high-security USB flash drives, first, we introduce six parameters into the original Henon map to adjust and obtain richer chaotic state responses. Then a discrete sliding mode scheme is proposed to solve the synchronization problem of discrete hyperchaotic Henon maps. The proposed sliding mode controller can ensure the synchronization of the master-slave Henon maps. The selection of the switching surface and the existence of the sliding motion are also addressed. Finally, the obtained results are applied to design a new high-security USB flash drive with chaos authentication. We built discrete hyperchaotic Henon maps in the smartphone (master and microcontroller (slave, respectively. The Bluetooth module is used to communicate between the master and the slave to achieve chaos synchronization such that the same random and dynamical chaos signal can be simultaneously obtained at both the USB flash drive and smartphone, and pass the chaos authentication. When users need to access data in the flash drive, they can easily enable the encryption APP in the smartphone (master for chaos authentication. After completing the chaos synchronization and authentication, the ARM-based microcontroller allows the computer to access the data in the high-security USB flash drive.

  6. Chaos: A Topic for Interdisciplinary Education in Physics

    Science.gov (United States)

    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…

  7. Controlling chaos faster

    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

  8. Fascination of chaos

    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)

  9. Controlling chaos faster.

    Science.gov (United States)

    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.

  10. Controlling chaos faster

    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.

  11. Elimination of spiral chaos by periodic force for the Aliev-Panfilov model

    OpenAIRE

    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.

  12. 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

  13. 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...

  14. Household chaos, sociodemographic risk, coparenting, and parent-infant relations during infants' first year.

    Science.gov (United States)

    Whitesell, Corey J; Teti, Douglas M; Crosby, Brian; Kim, Bo-Ram

    2015-04-01

    Household chaos is a construct often overlooked in studies of human development, despite its theoretical links with the integrity of individual well-being, family processes, and child development. The present longitudinal study examined relations between household chaos and well-established correlates of chaos (sociodemographic risk, major life events, and personal distress) and several constructs that, to date, are theoretically linked with chaos but never before assessed as correlates (quality of coparenting and emotional availability with infants at bedtime). In addressing this aim, we introduce a new measure of household chaos (the Descriptive In-home Survey of Chaos--Observer ReporteD, or DISCORD), wholly reliant on independent observer report, which draws from household chaos theory and prior empirical work but extends the measurement of chaos to include information about families' compliance with a home visiting protocol. Household chaos was significantly associated with socioeconomic risk, negative life events, less favorable coparenting, and less emotionally available bedtime parenting, but not with personal distress. These findings emphasize the need to examine household chaos as a direct and indirect influence on child and family outcomes, as a moderator of intervention attempts to improving parenting and child development, and as a target of intervention in its own right. (c) 2015 APA, all rights reserved).

  15. 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

  16. Chaos and order in models of black hole pairs

    International Nuclear Information System (INIS)

    Levin, Janna

    2006-01-01

    Chaos in the orbits of black hole pairs has by now been confirmed by several independent groups. While the chaotic behavior of binary black hole orbits is no longer argued, it remains difficult to quantify the importance of chaos to the evolutionary dynamics of a pair of comparable mass black holes. None of our existing approximations are robust enough to offer convincing quantitative conclusions in the most highly nonlinear regime. It is intriguing to note that, in three different approximations to a black hole pair built of a spinning black hole and a nonspinning companion, two approximations exhibit chaos and one approximation does not. The fully relativistic scenario of a spinning test mass around a Schwarzschild black hole shows chaos, as does the post-Newtonian Lagrangian approximation. However, the approximately equivalent post-Newtonian Hamiltonian approximation does not show chaos when only one body spins. It is well known in dynamical systems theory that one system can be regular while an approximately related system is chaotic, so there is no formal conflict. However, the physical question remains: Is there chaos for comparable mass binaries when only one object spins? We are unable to answer this question given the poor convergence of the post-Newtonian approximation to the fully relativistic system. A resolution awaits better approximations that can be trusted in the highly nonlinear regime

  17. Chaotic operation and chaos control of travelling wave ultrasonic motor.

    Science.gov (United States)

    Shi, Jingzhuo; Zhao, Fujie; Shen, Xiaoxi; Wang, Xiaojie

    2013-08-01

    The travelling wave ultrasonic motor, which is a nonlinear dynamic system, has complex chaotic phenomenon with some certain choices of system parameters and external inputs, and its chaotic characteristics have not been studied until now. In this paper, the preliminary study of the chaos phenomenon in ultrasonic motor driving system has been done. The experiment of speed closed-loop control is designed to obtain several groups of time sampling data sequence of the amplitude of driving voltage, and phase-space reconstruction is used to analyze the chaos characteristics of these time sequences. The largest Lyapunov index is calculated and the result is positive, which shows that the travelling wave ultrasonic motor has chaotic characteristics in a certain working condition Then, the nonlinear characteristics of travelling wave ultrasonic motor are analyzed which includes Lyapunov exponent map, the bifurcation diagram and the locus of voltage relative to speed based on the nonlinear chaos model of a travelling wave ultrasonic motor. After that, two kinds of adaptive delay feedback controllers are designed in this paper to control and suppress chaos in USM speed control system. Simulation results show that the method can control unstable periodic orbits, suppress chaos in USM control system. Proportion-delayed feedback controller was designed following and arithmetic of fuzzy logic was used to adaptively adjust the delay time online. Simulation results show that this method could fast and effectively change the chaos movement into periodic or fixed-point movement and make the system enter into stable state from chaos state. Finally the chaos behavior was controlled. Copyright © 2013 Elsevier B.V. All rights reserved.

  18. User-Driven Chaos

    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...

  19. Does chaos theory have major implications for philosophy of medicine?

    Science.gov (United States)

    Holm, S

    2002-12-01

    In the literature it is sometimes claimed that chaos theory, non-linear dynamics, and the theory of fractals have major implications for philosophy of medicine, especially for our analysis of the concept of disease and the concept of causation. This paper gives a brief introduction to the concepts underlying chaos theory and non-linear dynamics. It is then shown that chaos theory has only very minimal implications for the analysis of the concept of disease and the concept of causation, mainly because the mathematics of chaotic processes entail that these processes are fully deterministic. The practical unpredictability of chaotic processes, caused by their extreme sensitivity to initial conditions, may raise practical problems in diagnosis, prognosis, and treatment, but it raises no major theoretical problems. The relation between chaos theory and the problem of free will is discussed, and it is shown that chaos theory may remove the problem of predictability of decisions, but does not solve the problem of free will. Chaos theory may thus be very important for our understanding of physiological processes, and specific disease entities, without having any major implications for philosophy of medicine.

  20. Biologically inspired rate control of chaos.

    Science.gov (United States)

    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.

  1. 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

  2. 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

  3. 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

  4. Chaos in charged AdS black hole extended phase space

    Science.gov (United States)

    Chabab, M.; El Moumni, H.; Iraoui, S.; Masmar, K.; Zhizeh, S.

    2018-06-01

    We present an analytical study of chaos in a charged black hole in the extended phase space in the context of the Poincare-Melnikov theory. Along with some background on dynamical systems, we compute the relevant Melnikov function and find its zeros. Then we analyse these zeros either to identify the temporal chaos in the spinodal region, or to observe spatial chaos in the small/large black hole equilibrium configuration. As a byproduct, we derive a constraint on the Black hole' charge required to produce chaotic behaviour. To the best of our knowledge, this is the first endeavour to understand the correlation between chaos and phase picture in black holes.

  5. 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.

  6. 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.

  7. Chaos and Christianity: A Response to Butz and a Biblical Alternative.

    Science.gov (United States)

    Watts, Richard E.; Trusty, Jerry

    1997-01-01

    M.R. Butz's position regarding chaos theory and Christianity is reviewed. The compatibility of biblical theology and the sciences is discussed. Parallels between chaos theory and the philosophical perspective of Soren Kierkegaard are explored. A biblical model is offered for counselors in assisting Christian clients in embracing chaos. (Author/EMK)

  8. Metadata in CHAOS

    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...

  9. Effect of smoothing on robust chaos.

    Science.gov (United States)

    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.

  10. Chaos Concepts, Control and Constructive Use

    CERN Document Server

    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...

  11. Chaos-based hash function (CBHF) for cryptographic applications

    International Nuclear Information System (INIS)

    Amin, Mohamed; Faragallah, Osama S.; Abd El-Latif, Ahmed A.

    2009-01-01

    As the core of cryptography, hash is the basic technique for information security. Many of the hash functions generate the message digest through a randomizing process of the original message. Subsequently, a chaos system also generates a random behavior, but at the same time a chaos system is completely deterministic. In this paper, an algorithm for one-way hash function construction based on chaos theory is introduced. Theoretical analysis and computer simulation indicate that the algorithm can satisfy all performance requirements of hash function in an efficient and flexible manner and secure against birthday attacks or meet-in-the-middle attacks, which is good choice for data integrity or authentication.

  12. Chaos-based hash function (CBHF) for cryptographic applications

    Energy Technology Data Exchange (ETDEWEB)

    Amin, Mohamed [Dept. of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Koom 32511 (Egypt)], E-mail: mamin04@yahoo.com; Faragallah, Osama S. [Dept. of Computer Science and Engineering, Faculty of Electronic Engineering, Menoufia University, Menouf 32952 (Egypt)], E-mail: osam_sal@yahoo.com; Abd El-Latif, Ahmed A. [Dept. of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Koom 32511 (Egypt)], E-mail: ahmed_rahiem@yahoo.com

    2009-10-30

    As the core of cryptography, hash is the basic technique for information security. Many of the hash functions generate the message digest through a randomizing process of the original message. Subsequently, a chaos system also generates a random behavior, but at the same time a chaos system is completely deterministic. In this paper, an algorithm for one-way hash function construction based on chaos theory is introduced. Theoretical analysis and computer simulation indicate that the algorithm can satisfy all performance requirements of hash function in an efficient and flexible manner and secure against birthday attacks or meet-in-the-middle attacks, which is good choice for data integrity or authentication.

  13. Chaos and the (un)predictability of evolution in a changing environment.

    Science.gov (United States)

    Rego-Costa, Artur; Débarre, Florence; Chevin, Luis-Miguel

    2018-02-01

    Among the factors that may reduce the predictability of evolution, chaos, characterized by a strong dependence on initial conditions, has received much less attention than randomness due to genetic drift or environmental stochasticity. It was recently shown that chaos in phenotypic evolution arises commonly under frequency-dependent selection caused by competitive interactions mediated by many traits. This result has been used to argue that chaos should often make evolutionary dynamics unpredictable. However, populations also evolve largely in response to external changing environments, and such environmental forcing is likely to influence the outcome of evolution in systems prone to chaos. We investigate how a changing environment causing oscillations of an optimal phenotype interacts with the internal dynamics of an eco-evolutionary system that would be chaotic in a constant environment. We show that strong environmental forcing can improve the predictability of evolution by reducing the probability of chaos arising, and by dampening the magnitude of chaotic oscillations. In contrast, weak forcing can increase the probability of chaos, but it also causes evolutionary trajectories to track the environment more closely. Overall, our results indicate that, although chaos may occur in evolution, it does not necessarily undermine its predictability. © 2017 The Author(s). Evolution © 2017 The Society for the Study of Evolution.

  14. Chaos-induced resonant effects and its control

    International Nuclear Information System (INIS)

    Zambrano, Samuel; Casado, Jose M.; Sanjuan, Miguel A.F.

    2007-01-01

    This Letter shows that a suitable chaotic signal can induce resonant effects analogous to those observed in presence of noise in a bistable system under periodic forcing. By constructing groups of chaotic and random perturbations with similar one-time statistics we show that in some cases chaos and noise induce indistinguishable resonant effects. This reinforces the conjecture by which in some situations where noise is supposed to play a key role maybe chaos is the key ingredient. Here we also show that the presence of a chaotic signal as the perturbation leading to a resonance opens new control perspectives based on our ability to stabilize chaos in different periodic orbits. A discussion of the possible implications of these facts is also presented at the end of the Letter

  15. Modified projective synchronization with complex scaling factors of uncertain real chaos and complex chaos

    International Nuclear Information System (INIS)

    Zhang Fang-Fang; Liu Shu-Tang; Yu Wei-Yong

    2013-01-01

    To increase the variety and security of communication, we present the definitions of modified projective synchronization with complex scaling factors (CMPS) of real chaotic systems and complex chaotic systems, where complex scaling factors establish a link between real chaos and complex chaos. Considering all situations of unknown parameters and pseudo-gradient condition, we design adaptive CMPS schemes based on the speed-gradient method for the real drive chaotic system and complex response chaotic system and for the complex drive chaotic system and the real response chaotic system, respectively. The convergence factors and dynamical control strength are added to regulate the convergence speed and increase robustness. Numerical simulations verify the feasibility and effectiveness of the presented schemes. (general)

  16. Some new surprises in chaos.

    Science.gov (United States)

    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.

  17. Extension of spatiotemporal chaos in glow discharge-semiconductor systems.

    Science.gov (United States)

    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).].

  18. "I Had Seen Order and Chaos, but Had Thought They Were Different." The Challenges of the Chaos Theory for Career Development

    Science.gov (United States)

    Pryor, Robert; Bright, Jim

    2004-01-01

    This paper highlights five challenges to the accepted wisdom in career development theory and practice. It presents the chaos theory of careers and argues that the chaos theory provides a more complete and authentic account of human behaviour. The paper argues that positivism, reductionism and assumptions of linearity are inappropriate for…

  19. Applying Chaos Theory to Lesson Planning and Delivery

    Science.gov (United States)

    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…

  20. Early Exposure to Environmental Chaos and Children's Physical and Mental Health.

    Science.gov (United States)

    Coley, Rebekah Levine; Lynch, Alicia Doyle; Kull, Melissa

    Environmental chaos has been proposed as a central influence impeding children's health and development, with the potential for particularly pernicious effects during the earliest years when children are most susceptible to environmental insults. This study evaluated a high-risk sample, following 495 low-income children living in poor urban neighborhoods from infancy to age 6. Longitudinal multilevel models tested the main tenets of the ecobiodevelopmental theory, finding that: (1) numerous distinct domains of environmental chaos were associated with children's physical and mental health outcomes, including housing disorder, neighborhood disorder, and relationship instability, with no significant results for residential instability; (2) different patterns emerged in relation to the timing of exposure to chaos, with more proximal exposure most strongly associated with children's functioning; and (3) the intensity of chaos also was a robust predictor of child functioning. Contrary to expectations, neither biological vulnerability (proxied through low birth weight status), maternal sensitivity, nor maternal distress moderated the role of chaos. Rather, maternal psychological distress functioned as a pathway through which environmental chaos was associated with children's functioning.

  1. The Chaos Theory of Careers: A User's Guide

    Science.gov (United States)

    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…

  2. Patterns in chaos

    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

  3. Detecting Chaos from Agricultural Product Price Time Series

    Directory of Open Access Journals (Sweden)

    Xin Su

    2014-12-01

    Full Text Available Analysis of the characteristics of agricultural product price volatility and trend forecasting are necessary to formulate and implement agricultural price control policies. Taking wholesale cabbage prices as an example, a multiple test methodology has been adopted to identify the nonlinearity, fractality, and chaos of the data. The approaches used include the R/S analysis, the BDS test, the power spectra, the recurrence plot, the largest Lyapunov exponent, the Kolmogorov entropy, and the correlation dimension. The results show that there is chaos in agricultural wholesale price data, which provides a good theoretical basis for selecting reasonable forecasting models as prediction techniques based on chaos theory can be applied to forecasting agricultural prices.

  4. 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

  5. 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)

  6. 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.

  7. 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

  8. 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).

  9. 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

  10. 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

  11. 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

  12. Topographic variations in chaos on Europa: Implications for diapiric formation

    Science.gov (United States)

    Schenk, Paul M.; Pappalardo, Robert T.

    2004-01-01

    Disrupted terrain, or chaos, on Europa, might have formed through melting of a floating ice shell from a subsurface ocean [Cam et al., 1998; Greenberg et al., 19991, or breakup by diapirs rising from the warm lower portion of the ice shell [Head and Pappalardo, 1999; Collins et al., 20001. Each model makes specific and testable predictions for topographic expression within chaos and relative to surrounding terrains on local and regional scales. High-resolution stereo-controlled photoclinometric topography indicates that chaos topography, including the archetypal Conamara Chaos region, is uneven and commonly higher than surrounding plains by up to 250 m. Elevated and undulating topography is more consistent with diapiric uplift of deep material in a relatively thick ice shell, rather than melt-through and refreezing of regionally or globally thin ice by a subsurface ocean. Vertical and horizontal scales of topographic doming in Conamara Chaos are consistent with a total ice shell thickness >15 km. Contact between Europa's ocean and surface may most likely be indirectly via diapirism or convection.

  13. Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics.

    Science.gov (United States)

    Wang, Guanglei; Lai, Ying-Cheng; Grebogi, Celso

    2016-10-17

    Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law.

  14. 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 ...

  15. A new type of cascading synchronization for halo-chaos and its potential for communication applications

    International Nuclear Information System (INIS)

    Fang Jinqing; Yu Xinghuo

    2004-01-01

    Study of beam halo-chaos has become a key issue of concern for many future important applications. Control of halo-chaos has been researched intensively. This is the first time that the synchronization of beam halo-chaos has been realized in this field so far. Two nonlinear feedback control methods are proposed for the cascading synchronizing halo-chaos in coupled lattices of a periodic focusing channel. The simulation results show that the methods are effective. The realization of the synchronization of beam halo-chaos is significant not only for halo-chaos control itself but also for halo-chaos-based secure communication which may become an innovative technique

  16. Controlling Mackey-Glass chaos

    Science.gov (United States)

    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.

  17. Chaos in quantum channels

    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.

  18. Controlling Mackey-Glass chaos.

    Science.gov (United States)

    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.

  19. 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

  20. A quantum correction to chaos

    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.

  1. Controlling the optical field chaos in storage ring free-electron lasers

    International Nuclear Information System (INIS)

    Wang Wenjie

    1995-01-01

    The controlling of optical field chaos in a storage ring free-electron laser oscillator is discussed by using a phenomenal model. A novel method (which is called the 'beating method') of controlling chaos in a nonlinear dynamical system described by non-autonomous ordinary differential equations was developed. The result of theoretical analysis and numerical simulation shows that the optical field chaos in a storage ring free-electron laser oscillator can be suppressed and a periodic laser intensity can be obtained when a weak periodic control field is added to the optical cavity. The validity of this method of eliminating chaos is confirmed by the fact that the leading Lyapunov characteristic exponent of the system changes from a positive real number to a negative one. A further research is carried out, and it is found that only when the period of the control field equals to an integral multiple of that of the gain modulation in the optical cavity can the optical field chaos be suppressed. This means that the 'beating method' of controlling chaos is a kind of resonant method. A way to determine the 'best beating position' in the phase trajectory has also been obtained

  2. 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

  3. 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 ...

  4. 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.

  5. Classical and quantum chaos in a circular billiard with a straight cut

    International Nuclear Information System (INIS)

    Ree, S.; Reichl, L.E.

    1999-01-01

    We study classical and quantum dynamics of a particle in a circular billiard with a straight cut. Classically, this system can be integrable, nonintegrable with soft chaos, or nonintegrable with hard chaos as we vary the size of the cut. We plot Poincaracute e surfaces of section to study chaos. Quantum mechanically, we look at Husimi plots, and also use the quantum web, the technique primarily used in spin systems so far, to try to see differences in quantum manifestations of soft and hard chaos. copyright 1999 The American Physical Society

  6. Chaos induced by quantum effect due to breakdown of the Born-Oppenheimer adiabaticity

    International Nuclear Information System (INIS)

    Fujisaki, Hiroshi; Takatsuka, Kazuo

    2001-01-01

    Chaos in the multimode nonadiabatic system constructed by Heller [J. Chem. Phys. >92, 1718 (1990)], which consists of two diabatic two-dimensional harmonic potentials with the Condon coupling, is studied. A thorough investigation is carried out by scanning the magnitudes of the Condon coupling and the Duschinsky angle. To elucidate mechanisms that can cause chaos in this quantum system, the statistical properties of the energy levels and eigenfunctions of the system are investigated. We find an evidence in terms of the nearest-neighbor spacing distribution of energy levels and other measures that a certain class of chaos is purely induced by the nonadiabatic interaction due to breakdown of the Born-Oppenheimer approximation. Since the nonadiabatic transition can induce repeated bifurcation and merging of a wave packet around the region of quasicrossing between two potential surfaces, and since this interaction does not have a counterpart in the lower adiabatic system, the present chaos deserves being called 'nonadiabatic chaos.' Another type of chaos in a nonadiabatic system was previously identified [D. M. Leitner et al., J. Chem. Phys. >104, 434 (1996)] that reflects the inherent chaos of a corresponding adiabatic potential. We present a comparative study to establish the similarity and difference between these kinds of chaos

  7. 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

  8. Topological chaos of the spatial prisoner's dilemma game on regular networks.

    Science.gov (United States)

    Jin, Weifeng; Chen, Fangyue

    2016-02-21

    The spatial version of evolutionary prisoner's dilemma on infinitely large regular lattice with purely deterministic strategies and no memories among players is investigated in this paper. Based on the statistical inferences, it is pertinent to confirm that the frequency of cooperation for characterizing its macroscopic behaviors is very sensitive to the initial conditions, which is the most practically significant property of chaos. Its intrinsic complexity is then justified on firm ground from the theory of symbolic dynamics; that is, this game is topologically mixing and possesses positive topological entropy on its subsystems. It is demonstrated therefore that its frequency of cooperation could not be adopted by simply averaging over several steps after the game reaches the equilibrium state. Furthermore, the chaotically changing spatial patterns via empirical observations can be defined and justified in view of symbolic dynamics. It is worth mentioning that the procedure proposed in this work is also applicable to other deterministic spatial evolutionary games therein. Copyright © 2015 Elsevier Ltd. All rights reserved.

  9. How does the Xenopus laevis embryonic cell cycle avoid spatial chaos?

    Science.gov (United States)

    Gelens, Lendert; Huang, Kerwyn Casey; Ferrell, James E.

    2015-01-01

    Summary Theoretical studies have shown that a deterministic biochemical oscillator can become chaotic when operating over a sufficiently large volume, and have suggested that the Xenopus laevis cell cycle oscillator operates close to such a chaotic regime. To experimentally test this hypothesis, we decreased the speed of the post-fertilization calcium wave, which had been predicted to generate chaos. However, cell divisions were found to develop normally and eggs developed into normal tadpoles. Motivated by these experiments, we carried out modeling studies to understand the prerequisites for the predicted spatial chaos. We showed that this type of spatial chaos requires oscillatory reaction dynamics with short pulse duration, and postulated that the mitotic exit in Xenopus laevis is likely slow enough to avoid chaos. In systems with shorter pulses, chaos may be an important hazard, as in cardiac arrhythmias, or a useful feature, as in the pigmentation of certain mollusk shells. PMID:26212326

  10. Specifying the Links Between Household Chaos and Preschool Children’s Development

    Science.gov (United States)

    Martin, Anne; Razza, Rachel; Brooks-Gunn, Jeanne

    2011-01-01

    Household chaos has been linked to poorer cognitive, behavioral, 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 instability, lack of routine, and television usually on. Chaos was measured at age 2; outcomes measured at age 5 tap receptive vocabulary, attention and behavior problems, and effortful control. Results show that controlling for all other measures of chaos, children with a lack of routine scored lower on receptive vocabulary and delayed gratification, while children whose television was generally on scored higher on aggression and attention problems. The provision of learning materials mediated a small part of the association between television and receptive vocabulary. Family instability, crowding, and noise did not predict any outcomes once other measures of chaos were controlled. PMID:22919120

  11. [Chaos theory: a fascinating concept for oncologists].

    Science.gov (United States)

    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.

  12. Complex Modified Hybrid Projective Synchronization of Different Dimensional Fractional-Order Complex Chaos and Real Hyper-Chaos

    Directory of Open Access Journals (Sweden)

    Jian Liu

    2014-11-01

    Full Text Available This paper introduces a type of modified hybrid projective synchronization with complex transformationmatrix (CMHPS for different dimensional fractional-order complex chaos and fractional-order real hyper-chaos. The transformationmatrix in this type of chaotic synchronization is a non-square matrix, and its elements are complex numbers. Based on the stability theory of fractional-order systems, by employing the feedback control technique, necessary and sufficient criteria on CMHPS are derived. Furthermore, CMHPS between fractional-order real hyper-chaotic Rössler system and other two different dimensional fractional-order complex Lorenz-like chaotic systems is provided as two examples to discuss reduced order and increased order synchronization, respectively.

  13. Chaos on hyperspace

    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

  14. Dating the Late Archaic occupation of the Norte Chico region in Peru.

    Science.gov (United States)

    Haas, Jonathan; Creamer, Winifred; Ruiz, Alvaro

    2004-12-23

    The Norte Chico region on the coast of Peru north of Lima consists of four adjacent river valleys--Huaura, Supe, Pativilca and Fortaleza--in which archaeologists have been aware of a number of apparently early sites for more than 40 years (refs 1- 3). To clarify the early chronology in this region, we undertook fieldwork in 2002 and 2003 to determine the dates of occupation of sites in the Fortaleza and Pativilca valleys. Here we present 95 new radiocarbon dates from a sample of 13 of more than 20 large, early sites. These sites share certain basic characteristics, including large-scale monumental architecture, extensive residential architecture and a lack of ceramics. The 95 new dates confirm the emergence and development of a major cultural complex in this region during the Late Archaic period between 3000 and 1800 calibrated calendar years bc. The results help to redefine a broader understanding of the respective roles of agricultural and fishing economies in the beginnings of civilization in South America.

  15. Chaos Theory and Its Application to Education: Mehmet Akif Ersoy University Case

    Science.gov (United States)

    Akmansoy, Vesile; Kartal, Sadik

    2014-01-01

    Discussions have arisen regarding the application of the new paradigms of chaos theory to social sciences as compared to physical sciences. This study examines what role chaos theory has within the education process and what effect it has by describing the views of university faculty regarding chaos and education. The participants in this study…

  16. Error function attack of chaos synchronization based encryption schemes.

    Science.gov (United States)

    Wang, Xingang; Zhan, Meng; Lai, C-H; Gang, Hu

    2004-03-01

    Different chaos synchronization based encryption schemes are reviewed and compared from the practical point of view. As an efficient cryptanalysis tool for chaos encryption, a proposal based on the error function attack is presented systematically and used to evaluate system security. We define a quantitative measure (quality factor) of the effective applicability of a chaos encryption scheme, which takes into account the security, the encryption speed, and the robustness against channel noise. A comparison is made of several encryption schemes and it is found that a scheme based on one-way coupled chaotic map lattices performs outstandingly well, as judged from quality factor. Copyright 2004 American Institute of Physics.

  17. Early Exposure to Environmental Chaos and Children’s Physical and Mental Health

    Science.gov (United States)

    Coley, Rebekah Levine; Lynch, Alicia Doyle; Kull, Melissa

    2015-01-01

    Environmental chaos has been proposed as a central influence impeding children’s health and development, with the potential for particularly pernicious effects during the earliest years when children are most susceptible to environmental insults. This study evaluated a high-risk sample, following 495 low-income children living in poor urban neighborhoods from infancy to age 6. Longitudinal multilevel models tested the main tenets of the ecobiodevelopmental theory, finding that: (1) numerous distinct domains of environmental chaos were associated with children’s physical and mental health outcomes, including housing disorder, neighborhood disorder, and relationship instability, with no significant results for residential instability; (2) different patterns emerged in relation to the timing of exposure to chaos, with more proximal exposure most strongly associated with children’s functioning; and (3) the intensity of chaos also was a robust predictor of child functioning. Contrary to expectations, neither biological vulnerability (proxied through low birth weight status), maternal sensitivity, nor maternal distress moderated the role of chaos. Rather, maternal psychological distress functioned as a pathway through which environmental chaos was associated with children’s functioning. PMID:25844016

  18. Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics

    Science.gov (United States)

    Wang, Guanglei; Lai, Ying-Cheng; Grebogi, Celso

    2016-01-01

    Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law. PMID:27748418

  19. Relations between distributional, Li-Yorke and ω chaos

    International Nuclear Information System (INIS)

    Guirao, Juan Luis Garcia; Lampart, Marek

    2006-01-01

    The forcing relations between notions of distributional, Li-Yorke and ω chaos were studied by many authors. In this paper we summarize all known connections between these three different types of chaos and fulfill the results for general compact metric spaces by the construction of a selfmap on a compact perfect set which is ω chaotic, not distributionally chaotic and has zero topological entropy

  20. 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.

  1. Relations between distributional, Li-Yorke and {omega} chaos

    Energy Technology Data Exchange (ETDEWEB)

    Guirao, Juan Luis Garcia [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, C/Paseo Alfonso XIII, 30203-Cartagena (Region de Murcia) (Spain)]. E-mail: juan.garcia@upct.es; Lampart, Marek [Mathematical Institute at Opava, Silesian University at Opava, Na Rybnicku 1, 746 01 Opava (Czech Republic)]. E-mail: marek.lampart@math.slu.cz

    2006-05-15

    The forcing relations between notions of distributional, Li-Yorke and {omega} chaos were studied by many authors. In this paper we summarize all known connections between these three different types of chaos and fulfill the results for general compact metric spaces by the construction of a selfmap on a compact perfect set which is {omega} chaotic, not distributionally chaotic and has zero topological entropy.

  2. The Application of Chaos Theory to the Career-Plateaued Worker.

    Science.gov (United States)

    Duffy, Jean Ann

    2000-01-01

    Applies some of the principles of chaos theory to career-plateaued workers on the basis of a case study. Concludes that chaos theory provides career practitioners a useful application for working with this type of client. (Author/JDM)

  3. A quantum correction to chaos

    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.

  4. On the definition of 'chaos'

    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.

  5. The transition to chaos conservative classical systems and quantum manifestations

    CERN Document Server

    Reichl, Linda E

    2004-01-01

    This book provides a thorough and comprehensive discussion of classical and quantum chaos theory for bounded systems and for scattering processes Specific discussions include • Noether’s theorem, integrability, KAM theory, and a definition of chaotic behavior • Area-preserving maps, quantum billiards, semiclassical quantization, chaotic scattering, scaling in classical and quantum dynamics, dynamic localization, dynamic tunneling, effects of chaos in periodically driven systems and stochastic systems • Random matrix theory and supersymmetry The book is divided into several parts Chapters 2 through 4 deal with the dynamics of nonlinear conservative classical systems Chapter 5 and several appendices give a thorough grounding in random matrix theory and supersymmetry techniques Chapters 6 and 7 discuss the manifestations of chaos in bounded quantum systems and open quantum systems respectively Chapter 8 focuses on the semiclassical description of quantum systems with underlying classical chaos, and Chapt...

  6. Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet

    Science.gov (United States)

    Valdez, Marc Andrew; Shchedrin, Gavriil; Heimsoth, Martin; Creffield, Charles E.; Sols, Fernando; Carr, Lincoln D.

    2018-06-01

    We uncover signatures of quantum chaos in the many-body dynamics of a Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose measures including entanglement, condensate depletion, and spreading over a fixed basis in many-body Hilbert space, which quantitatively identify the region in which quantum chaotic many-body dynamics occurs, where random matrix theory is limited or inaccessible. With these tools, we show that many-body quantum chaos is neither highly entangled nor delocalized in the Hilbert space, contrary to conventionally expected signatures of quantum chaos.

  7. Dynamical topology and statistical properties of spatiotemporal chaos.

    Science.gov (United States)

    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.

  8. 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

  9. Entanglement as a signature of quantum chaos.

    Science.gov (United States)

    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.

  10. Nonlinear dynamics and quantum chaos an introduction

    CERN Document Server

    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.

  11. 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.

  12. Controlling chaos and synchronization for new chaotic system using linear feedback control

    International Nuclear Information System (INIS)

    Yassen, M.T.

    2005-01-01

    This paper is devoted to study the problem of controlling chaos for new chaotic dynamical system (four-scroll dynamical system). Linear feedback control is used to suppress chaos to unstable equilibria and to achieve chaos synchronization of two identical four-scroll systems. Routh-Hurwitz criteria is used to study the conditions of the asymptotic stability of the equilibrium points of the controlled system. The sufficient conditions for achieving synchronization of two identical four-scroll systems are derived by using Lyapunov stability theorem. Numerical simulations are presented to demonstrate the effectiveness of the proposed chaos control and synchronization schemes

  13. Intermittency route to chaos in a biochemical system.

    Science.gov (United States)

    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'.

  14. Chaos synchronization of the fractional-order Chen's system

    International Nuclear Information System (INIS)

    Zhu Hao; Zhou Shangbo; He Zhongshi

    2009-01-01

    In this paper, based on the stability theorem of linear fractional systems, a necessary condition is given to check the chaos synchronization of fractional systems with incommensurate order. Chaos synchronization is studied by utilizing the Pecora-Carroll (PC) method and the coupling method. The necessary condition can also be used as a tool to confirm results of a numerical simulation. Numerical simulation results show the effectiveness of the necessary condition.

  15. Aram Chaos Rocks

    Science.gov (United States)

    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

  16. Chaos and Structures in Nonlinear Plasmas

    Science.gov (United States)

    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.

  17. 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.

  18. Chaos and its control in an impulsive differential system

    International Nuclear Information System (INIS)

    Jiang Guirong; Lu Qishao; Qian Linning

    2007-01-01

    In this paper, the existence of chaos and its control in an autonomous impulsive differential system are discussed both theoretically and numerically. The existence of a snap-back repeller, as well as the chaos in the sense of Li-Yorke, is proved based on the qualitative analysis using the Poincare map and the Lambert W-function. Moreover, the existence of the period-3 periodic window embedded in the chaotic region is also demonstrated. An algorithm of chaos control to stabilize the unstable periodic solutions is proposed. Detailed numerical results of chaotic attractors and stabilization of unstable periodic orbits by the impulsive effects, which are illustrated by an example, are in good agreement with the theoretical analysis

  19. Complex Nonlinearity Chaos, Phase Transitions, Topology Change and Path Integrals

    CERN Document Server

    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...

  20. Suppression of chaos at slow variables by rapidly mixing fast dynamics

    Science.gov (United States)

    Abramov, R.

    2012-04-01

    One of the key questions about chaotic multiscale systems is how the fast dynamics affects chaos at the slow variables, and, therefore, impacts uncertainty and predictability of the slow dynamics. Here we demonstrate that the linear slow-fast coupling with the total energy conservation property promotes the suppression of chaos at the slow variables through the rapid mixing at the fast variables, both theoretically and through numerical simulations. A suitable mathematical framework is developed, connecting the slow dynamics on the tangent subspaces to the infinite-time linear response of the mean state to a constant external forcing at the fast variables. Additionally, it is shown that the uncoupled dynamics for the slow variables may remain chaotic while the complete multiscale system loses chaos and becomes completely predictable at the slow variables through increasing chaos and turbulence at the fast variables. This result contradicts the common sense intuition, where, naturally, one would think that coupling a slow weakly chaotic system with another much faster and much stronger mixing system would result in general increase of chaos at the slow variables.

  1. 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)

  2. Chaos detection and predictability

    CERN Document Server

    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...

  3. 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

  4. Parrondo’s paradox for chaos control and anticontrol of fractional-order systems

    International Nuclear Information System (INIS)

    Danca, Marius-F; Tang, Wallace K S

    2016-01-01

    We present the generalized forms of Parrondo’s paradox existing in fractional-order nonlinear systems. The generalization is implemented by applying a parameter switching (PS) algorithm to the corresponding initial value problems associated with the fractional-order nonlinear systems. The PS algorithm switches a system parameter within a specific set of N ≥ 2 values when solving the system with some numerical integration method. It is proven that any attractor of the concerned system can be approximated numerically. By replacing the words “winning” and “loosing” in the classical Parrondo’s paradox with “order” and “chaos', respectively, the PS algorithm leads to the generalized Parrondo’s paradox: chaos 1 + chaos 2 + ··· + chaos N = order and order 1 + order 2 + ··· + order N = chaos. Finally, the concept is well demonstrated with the results based on the fractional-order Chen system. (paper)

  5. A history of chaos theory.

    Science.gov (United States)

    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.

  6. Magnetic field induced dynamical chaos.

    Science.gov (United States)

    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.

  7. A history of chaos theory

    Science.gov (United States)

    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

  8. Next-order spin-orbit contributions to chaos in compact binaries

    International Nuclear Information System (INIS)

    Wang Yuzhao; Wu Xin

    2011-01-01

    This paper is mainly devoted to numerically investigating the effects of the next-order spin-orbit interactions including the 2.5 post-Newtonian order term of the equations of motion and the second post-Newtonian order terms of the spin precession equations on chaos in the conservative Lagrangian dynamics of a spinning compact binary system. It is shown sufficiently through individual orbit simulations, the dependence of the invariant fast Lyapunov indicators on the variations of initial spin angles and the phase space scans for chaos, that the next-order spin-orbit contributions do play an important role in the amplification of chaos.

  9. Chaos in an imperfectly premixed model combustor.

    Science.gov (United States)

    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.

  10. Control and synchronization of chaos in nonlinear systems and prospects for application. Pt.1

    International Nuclear Information System (INIS)

    Fang Jinqing

    1996-01-01

    Main progress in one challenging subject of nonlinear science--control and synchronization of chaos in nonlinear systems are reviewed systematically, including recent advance in controlling and synchronizing hyperchaos. Current methods and principles of schemes of chaos control and synchronization are classified and summarized in detail. Potential prospects for application are commented both in theory and experiment. The whole review is divided into two parts. In the first one, subject on the mechanism and method of chaos control are analyzed and discussed extensively. In the second one, the synchronization of non-chaos, chaos, hyperchaos and their control and application are described. Main trends for development of the subject is mentioned. (101 refs.)

  11. Chaos in drive systems

    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.

  12. Chaos based on Riemannian geometric approach to Abelian-Higgs dynamical system

    International Nuclear Information System (INIS)

    Kawabe, Tetsuji

    2003-01-01

    Based on the Riemannian geometric approach, we study chaos of the Abelian-Higgs dynamical system derived from a classical field equation consisting of a spatially homogeneous Abelian gauge field and Higgs field. Using the global indicator of chaos formulated by the sectional curvature of the ambient manifold, we show that this approach brings the same qualitative and quantitative information about order and chaos as has been provided by the Lyapunov exponents in the conventional and phenomenological approach. We confirm that the mechanism of chaos is a parametric instability of the system. By analyzing a close relation between the sectional curvature and the Gaussian curvature, we point out that the Toda-Brumer criterion becomes a sufficient condition to the criterion based on this geometric approach as to the stability condition

  13. Chaos Theory and James Joyce's "ulysses": Leopold Bloom as a Human COMPLEX@SYSTEM^

    Science.gov (United States)

    Mackey, Peter Francis

    1995-01-01

    These four ideas apply as much to our lives as to the life of Leopold Bloom: (1) A trivial decision can wholly change a life. (2) A chance encounter can dramatically alter life's course. (3) A contingent nexus exists between consciousness and environment. (4) A structure of meaning helps us interpret life's chaos. These ideas also relate to a contemporary science called by some "chaos theory." The connection between Ulysses and chaos theory enhances our understanding of Bloom's day; it also suggests that this novel may be about the real process of life itself. The first chapter explains how Joyce's own essays and comments to friends compel attention to the links between Ulysses and chaos theory. His scientific contemporaries anticipated chaos theory, and their ideas seem to have rubbed off on him. We see this in his sense of trivial things and chance, his modernistic organizational impulses, and the contingent nature of Bloom's experience. The second chapter studies what chaos theory and Joyce's ideas tell us about "Ithaca," the episode which particularly implicates our processes of interpreting this text as well as life itself as we face their chaos. The third chapter examines Bloom's close feel for the aboriginal world, a contingency that clarifies his vulnerability to trivial changes. The fourth chapter studies how Bloom's stream of consciousness unfolds--from his chance encounters with trivial things. Beneath this stream's seeming chaos, Bloom's distinct personality endures, similar to how Joyce's schemas give Ulysses an imbedded, underlying order. The fifth chapter examines how trivial perturbations, such as Lyons' misunderstanding about "Throwaway," produce small crises for Bloom, exacerbating his seeming impotence before his lonely "fate.". The final chapter analyzes Bloom's views that fate and chance dictate his life. His views provide an opportunity to explore the implications chaos theory has for our understanding of free will and determinism. Ultimately

  14. Parameter identification of chaos system based on unknown parameter observer

    International Nuclear Information System (INIS)

    Wang Shaoming; Luo Haigeng; Yue Chaoyuan; Liao Xiaoxin

    2008-01-01

    Parameter identification of chaos system based on unknown parameter observer is discussed generally. Based on the work of Guan et al. [X.P. Guan, H.P. Peng, L.X. Li, et al., Acta Phys. Sinica 50 (2001) 26], the design of unknown parameter observer is improved. The application of the improved approach is extended greatly. The works in some literatures [X.P. Guan, H.P. Peng, L.X. Li, et al., Acta Phys. Sinica 50 (2001) 26; J.H. Lue, S.C. Zhang, Phys. Lett. A 286 (2001) 148; X.Q. Wu, J.A. Lu, Chaos Solitons Fractals 18 (2003) 721; J. Liu, S.H. Chen, J. Xie, Chaos Solitons Fractals 19 (2004) 533] are only the special cases of our Corollaries 1 and 2. Some observers for Lue system and a new chaos system are designed to test our improved method, and simulations results demonstrate the effectiveness and feasibility of the improved approach

  15. Geometric and dynamic perspectives on phase-coherent and noncoherent chaos.

    Science.gov (United States)

    Zou, Yong; Donner, Reik V; Kurths, Jürgen

    2012-03-01

    Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic Rössler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given.

  16. Mesoscopic chaos mediated by Drude electron-hole plasma in silicon optomechanical oscillators

    Science.gov (United States)

    Wu, Jiagui; Huang, Shu-Wei; Huang, Yongjun; Zhou, Hao; Yang, Jinghui; Liu, Jia-Ming; Yu, Mingbin; Lo, Guoqiang; Kwong, Dim-Lee; Duan, Shukai; Wei Wong, Chee

    2017-01-01

    Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to physics of electron transport. Recent studies in cavity optomechanics provide a new platform to uncover quintessential architectures of chaos generation and the underlying physics. Here, we report the generation of dynamical chaos in silicon-based monolithic optomechanical oscillators, enabled by the strong and coupled nonlinearities of two-photon absorption induced Drude electron–hole plasma. Deterministic chaotic oscillation is achieved, and statistical and entropic characterization quantifies the chaos complexity at 60 fJ intracavity energies. The correlation dimension D2 is determined at 1.67 for the chaotic attractor, along with a maximal Lyapunov exponent rate of about 2.94 times the fundamental optomechanical oscillation for fast adjacent trajectory divergence. Nonlinear dynamical maps demonstrate the subharmonics, bifurcations and stable regimes, along with distinct transitional routes into chaos. This provides a CMOS-compatible and scalable architecture for understanding complex dynamics on the mesoscopic scale. PMID:28598426

  17. Onset of dynamical chaos in topologically massive gauge theories

    International Nuclear Information System (INIS)

    Giansanti, A.; Simic, P.D.

    1988-01-01

    The onset of dynamical chaos is studied numerically in (2+1)-dimensional non-Abelian field theory with the Chern-Simons topological term. In the limit of strong fields, slowly varying in space (spatially homogeneous fields), this theory is an analog to a system of three charged particles moving in a plane in an orthogonal magnetic field and under the influence of a quartic potential. The ''phase transition'' (order chaos) is observed within a narrow energy range. The threshold of the transition depends on the sign of the angular momentum of the field reflecting parity violation in the underlying field theory. The transition region is investigated in some detail and the hyperfine structure of order-chaos-order-... transitions is observed suggesting the necessity of probabilistic description

  18. Rank one chaos in a class of planar systems with heteroclinic cycle.

    Science.gov (United States)

    Chen, Fengjuan; Han, Maoan

    2009-12-01

    In this paper, we study rank one chaos in a class of planar systems with heteroclinic cycle. We first find a stable limit cycle inside the heteroclinic cycle. We then add an external periodic forcing to create rank one chaos. We follow a step-by-step procedure guided by the theory of rank one chaos to find experimental evidence of strange attractors with Sinai, Ruelle, and Bowen measures.

  19. Prediction of chaos in a Josephson junction by the Melnikov-function technique

    DEFF Research Database (Denmark)

    Bartuccelli, M.; Christiansen, Peter Leth; Pedersen, Niels Falsig

    1986-01-01

    The Melnikov function for prediction of Smale horseshoe chaos is applied to the rf-driven Josephson junction. Linear and quadratic damping resistors are considered. In the latter case the analytic solution including damping and dc bias is used to obtain an improved threshold curve for the onset...... of chaos. The prediction is compared to new computational solutions. The Melnikov technique provides a good, but slightly low, estimate of the chaos threshold....

  20. Specifying the Links between Household Chaos and Preschool Children's Development

    Science.gov (United States)

    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…

  1. On the olfactory anatomy in an archaic whale (Protocetidae, Cetacea) and the minke whale Balaenoptera acutorostrata (Balaenopteridae, Cetacea).

    Science.gov (United States)

    Godfrey, Stephen J; Geisler, Jonathan; Fitzgerald, Erich M G

    2013-02-01

    The structure of the olfactory apparatus is not well known in both archaic and extant whales; the result of poor preservation in most fossils and locational isolation deep within the skulls in both fossil and Recent taxa. Several specimens now shed additional light on the subject. A partial skull of an archaic cetacean is reported from the Pamunkey River, Virginia, USA. The specimen probably derives from the upper middle Eocene (Piney Point Formation) and is tentatively assigned to the Protocetidae. Uncrushed cranial cavities associated with the olfactory apparatus were devoid of sediment. CT scans clearly reveal the dorsal nasal meatus, ethmoturbinates within the olfactory recess, the cribriform plate, the area occupied by the olfactory bulbs, and the olfactory nerve tract. Several sectioned skulls of the minke whale (Balaenoptera acutorostrata) were also examined, and olfactory structures are remarkably similar to those observed in the fossil skull from the Pamunkey River. One important difference between the two is that the fossil specimen has an elongate olfactory nerve tract. The more forward position of the external nares in extant balaenopterids when compared with those of extant odontocetes is interpreted to be the result of the need to retain a functional olfactory apparatus and the forward position of the supraoccipital/cranial vertex. An increase in the distance between the occipital condyles and the vertex in balaenopterids enhances the mechanical advantage of the epaxial musculature that inserts on the occiput, a specialization that likely stabilizes the head of these enormous mammals during lunge feeding. Copyright © 2012 Wiley Periodicals, Inc.

  2. Origin of chaos in 3-d Bohmian trajectories

    International Nuclear Information System (INIS)

    Tzemos, Athanasios C.; Contopoulos, George; Efthymiopoulos, Christos

    2016-01-01

    We study the 3-d Bohmian trajectories of a quantum system of three harmonic oscillators. We focus on the mechanism responsible for the generation of chaotic trajectories. We demonstrate the existence of a 3-d analogue of the mechanism found in earlier studies of 2-d systems [1,2], based on moving 2-d ‘nodal point–X-point complexes’. In the 3-d case, we observe a foliation of nodal point–X-point complexes, forming a ‘3-d structure of nodal and X-points’. Chaos is generated when the Bohmian trajectories are scattered at one or more close encounters with such a structure. - Highlights: • A mechanism for the emergence of 3-d Bohmian chaos is proposed. • We demonstrate the existence of a 3-d structure of nodal and X-points. • Chaos is generated when the trajectories are scattered by the X-points.

  3. Origin of chaos in 3-d Bohmian trajectories

    Energy Technology Data Exchange (ETDEWEB)

    Tzemos, Athanasios C., E-mail: thanasistzemos@gmail.com; Contopoulos, George, E-mail: gcontop@academyofathens.gr; Efthymiopoulos, Christos, E-mail: cefthim@academyofathens.gr

    2016-11-25

    We study the 3-d Bohmian trajectories of a quantum system of three harmonic oscillators. We focus on the mechanism responsible for the generation of chaotic trajectories. We demonstrate the existence of a 3-d analogue of the mechanism found in earlier studies of 2-d systems [1,2], based on moving 2-d ‘nodal point–X-point complexes’. In the 3-d case, we observe a foliation of nodal point–X-point complexes, forming a ‘3-d structure of nodal and X-points’. Chaos is generated when the Bohmian trajectories are scattered at one or more close encounters with such a structure. - Highlights: • A mechanism for the emergence of 3-d Bohmian chaos is proposed. • We demonstrate the existence of a 3-d structure of nodal and X-points. • Chaos is generated when the trajectories are scattered by the X-points.

  4. 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

  5. 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)

  6. Global chaos synchronization of three coupled nonlinear autonomous systems and a novel method of chaos encryption

    International Nuclear Information System (INIS)

    An Xinlei; Yu Jianning; Chu Yandong; Zhang Jiangang; Zhang Li

    2009-01-01

    In this paper, we discussed the fixed points and their linear stability of a new nonlinear autonomous system that introduced by J.C. Sprott. Based on Lyapunov stabilization theorem, a global chaos synchronization scheme of three coupled identical systems is investigated. By choosing proper coupling parameters, the states of all the three systems can be synchronized. Then this method was applied to secure communication through chaotic masking, used three coupled identical systems, propose a novel method of chaos encryption, after encrypting in the previous two transmitters, information signal can be recovered exactly at the receiver end. Simulation results show that the method can realize monotonous synchronization. Further more, the information signal can be recovered undistorted when applying this method to secure communication.

  7. SECULAR CHAOS AND THE PRODUCTION OF HOT JUPITERS

    International Nuclear Information System (INIS)

    Wu Yanqin; Lithwick, Yoram

    2011-01-01

    In a planetary system with two or more well-spaced, eccentric, inclined planets, secular interactions may lead to chaos. The innermost planet may gradually become very eccentric and/or inclined as a result of the secular degrees of freedom drifting toward equipartition of angular momentum deficit. Secular chaos is known to be responsible for the eventual destabilization of Mercury in our own solar system. Here we focus on systems with three giant planets. We characterize the secular chaos and demonstrate the criterion for it to occur, but leave a detailed understanding of secular chaos to a companion paper. After an extended period of eccentricity diffusion, the inner planet's pericenter can approach the star to within a few stellar radii. Strong tidal interactions and ensuing tidal dissipation extract orbital energy from the planet and pull it inward, creating a hot Jupiter. In contrast to other proposed channels for the production of hot Jupiters, such a scenario (which we term 'secular migration') explains a range of observations: the pile-up of hot Jupiters at 3 day orbital periods, the fact that hot Jupiters are in general less massive than other radial velocity planets, that they may have misaligned inclinations with respect to stellar spin, and that they have few easily detectable companions (but may have giant companions in distant orbits). Secular migration can also explain close-in planets as low in mass as Neptune; and an aborted secular migration can explain the 'warm Jupiters' at intermediate distances. In addition, the frequency of hot Jupiters formed via secular migration increases with stellar age. We further suggest that secular chaos may be responsible for the observed eccentricities of giant planets at larger distances and that these planets could exhibit significant spin-orbit misalignment.

  8. Socioeconomic Risk Moderates the Link between Household Chaos and Maternal Executive Function

    Science.gov (United States)

    Deater-Deckard, Kirby; Chen, Nan; Wang, Zhe; Bell, Martha Ann

    2012-01-01

    We examined the link between household chaos (i.e., noise, clutter, disarray, lack of routines) and maternal executive function (i.e., effortful regulation of attention and memory), and whether it varied as a function of socioeconomic risk (i.e., single parenthood, lower mother and father educational attainment, housing situation, and father unemployment). We hypothesized that: 1) higher levels of household chaos would be linked with poorer maternal executive function, even when controlling for other measures of cognitive functioning (e.g., verbal ability), and 2) this link would be strongest in the most socioeconomically distressed or lowest-socioeconomic status households. The diverse sample included 153 mothers from urban and rural areas who completed a questionnaire and a battery of cognitive executive function tasks and a verbal ability task in the laboratory. Results were mixed for hypothesis 1, and consistent with hypothesis 2. Two-thirds of the variance overlapped between household chaos and maternal executive function, but only in families with high levels of socioeconomic risk. This pattern was not found for chaos and maternal verbal ability, suggesting that the potentially deleterious effects of household chaos may be specific to maternal executive function. The findings implicate household chaos as a powerful statistical predictor of maternal executive function in socioeconomically distressed contexts. PMID:22563703

  9. Controlling chaos (OGY) implemented on a reconstructed ecological two-dimensional map

    International Nuclear Information System (INIS)

    Sakai, Kenshi; Noguchi, Yuko

    2009-01-01

    We numerically demonstrate a way to stabilize an unstable equilibrium in the ecological dynamics reconstructed from real-world time series data, namely, alternate bearing of citrus trees. The reconstruction of deterministic dynamics from short and noisy ecological time series has been a crucial issue since May's historical work [May RM. Biological populations with nonoverlapping generations: stable points, stable cycles and chaos. Science 1974;186:645-7; Hassell MP, Lawton JH, May RM. Patterns of dynamical behavior in single species populations. J Anim Ecol 1976;45:471-86]. Response surface methodology, followed by the differential equation approach is recognized as a promising method of reconstruction [Turchin P. Rarity of density dependence or population with lags? Nature 1990;344:660-3; Turchin P, Taylor AD. Complex dynamics in ecological time series. Ecology 1992;73:289-305; Ellner S, Turchin P. Chaos in a noisy world: new method and evidence from time series analysis. Am Nat 1995;145(3):343-75; Turchin P, Ellner S. Living on the edge of chaos: population dynamics of fennoscandian voles. Ecology 2000;8(11):3116]. Here, the reconstructed ecological dynamics was described by a two-dimensional map derived from the response surface created by the data. The response surface created was experimentally validated in four one-year forward predictions in 2001, 2002, 2003 and 2004. Controlling chaos is very important when applying chaos theory to solving real-world problems. The OGY method is the first and most popular methodology for controlling chaos and can be used as an algorithm to stabilize an unstable fixed point by putting the state on a stable manifold [Ott E, Grebogi C, York JA. Controlling chaos. Phys Rev Lett 1990;64:1996-9]. We applied the OGY method to our reconstructed two-dimensional map and as a result were able to control alternate bearing in numerical simulations.

  10. Chaos in reversed-field-pinch plasma simulation and experiment

    International Nuclear Information System (INIS)

    Watts, C.; Newman, D.E.; Sprott, J.C.

    1994-01-01

    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 Poincare 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 computer code, which models global RFP dynamics, and the dissipative trapped-electron-mode 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 that the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system

  11. Quantum Instantons and Quantum Chaos

    OpenAIRE

    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.

  12. Chaos and order in stateless societies: Intercommunity exchange as a factor impacting the population dynamical patterns

    International Nuclear Information System (INIS)

    Medvinsky, Alexander B.; Rusakov, Alexey V.

    2011-01-01

    Highlights: → We model community dynamics in stateless societies. → Intercommunity barter is shown to be a factor impacting the societies dynamics. → Increase in the human population growth rate can lead to appearance of chaos. → Secular and millennial cycles are found to arise as a result of the barter. - Abstract: The once abstract notions of dynamical chaos now appear naturally in various systems [Kaplan D, Glass L. Understanding nonlinear dynamics. New York: Springer; 1995]. As a result, future trajectories of the systems may be difficult to predict. In this paper, we demonstrate the appearance of chaotic dynamics in model human communities, which consist of producers of agricultural product and producers of agricultural equipment. In the case of a solitary community, the horizon of predictability of the human population dynamics is shown to be dependent on both intrinsic instability of the dynamics and the chaotic attractor sizes. Since a separate community is usually a part of a larger commonality, we study the dynamics of social systems consisting of two interacting communities. We show that intercommunity barter can lead to stabilization of the dynamics in one of the communities, which implies persistence of stable equilibrium under changes of the maximum value of the human population growth rate. However, in the neighboring community, the equilibrium turns into a stable limit cycle as the maximum value of the human population growth rate increases. Following an increase in the maximum value of the human population growth rate leads to period-doubling bifurcations resulting in chaotic dynamics. The horizon of predictability of the chaotic oscillations is found to be limited by 5 years. We demonstrate that the intercommunity interaction can lead to the appearance of long-period harmonics in the chaotic time series. The period of the harmonics is of order 100 and 1000 years. Hence the long-period changes in the population size may be considered as an

  13. Chaos and order in stateless societies: Intercommunity exchange as a factor impacting the population dynamical patterns

    Energy Technology Data Exchange (ETDEWEB)

    Medvinsky, Alexander B., E-mail: medvinsky@iteb.ru [Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Pushchino 142290, Moscow Region (Russian Federation); Rusakov, Alexey V. [Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Pushchino 142290, Moscow Region (Russian Federation)

    2011-06-15

    Highlights: > We model community dynamics in stateless societies. > Intercommunity barter is shown to be a factor impacting the societies dynamics. > Increase in the human population growth rate can lead to appearance of chaos. > Secular and millennial cycles are found to arise as a result of the barter. - Abstract: The once abstract notions of dynamical chaos now appear naturally in various systems [Kaplan D, Glass L. Understanding nonlinear dynamics. New York: Springer; 1995]. As a result, future trajectories of the systems may be difficult to predict. In this paper, we demonstrate the appearance of chaotic dynamics in model human communities, which consist of producers of agricultural product and producers of agricultural equipment. In the case of a solitary community, the horizon of predictability of the human population dynamics is shown to be dependent on both intrinsic instability of the dynamics and the chaotic attractor sizes. Since a separate community is usually a part of a larger commonality, we study the dynamics of social systems consisting of two interacting communities. We show that intercommunity barter can lead to stabilization of the dynamics in one of the communities, which implies persistence of stable equilibrium under changes of the maximum value of the human population growth rate. However, in the neighboring community, the equilibrium turns into a stable limit cycle as the maximum value of the human population growth rate increases. Following an increase in the maximum value of the human population growth rate leads to period-doubling bifurcations resulting in chaotic dynamics. The horizon of predictability of the chaotic oscillations is found to be limited by 5 years. We demonstrate that the intercommunity interaction can lead to the appearance of long-period harmonics in the chaotic time series. The period of the harmonics is of order 100 and 1000 years. Hence the long-period changes in the population size may be considered as an

  14. 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)

  15. Transient chaos in a globally coupled system of nearly conservative Hamiltonian Duffing oscillators

    International Nuclear Information System (INIS)

    Sabarathinam, S.; Thamilmaran, K.

    2015-01-01

    Highlights: •We have examined transient chaos in globally coupled oscillators. •We analyze transient chaos using new techniques. •We give experimental confirmation of transient chaos. -- Abstract: In this work, transient chaos in a ring and globally coupled system of nearly conservative Hamiltonian Duffing oscillators is reported. The networks are formed by coupling of three, four and six Duffing oscillators. The nearly conservative Hamiltonian nature of the coupled system is proved by stability analysis. The transient phenomenon is confirmed through various numerical investigations such as recurrence analysis, 0–1 test and Finite Time Lyapunov Exponents. Further, the effect of damping and the average transient lifetime of three, four and six coupled schemes for randomly generated initial conditions have been analyzed. The experimental confirmation of transient chaos in an illustrative system of three ringly coupled Duffing oscillators is also presented

  16. Chaos as the hub of systems dynamics. The part I-The attitude control of spacecraft by involving in the heteroclinic chaos

    Science.gov (United States)

    Doroshin, Anton V.

    2018-06-01

    In this work the chaos in dynamical systems is considered as a positive aspect of dynamical behavior which can be applied to change systems dynamical parameters and, moreover, to change systems qualitative properties. From this point of view, the chaos can be characterized as a hub for the system dynamical regimes, because it allows to interconnect separated zones of the phase space of the system, and to fulfill the jump into the desirable phase space zone. The concretized aim of this part of the research is to focus on developing the attitude control method for magnetized gyrostat-satellites, which uses the passage through the intentionally generated heteroclinic chaos. The attitude dynamics of the satellite/spacecraft in this case represents the series of transitions from the initial dynamical regime into the chaotic heteroclinic regime with the subsequent exit to the final target dynamical regime with desirable parameters of the attitude dynamics.

  17. Self-generation and management of spin-electromagnetic wave solitons and chaos

    International Nuclear Information System (INIS)

    Ustinov, Alexey B.; Kondrashov, Alexandr V.; Nikitin, Andrey A.; Kalinikos, Boris A.

    2014-01-01

    Self-generation of microwave spin-electromagnetic wave envelope solitons and chaos has been observed and studied. For the investigation, we used a feedback active ring oscillator based on artificial multiferroic, which served as a nonlinear waveguide. We show that by increasing the wave amplification in the feedback ring circuit, a transition from monochromatic auto-generation to soliton train waveform and then to dynamical chaos occurs in accordance with the Ruelle-Takens scenario. Management of spin-electromagnetic-wave solitons and chaos parameters by both dielectric permittivity and magnetic permeability of the multiferroic waveguiding structure is demonstrated.

  18. Bifurcation and chaos response of a cracked rotor with random disturbance

    Science.gov (United States)

    Leng, Xiaolei; Meng, Guang; Zhang, Tao; Fang, Tong

    2007-01-01

    The Monte-Carlo method is used to investigate the bifurcation and chaos characteristics of a cracked rotor with a white noise process as its random disturbance. Special attention is paid to the influence of the stiffness change ratio and the rotating speed ratio on the bifurcation and chaos response of the system. Numerical simulations show that the affect of the random disturbance is significant as the undisturbed response of the cracked rotor system is a quasi-periodic or chaos one, and such affect is smaller as the undisturbed response is a periodic one.

  19. Fibonacci order in the period-doubling cascade to chaos

    International Nuclear Information System (INIS)

    Linage, G.; Montoya, Fernando; Sarmiento, A.; Showalter, K.; Parmananda, P.

    2006-01-01

    In this contribution, we describe how the Fibonacci sequence appears within the Feigenbaum scaling of the period-doubling cascade to chaos. An important consequence of this discovery is that the ratio of successive Fibonacci numbers converges to the golden mean in every period-doubling sequence and therefore the convergence to φ, the most irrational number, occurs in concert with the onset of deterministic chaos

  20. Fibonacci order in the period-doubling cascade to chaos

    Energy Technology Data Exchange (ETDEWEB)

    Linage, G. [Facultad de Ciencias UAEM, Avenida Universidad 1001, Colonia Chamilpa, C.P. 62210 Cuernavaca, Morelos (Mexico); Montoya, Fernando [Facultad de Ciencias UAEM, Avenida Universidad 1001, Colonia Chamilpa, C.P. 62210 Cuernavaca, Morelos (Mexico); Sarmiento, A. [Instituto de Matematicas, UNAM, Colonia Chamilpa, C.P. 62210 Cuernavaca, Morelos (Mexico); Showalter, K. [Department of Chemistry, West Virginia University, Morgantown, WV 26506-6045 (United States); Parmananda, P. [Facultad de Ciencias UAEM, Avenida Universidad 1001, Colonia Chamilpa, C.P. 62210 Cuernavaca, Morelos (Mexico)]. E-mail: punit@servm.fc.uaem.mx

    2006-12-11

    In this contribution, we describe how the Fibonacci sequence appears within the Feigenbaum scaling of the period-doubling cascade to chaos. An important consequence of this discovery is that the ratio of successive Fibonacci numbers converges to the golden mean in every period-doubling sequence and therefore the convergence to {phi}, the most irrational number, occurs in concert with the onset of deterministic chaos.

  1. CHAOS-BASED ADVANCED ENCRYPTION STANDARD

    KAUST Repository

    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

  2. Analysis of chaos attractors of MCG-recordings.

    Science.gov (United States)

    Jiang, Shiqin; Yang, Fan; Yi, Panke; Chen, Bo; Luo, Ming; Wang, Lemin

    2006-01-01

    By studying the chaos attractor of cardiac magnetic induction strength B(z) generated by the electrical activity of the heart, we found that its projection in the reconstructed phase space has a similar shape with the map of the total current dipole vector. It is worth noting that the map of the total current dipole vector is computed with MCG recordings measured at 36 locations, whereas the chaos attractor of B(z) is generated by only one cardiac magnetic field recordings on the measured plan. We discuss only two subjects of different ages in this paper.

  3. Chaos and random matrices in supersymmetric SYK

    Science.gov (United States)

    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.

  4. Signatures of chaos in the Brillouin zone.

    Science.gov (United States)

    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.

  5. 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)

  6. 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)

  7. Chaos Control in a New Three-Dimensional Chaotic T System

    International Nuclear Information System (INIS)

    Chen Yong; Yan Zhenya

    2008-01-01

    In this paper, we study chaos control of the new 3D chaotic system. We use three feedback methods (the linear, speed, doubly-periodic function controller) to suppress the chaos to unstable equilibrium. As a result, some controllers are obtained. Moreover, numerical simulations are used to verify the effectiveness of the obtained controllers

  8. Analysis of chaos in high-dimensional wind power system.

    Science.gov (United States)

    Wang, Cong; Zhang, Hongli; Fan, Wenhui; Ma, Ping

    2018-01-01

    A comprehensive analysis on the chaos of a high-dimensional wind power system is performed in this study. A high-dimensional wind power system is more complex than most power systems. An 11-dimensional wind power system proposed by Huang, which has not been analyzed in previous studies, is investigated. When the systems are affected by external disturbances including single parameter and periodic disturbance, or its parameters changed, chaotic dynamics of the wind power system is analyzed and chaotic parameters ranges are obtained. Chaos existence is confirmed by calculation and analysis of all state variables' Lyapunov exponents and the state variable sequence diagram. Theoretical analysis and numerical simulations show that the wind power system chaos will occur when parameter variations and external disturbances change to a certain degree.

  9. Chaos, Hubbub, and Order Scale and Health Risk Behaviors in Adolescents in Los Angeles.

    Science.gov (United States)

    Chatterjee, Avik; Gillman, Matthew W; Wong, Mitchell D

    2015-12-01

    To determine the relationship between household chaos and substance use, sexual activity, and violence-related risk behaviors in adolescents. We analyzed cross-sectional data among 929 high-school students in Los Angeles who completed a 90-minute interview that assessed health behaviors and household chaos with the 14-question Chaos, Hubbub, and Order Scale (CHAOS). Using the generalized estimating equation and adjusting for personal, parental, and family covariates, we examined associations of CHAOS score with substance use, sexual activity, and violent behavior outcome variables. We also examined the role of depression and school engagement as mediators. Mean (SD) age of the 929 students was 16.4 (1.3) years, 516 (55%) were female, and 780 (84%) were Latino. After adjustment, compared with students with CHAOS score 0, those students with the greatest scores (5-14) had ORs of 3.1 (95% CI 1.1-8.7) for smoking, 2.6 (95% CI 1.6-4.4) for drinking, 6.1 (95% CI 1.8-21) for substance use at school, and 1.9 (95% CI 1.1-3.3) for fighting in the past 12 months. Associations between CHAOS score and sexual risk and other violent behaviors were not significant. Depression and school engagement attenuated the associations. In this group of adolescents, greatest CHAOS score was associated with increased odds of risky health behaviors, with depression and school engagement as potential mediators. In the future, CHAOS score could be measured to assess risk for such behaviors or be a target for intervention to reduce chances of engaging in these behaviors. Copyright © 2015 Elsevier Inc. All rights reserved.

  10. Chaos and insect ecology

    Science.gov (United States)

    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...

  11. Hyperchaos-chaos-hyperchaos transition in modified Roessler systems

    International Nuclear Information System (INIS)

    Nikolov, Svetoslav; Clodong, Sebastien

    2006-01-01

    We consider in this paper a family of modified hyperchaotic Roessler systems and investigate both problems of understanding hyperchaos-chaos-hyperchaos transition and computing the prediction time. These systems were obtained and numerically investigated by Nikolov and Clodong [Nikolov S, Clodong S. Occurrence of regular, chaotic and hyperchaotic behavior in a family of modified Rossler hyperchaotic systems. Chaos, Solitons and Fractals 2004;22:407-31]. Our studies confirm that transition hyperchaos-chaos-hyperchaos (i) depends on the change of the sign of the corresponding characteristic equation roots or (ii) can be obtained as a result of the absorption/repulsion of the repeller originally located out of the attractor by the growing attractor. It is also shown that the prediction time is a more reliable predictor of the evolution than the information dimension. We conclude that the prediction time in hyperchaotic regimes is at least one order of magnitude smaller than those in chaotic zones

  12. Chaos in oil prices? Evidence from futures markets

    International Nuclear Information System (INIS)

    Adrangi, B.; Chatrath, A.; Dhanda, K.K.; Raffiee, K.

    2001-01-01

    We test for the presence of low-dimensional chaotic structure in crude oil, heating oil, and unleaded gasoline futures prices from the early 1980s. Evidence on chaos will have important implications for regulators and short-term trading strategies. While we find strong evidence of non-linear dependencies, the evidence is not consistent with chaos. Our test results indicate that ARCH-type processes, with controls for seasonal variation in prices, generally explain the non-linearities in the data. We also demonstrate that employing seasonally adjusted price series contributes to obtaining robust results via the existing tests for chaotic structure. Maximum likelihood methodologies, that are robust to the non-linear dynamics, lend support for Samuelson's hypothesis on contract-maturity effects in futures price-changes. However, the tests for chaos are not found to be sensitive to the maturity effects in the futures contracts. The results are robust to controls for the oil shocks of 1986 and 1991

  13. Examining the Relationship Between Children's ADHD Symptomatology and Inadequate Parenting: The Role of Household Chaos.

    Science.gov (United States)

    Wirth, Andrea; Reinelt, Tilman; Gawrilow, Caterina; Schwenck, Christina; Freitag, Christine M; Rauch, Wolfgang A

    2017-02-01

    This study examines the interrelations of parenting practices, emotional climate, and household chaos in families with children with and without ADHD. In particular, indirect pathways from children's ADHD symptomatology to inadequate parenting and negative emotional climate via household chaos were investigated. Parenting, emotional climate, and household chaos were assessed using questionnaires and a speech sample of parents of 31 children with and 53 without ADHD, aged 7 to 13 years. Group differences were found for certain parenting dimensions, the parent-child relationship, critical comments, and household chaos. While we found significant indirect effects between children's ADHD and certain parenting dimensions through household chaos, no effects were found for any aspect of emotional climate. Children's ADHD symptoms translate into inadequate parenting through household chaos, which underlines the need for interventions to improve household organization skills in parents of children with ADHD.

  14. Socioeconomic risk moderates the link between household chaos and maternal executive function.

    Science.gov (United States)

    Deater-Deckard, Kirby; Chen, Nan; Wang, Zhe; Bell, Martha Ann

    2012-06-01

    We examined the link between household chaos (i.e., noise, clutter, disarray, lack of routines) and maternal executive function (i.e., effortful regulation of attention and memory), and whether it varied as a function of socioeconomic risk (i.e., single parenthood, lower mother and father educational attainment, housing situation, and father unemployment). We hypothesized that: 1) higher levels of household chaos would be linked with poorer maternal executive function, even when controlling for other measures of cognitive functioning (e.g., verbal ability), and 2) this link would be strongest in the most socioeconomically distressed or lowest-socioeconomic status households. The diverse sample included 153 mothers from urban and rural areas who completed a questionnaire and a battery of cognitive executive function tasks and a verbal ability task in the laboratory. Results were mixed for Hypothesis 1, and consistent with Hypothesis 2. Two-thirds of the variance overlapped between household chaos and maternal executive function, but only in families with high levels of socioeconomic risk. This pattern was not found for chaos and maternal verbal ability, suggesting that the potentially deleterious effects of household chaos may be specific to maternal executive function. The findings implicate household chaos as a powerful statistical predictor of maternal executive function in socioeconomically distressed contexts. PsycINFO Database Record (c) 2012 APA, all rights reserved.

  15. Chaos Theory and International Relations

    Science.gov (United States)

    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

  16. Some archaic traits in social life of Brskuceans: Ethnographical notes

    Directory of Open Access Journals (Sweden)

    Gudović Zoran

    2004-01-01

    Full Text Available In this paper the author has, using the descriptive method, pointed out some archaic aspects of the social life of an undeveloped and isolated village in Montenegro. By a brief analysis of the whole of its spiritual and material self-realization, it has been possible to recognize the important traits of traditional, tribal-brotherhood way of thinking and behavior. In that sense it is a noticeable proof that they survived notwithstanding the inevitable modernization of the village. The paper has involved the following four parts: The general data about the village; the social organization; the spiritual culture and customs, and finally the social processes and the ways of thinking and behavior. The intrinsic organization of living has been expressed by the hierarchical position of each family member. The position each member has taken has been less determined by the traditional elements of the rural economy and much more by the interiorization and preservation of spiritual worthiness wherein the remembering of them has given the life a peculiar meaning. The village of Brskut has been a patriarchal milieu with an accent to the epic and combatant traditions where a child has been treated as an unfinished personality, so that the parents have cherished the merited regard only to the friends and grown-up persons as well as to the friendly oriented foreigners. Proceeding from the judgment relatives tribesmen, brotherhood men and other friends are able to form of him or her of their opinion he or she has held, he or she pleased them, experiencing the child as a disturbance by which the said relationship has been thwarted. Therefore the child has been generally neglected by the customary regulations in that milieu. The brotherhood links have been solid. The members of the same brotherhood have been visiting one another, respecting one another and helping one another believing that they have been originating from the same common ancestor. The common

  17. Secure image encryption algorithm design using a novel chaos based S-Box

    International Nuclear Information System (INIS)

    Çavuşoğlu, Ünal; Kaçar, Sezgin; Pehlivan, Ihsan; Zengin, Ahmet

    2017-01-01

    Highlights: • A new chaotic system is developed for creating S-Box and image encryption algorithm. • Chaos based random number generator is designed with the help of the new chaotic system. NIST tests are run on generated random numbers to verify randomness. • A new S-Box design algorithm is developed to create the chaos based S-Box to be utilized in encryption algorithm and performance tests are made. • The new developed S-Box based image encryption algorithm is introduced and image encryption application is carried out. • To show the quality and strong of the encryption process, security analysis are performed and compared with the AES and chaos algorithms. - Abstract: In this study, an encryption algorithm that uses chaos based S-BOX is developed for secure and speed image encryption. First of all, a new chaotic system is developed for creating S-Box and image encryption algorithm. Chaos based random number generator is designed with the help of the new chaotic system. Then, NIST tests are run on generated random numbers to verify randomness. A new S-Box design algorithm is developed to create the chaos based S-Box to be utilized in encryption algorithm and performance tests are made. As the next step, the new developed S-Box based image encryption algorithm is introduced in detail. Finally, image encryption application is carried out. To show the quality and strong of the encryption process, security analysis are performed. Proposed algorithm is compared with the AES and chaos algorithms. According to tests results, the proposed image encryption algorithm is secure and speed for image encryption application.

  18. Effects on the upstream flood inundation caused from the operation of Chao Phraya Dam

    Directory of Open Access Journals (Sweden)

    Sutham Visutimeteegorn

    2007-11-01

    Full Text Available During the flooding events, the operation of Chao Phraya Dam to control downstream water discharge is one of the causes of the inundation occuring over the upstream area. The purposes of this research are to study the effects of the operation of Chao Phraya Dam upon the upstream flood inundation and to find out the new measures of the flood mitigation in the upstream areas of Chao Phraya Dam by using a hydrodynamic model. The results show that Manning's n in the Chao Phraya River and its tributaries is 0.030-0.035 in the main channels and 0.050-0.070 in the flood plain areas. The backwater due to the operation of the Chao Praya dam affects as far as 110 kilometers upstream. New methods of water diversion can mitigate the flood inundation without the effect on the floating rice fields. The construction of reservoirs in the Upper Sakaekang River Basin and the Upper Yom River Basin will mitigate the flood not only in their own basins but also in the Lower Chao Phraya River Basin. The coordinated operation of the Chao Phraya Dam, the regulators and the upper basin reservoirs will efficiently mitigate the flood inundation.

  19. 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

  20. Lack of evidence for low-dimensional chaos in heart rate variability

    DEFF Research Database (Denmark)

    Kanters, J K; Holstein-Rathlou, N H; Agner, E

    1994-01-01

    INTRODUCTION: The term chaos is used to describe erratic or apparently random time-dependent behavior in deterministic systems. It has been suggested that the variability observed in the normal heart rate may be due to chaos, but this question has not been settled. METHODS AND RESULTS: Heart rate...... in the experimental data, but the prediction error as a function of the prediction length increased at a slower rate than characteristic of a low-dimensional chaotic system. CONCLUSION: There is no evidence for low-dimensional chaos in the time series of RR intervals from healthy human subjects. However, nonlinear...

  1. Application of Chaos Theory to Psychological Models

    Science.gov (United States)

    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

  2. Direct generation of all-optical random numbers from optical pulse amplitude chaos.

    Science.gov (United States)

    Li, Pu; Wang, Yun-Cai; Wang, An-Bang; Yang, Ling-Zhen; Zhang, Ming-Jiang; Zhang, Jian-Zhong

    2012-02-13

    We propose and theoretically demonstrate an all-optical method for directly generating all-optical random numbers from pulse amplitude chaos produced by a mode-locked fiber ring laser. Under an appropriate pump intensity, the mode-locked laser can experience a quasi-periodic route to chaos. Such a chaos consists of a stream of pulses with a fixed repetition frequency but random intensities. In this method, we do not require sampling procedure and external triggered clocks but directly quantize the chaotic pulses stream into random number sequence via an all-optical flip-flop. Moreover, our simulation results show that the pulse amplitude chaos has no periodicity and possesses a highly symmetric distribution of amplitude. Thus, in theory, the obtained random number sequence without post-processing has a high-quality randomness verified by industry-standard statistical tests.

  3. Multielement analysis of archaic Chinese bronze and antique coins by fast neutron activation analysis

    Energy Technology Data Exchange (ETDEWEB)

    Tian, Y.H. (Academia Sinica, Lanzhou, Gansu (China). Inst. of Modern Physics); Pepelnik, R.; Fanger, H.U. (GKSS-Forschungszentrum Geesthacht GmbH, Geesthacht-Tesperhude (Germany, F.R.). Inst. fuer Physik)

    1990-01-01

    Samples of archaic bronze have been investigated by fast neutron activation analysis using both the absolute and relative method. The components Cu, Zn, Sn and Pb have been determined quantitatively. For the detection of lead via the short-lived isomeric state {sup 207m}Pb, cyclic activation and measurement technique was used with pneumatic sample transfer between detector and central irradiation position of the neutron tube. For non-destructive analysis of antique Chinese coins the samples had to be irradiated outside the neutron generator KORONA. The activation reactions, the evaluation of the elemental concentrations and the accuracy of the results are discussed. The data were corrected for {gamma}-ray self-absorption in the samples and summing of coincident {gamma}-rays in the detector. According to reported typical compositions of Chinese bronze from different dynasties, the age of the samples has been derived from the results obtained. (orig.).

  4. Detecting chaos in irregularly sampled time series.

    Science.gov (United States)

    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.

  5. Melnikov's criteria, parametric control of chaos, and stationary chaos occurrence in systems with asymmetric potential subjected to multiscale type excitation.

    Science.gov (United States)

    Kwuimy, C A Kitio; Nataraj, C; Litak, G

    2011-12-01

    We consider the problems of chaos and parametric control in nonlinear systems under an asymmetric potential subjected to a multiscale type excitation. The lower bound line for horseshoes chaos is analyzed using the Melnikov's criterion for a transition to permanent or transient nonperiodic motions, complement by the fractal or regular shape of the basin of attraction. Numerical simulations based on the basins of attraction, bifurcation diagrams, Poincaré sections, Lyapunov exponents, and phase portraits are used to show how stationary dissipative chaos occurs in the system. Our attention is focussed on the effects of the asymmetric potential term and the driven frequency. It is shown that the threshold amplitude ∣γ(c)∣ of the excitation decreases for small values of the driven frequency ω and increases for large values of ω. This threshold value decreases with the asymmetric parameter α and becomes constant for sufficiently large values of α. γ(c) has its maximum value for asymmetric load in comparison with the symmetric load. Finally, we apply the Melnikov theorem to the controlled system to explore the gain control parameter dependencies.

  6. An introduction to chaos theory in CFD

    Science.gov (United States)

    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.

  7. The foundations of chaos revisited from Poincaré to recent advancements

    CERN Document Server

    2016-01-01

    With contributions from a number of pioneering researchers in the field, this collection is aimed not only at researchers and scientists in nonlinear dynamics but also at a broader audience interested in understanding and exploring how modern chaos theory has developed since the days of Poincaré. This book was motivated by and is an outcome of the CHAOS 2015 meeting held at the Henri Poincaré Institute in Paris, which provided a perfect opportunity to gain inspiration and discuss new perspectives on the history, development and modern aspects of chaos theory. Henri Poincaré is remembered as a great mind in mathematics, physics and astronomy. His works, well beyond their rigorous mathematical and analytical style, are known for their deep insights into science and research in general, and the philosophy of science in particular. The Poincaré conjecture (only proved in 2006) along with his work on the three-body problem are considered to be the foundation of modern chaos theory.

  8. Emergent dynamics of spatio-temporal chaos in a heterogeneous excitable medium.

    Science.gov (United States)

    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.

  9. Chaos synchronizations of chaotic systems via active nonlinear control

    International Nuclear Information System (INIS)

    Huang, J; Xiao, T J

    2008-01-01

    This paper not only investigates the chaos synchronization between two LCC chaotic systems, but also discusses the chaos synchronization between LCC system and Genesio system. Some novel active nonlinear controllers are designed to achieve synchronizations between drive and response systems effectively. Moreover, the sufficient conditions of synchronizations are derived by using Lyapunov stability theorem. Numerical simulations are presented to verify the theoretical analysis, which shows that the synchronization schemes are global effective

  10. Searching for chaos on low frequency

    OpenAIRE

    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.

  11. Wave chaos in quantum systems with point interaction

    International Nuclear Information System (INIS)

    Albeverio, S.; Seba, P.

    1991-01-01

    The authors study perturbations H of the quantized version H 0 of integrable Hamiltonian systems by point interactions. They relate the eigenvalues of H to the zeros of a certain meromorphic function ξ. Assuming the eigenvalues of H 0 are Poisson distributed, they get detailed information on the joint distribution of the zeros of ξ and give bounds on the probability density for the spacings of eigenvalues of H. Their results confirm the wave chaos phenomenon, as different from the quantum chaos phenomenon predicted by random matrix theory

  12. Chaos synchronization communication using extremely unsymmetrical bidirectional injections.

    Science.gov (United States)

    Zhang, Wei Li; Pan, Wei; Luo, Bin; Zou, Xi Hua; Wang, Meng Yao; Zhou, Zhi

    2008-02-01

    Chaos synchronization and message transmission between two semiconductor lasers with extremely unsymmetrical bidirectional injections (EUBIs) are discussed. By using EUBIs, synchronization is realized through injection locking. Numerical results show that if the laser subjected to strong injection serves as the receiver, chaos pass filtering (CPF) of the system is similar to that of unidirectional coupled systems. Moreover, if the other laser serves as the receiver, a stronger CPF can be obtained. Finally, we demonstrate that messages can be extracted successfully from either of the two transmission directions of the system.

  13. Application of chaos and fractals to computer vision

    CERN Document Server

    Farmer, Michael E

    2014-01-01

    This book provides a thorough investigation of the application of chaos theory and fractal analysis to computer vision. The field of chaos theory has been studied in dynamical physical systems, and has been very successful in providing computational models for very complex problems ranging from weather systems to neural pathway signal propagation. Computer vision researchers have derived motivation for their algorithms from biology and physics for many years as witnessed by the optical flow algorithm, the oscillator model underlying graphical cuts and of course neural networks. These algorithm

  14. The chaos and order in nuclear molecular dynamics

    International Nuclear Information System (INIS)

    Srokowski, T.

    1995-01-01

    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 12 C, 16 O and 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

  15. Controlling chaos-assisted directed transport via quantum resonance.

    Science.gov (United States)

    Tan, Jintao; Zou, Mingliang; Luo, Yunrong; Hai, Wenhua

    2016-06-01

    We report on the first demonstration of chaos-assisted directed transport of a quantum particle held in an amplitude-modulated and tilted optical lattice, through a resonance-induced double-mean displacement relating to the true classically chaotic orbits. The transport velocity is controlled by the driving amplitude and the sign of tilt, and also depends on the phase of the initial state. The chaos-assisted transport feature can be verified experimentally by using a source of single atoms to detect the double-mean displacement one by one, and can be extended to different scientific fields.

  16. Chaos: a topic for interdisciplinary education in physics

    International Nuclear Information System (INIS)

    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 seems useful and good. In addition, we discuss some issues which can be important to interdisciplinary education in physics: for example the possible difficulties in programme design, the expertise barriers of non-major fields, the role of non-theoretical education in understanding and the project-type team activities

  17. Controlling chaos-assisted directed transport via quantum resonance

    Energy Technology Data Exchange (ETDEWEB)

    Tan, Jintao; Zou, Mingliang; Luo, Yunrong; Hai, Wenhua, E-mail: whhai2005@aliyun.com [Department of Physics and Key Laboratory of Low-dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha 410081, China and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081 (China)

    2016-06-15

    We report on the first demonstration of chaos-assisted directed transport of a quantum particle held in an amplitude-modulated and tilted optical lattice, through a resonance-induced double-mean displacement relating to the true classically chaotic orbits. The transport velocity is controlled by the driving amplitude and the sign of tilt, and also depends on the phase of the initial state. The chaos-assisted transport feature can be verified experimentally by using a source of single atoms to detect the double-mean displacement one by one, and can be extended to different scientific fields.

  18. Arsinoes Chaos

    Science.gov (United States)

    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.

  19. 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.

  20. Identification and control of chaos in nonlinear gear dynamic systems using Melnikov analysis

    International Nuclear Information System (INIS)

    Farshidianfar, A.; Saghafi, A.

    2014-01-01

    In this paper, the Melnikov analysis is extended to develop a practical model of gear system to control and eliminate the chaotic behavior. To this end, a nonlinear dynamic model of a spur gear pair with backlash, time-varying stiffness and static transmission error is established. Based on the Melnikov analysis the global homoclinic bifurcation and transition to chaos in this model are predicted. Then non-feedback control method is used to eliminate the chaos by applying an additional control excitation. The regions of the parameter space for the control excitation are obtained analytically. The accuracy of the theoretical predictions and also the performance of the proposed control system are verified by the comparison with the numerical simulations. The simulation results show effectiveness of the proposed control system and present some useful information to analyze and control the gear dynamical systems. - Highlights: • This study deals with the prediction and control of chaos in a nonlinear gear system. • Melnikov analysis is extended to present a practical gear system to control the chaos. • The proposed system is effective to eliminate the homoclinic bifurcation and chaos. • This controller is proposed as a way of implementing the chaos control in gear system

  1. 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.

  2. Quantum Chaos

    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

  3. Quantum Chaos

    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.

  4. Poincaré chaos and unpredictable functions

    Science.gov (United States)

    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.

  5. Introduction to the focus issue: fifty years of chaos: applied and theoretical.

    Science.gov (United States)

    Hikihara, Takashi; Holmes, Philip; Kambe, Tsutomu; Rega, Giuseppe

    2012-12-01

    The discovery of deterministic chaos in the late nineteenth century, its subsequent study, and the development of mathematical and computational methods for its analysis have substantially influenced the sciences. Chaos is, however, only one phenomenon in the larger area of dynamical systems theory. This Focus Issue collects 13 papers, from authors and research groups representing the mathematical, physical, and biological sciences, that were presented at a symposium held at Kyoto University from November 28 to December 2, 2011. The symposium, sponsored by the International Union of Theoretical and Applied Mechanics, was called 50 Years of Chaos: Applied and Theoretical. Following some historical remarks to provide a background for the last 50 years, and for chaos, this Introduction surveys the papers and identifies some common themes that appear in them and in the theory of dynamical systems.

  6. Anticontrol of chaos in continuous-time systems via time-delay feedback.

    Science.gov (United States)

    Wang, Xiao Fan; Chen, Guanrong; Yu, Xinghuo

    2000-12-01

    In this paper, a systematic design approach based on time-delay feedback is developed for anticontrol of chaos in a continuous-time system. This anticontrol method can drive a finite-dimensional, continuous-time, autonomous system from nonchaotic to chaotic, and can also enhance the existing chaos of an originally chaotic system. Asymptotic analysis is used to establish an approximate relationship between a time-delay differential equation and a discrete map. Anticontrol of chaos is then accomplished based on this relationship and the differential-geometry control theory. Several examples are given to verify the effectiveness of the methodology and to illustrate the systematic design procedure. (c) 2000 American Institute of Physics.

  7. Dynamic behavior and chaos control in a complex Riccati-type map ...

    African Journals Online (AJOL)

    This paper is devoted to analyze the dynamic behavior of a Riccati- type map with complex variables and complex parameters. Fixed points and their asymptotic stability are studied. Lyapunov exponent is computed to indicate chaos. Bifurcation and chaos are discussed. Chaotic behavior of the map has been controlled by ...

  8. Chaos synchronization of a chaotic system via nonlinear control

    International Nuclear Information System (INIS)

    Park, Ju H.

    2005-01-01

    In this letter, the problem of chaos synchronization of a chaotic system which is proposed by Lue et al. [Int J Bifurcat Chaos 2004;14:1507] 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

  9. Many-body quantum chaos: Recent developments and applications to nuclei

    International Nuclear Information System (INIS)

    Gomez, J.M.G.; Kar, K.; Kota, V.K.B.; Molina, R.A.; Relano, A.; Retamosa, J.

    2011-01-01

    In the last decade, there has been an increasing interest in the analysis of energy level spectra and wave functions of nuclei, particles, atoms and other quantum many-body systems by means of statistical methods and random matrix ensembles. The concept of quantum chaos plays a central role for understanding the universal properties of the energy spectrum of quantum systems. Since these properties concern the whole spectrum, statistical methods become an essential tool. Besides random matrix theory, new theoretical developments making use of information theory, time series analysis, and the merging of thermodynamics and the semiclassical approximation are emphasized. Applications of these methods to quantum systems, especially to atomic nuclei, are reviewed. We focus on recent developments like the study of 'imperfect spectra' to estimate the degree of symmetry breaking or the fraction of missing levels, the existence of chaos remnants in nuclear masses, the onset of chaos in nuclei, and advances in the comprehension of the Hamiltonian structure in many-body systems. Finally, some applications of statistical spectroscopy methods generated by many-body chaos and two-body random matrix ensembles are described, with emphasis on Gamow-Teller strength sums and beta decay rates for stellar evolution and supernovae.

  10. Application of Chaos Theory in Trucks' Overloading Enforcement

    Directory of Open Access Journals (Sweden)

    Abbas Mahmoudabadi

    2013-01-01

    Full Text Available Trucks' overloading is considered as one of the most substantial concerns in road transport due to a possible road surface damage, as well as, are less reliable performance of trucks' braking system. Sufficient human resource and adequate time scheduling are to be planned for surveying trucks' overloading; hence, it seems required to prepare an all-around model to be able to predict the number of overloaded vehicles. In the present research work, the concept of chaos theory has been utilized to predict the ratio of trucks which might be guessed overloaded. The largest Lyapunov exponent is utilized to determine the presence of chaos using experimental data and concluded that the ratio of overloaded trucks reflects chaotic behavior. The prediction based on chaos theory is compared with the results of simple smoothing and moving average methods according to the well-known criterion of mean square errors. The results have also revealed that the chaotic prediction model would act more capably comparing the analogous methods including simple smoothing and moving average to predict the ratio of passing trucks to be possibly overloaded.

  11. Noise-induced chaos in a quadratically nonlinear oscillator

    International Nuclear Information System (INIS)

    Gan Chunbiao

    2006-01-01

    The present paper focuses on the noise-induced chaos in a quadratically nonlinear oscillator. Simple zero points of the stochastic Melnikov integral theoretically mean the necessary rising of noise-induced chaotic response in the system based on the stochastic Melnikov method. To quantify the noise-induced chaos, the boundary of the system's safe basin is firstly studied and it is shown to be incursively fractal when chaos arises. Three cases are considered in simulating the safe basin of the system, i.e., the system is excited only by the harmonic excitation, by both the harmonic and the Gaussian white noise excitations, and only by the Gaussian white noise excitation. Secondly, the leading Lyapunov exponent by Rosenstein's algorithm is shown to quantify the chaotic nature of the sample time series of the system. The results show that the boundary of the safe basin can also be fractal even if the system is excited only by the external Gaussian white noise. Most importantly, the almost-harmonic, the noise-induced chaotic and the thoroughly random responses can be found in the system

  12. Quantum chaos in the Heisenberg spin chain: The effect of Dzyaloshinskii-Moriya interaction.

    Science.gov (United States)

    Vahedi, J; Ashouri, A; Mahdavifar, S

    2016-10-01

    Using one-dimensional spin-1/2 systems as prototypes of quantum many-body systems, we study the emergence of quantum chaos. The main purpose of this work is to answer the following question: how the spin-orbit interaction, as a pure quantum interaction, may lead to the onset of quantum chaos? We consider the three integrable spin-1/2 systems: the Ising, the XX, and the XXZ limits and analyze whether quantum chaos develops or not after the addition of the Dzyaloshinskii-Moriya interaction. We find that depending on the strength of the anisotropy parameter, the answer is positive for the XXZ and Ising models, whereas no such evidence is observed for the XX model. We also discuss the relationship between quantum chaos and thermalization.

  13. The butterfly and the tornado: chaos theory and climate change

    International Nuclear Information System (INIS)

    Madrid, Carlos

    2013-01-01

    In this book, the author addresses two topics: the theory of chaos, and climate change. The first chapters propose a prehistory and history of chaos, from Newton, Laplace and Lorenz and their controversies as far as prehistory of chaos is concerned, and with different works performed during the twentieth century (Hadamard, Birkhoff, van der Pol, and so on, until Lorenz, the MIT meteorologist and the discovery of the Butterfly Effect, and more recent works by Yorke and Feigenbaum about the logistic equation and the transition to chaos) as far as recent history is concerned. The next chapter describes the deterministic chaos by introducing non linear dynamic systems and distinguishing three regimes: steady, periodic or chaotic. The second part addresses climate change, outlines that global warming is a reality, that the main origin is the increase of greenhouse effect, and that CO 2 emissions related to human activity are the main origin of this additional greenhouse effect. The author notably recalls the controversy about the analysis of the global average temperature curve, discusses the assessment of average temperatures from a statistical point of view and in relationship with the uneven distribution of survey stations. The last chapter discusses the numerical modelling of time and climate, and the validity of the Butterfly Effect. The author also proposes a brief overview of the IPCC, discusses the emergence of an international climate policy (UN convention, Kyoto protocol), evokes the use of game theory to ensure a convergence of treaties, and analyses the economic situation of several countries (including Spain) since the Kyoto protocol

  14. 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...

  15. Hyper-chaos encryption using convolutional masking and model free unmasking

    International Nuclear Information System (INIS)

    Qi Guo-Yuan; Matondo Sandra Bazebo

    2014-01-01

    In this paper, during the masking process the encrypted message is convolved and embedded into a Qi hyper-chaotic system characterizing a high disorder degree. The masking scheme was tested using both Qi hyper-chaos and Lorenz chaos and indicated that Qi hyper-chaos based masking can resist attacks of the filtering and power spectrum analysis, while the Lorenz based scheme fails for high amplitude data. To unmask the message at the receiving end, two methods are proposed. In the first method, a model-free synchronizer, i.e. a multivariable higher-order differential feedback controller between the transmitter and receiver is employed to de-convolve the message embedded in the receiving signal. In the second method, no synchronization is required since the message is de-convolved using the information of the estimated derivative. (general)

  16. Shear-induced chaos

    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

  17. Shear-induced chaos

    Science.gov (United States)

    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.

  18. Chaos control of chaotic dynamical systems using backstepping design

    International Nuclear Information System (INIS)

    Yassen, M.T.

    2006-01-01

    This work presents chaos control of chaotic dynamical systems by using backstepping design method. This technique is applied to achieve chaos control for each of the dynamical systems Lorenz, Chen and Lue systems. Based on Lyapunov stability theory, control laws are derived. We used the same technique to enable stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory to be achieved in a systematic way. Numerical simulations are shown to verify the results

  19. Suppression of chaos via control of energy flow

    Science.gov (United States)

    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.

  20. Adventures in order and chaos a scientific autobiography

    CERN Document Server

    Contopoulos, George

    2004-01-01

    The field of Order and Chaos had a remarkable expansion in the last 50 years. The main reason was the use of computers, and the development of new theoretical methods that we call now 'the theory of chaos'. The author describes this fascinating period in a relaxed and sometimes humorous autobiographical way. He relates his interactions with many people in dynamical astronomy and he quotes several anecdotes from these interactions. He refers also to his experiences when he served in various international positions, such as general secretary of the IAU and chairman of the journal Astronomy and A

  1. Train flow chaos analysis based on an improved cellular automata model

    International Nuclear Information System (INIS)

    Meng, Xuelei; Xiang, Wanli; Jia, Limin; Xu, Jie

    2015-01-01

    To control the chaos in the railway traffic flow and offer valuable information for the dispatchers of the railway system, an improved cellular model is presented to detect and analyze the chaos in the traffic flow. We first introduce the working mechanism of moving block system, analyzing the train flow movement characteristics. Then we improve the cellular model on the evolution rules to adjust the train flow movement. We give the train operation steps from three cases: the trains running on a railway section, a train will arrive in a station and a train will departure from a station. We simulate 4 trains to run on a high speed section fixed with moving block system and record the distances between the neighbor trains and draw the Poincare section to analyze the chaos in the train operation. It is concluded that there is not only chaos but order in the train operation system with moving blocking system and they can interconvert to each other. The findings have the potential value in train dispatching system construction and offer supporting information for the daily dispatching work.

  2. Short-term data forecasting based on wavelet transformation and chaos theory

    Science.gov (United States)

    Wang, Yi; Li, Cunbin; Zhang, Liang

    2017-09-01

    A sketch of wavelet transformation and its application was given. Concerning the characteristics of time sequence, Haar wavelet was used to do data reduction. After processing, the effect of “data nail” on forecasting was reduced. Chaos theory was also introduced, a new chaos time series forecasting flow based on wavelet transformation was proposed. The largest Lyapunov exponent was larger than zero from small data sets, it verified the data change behavior still met chaotic behavior. Based on this, chaos time series to forecast short-term change behavior could be used. At last, the example analysis of the price from a real electricity market showed that the forecasting method increased the precision of the forecasting more effectively and steadily.

  3. A period-doubling cascade precedes chaos for planar maps.

    Science.gov (United States)

    Sander, Evelyn; Yorke, James A

    2013-09-01

    A period-doubling cascade is often seen in numerical studies of those smooth (one-parameter families of) maps for which as the parameter is varied, the map transitions from one without chaos to one with chaos. Our emphasis in this paper is on establishing the existence of such a cascade for many maps with phase space dimension 2. We use continuation methods to show the following: under certain general assumptions, if at one parameter there are only finitely many periodic orbits, and at another parameter value there is chaos, then between those two parameter values there must be a cascade. We investigate only families that are generic in the sense that all periodic orbit bifurcations are generic. Our method of proof in showing there is one cascade is to show there must be infinitely many cascades. We discuss in detail two-dimensional families like those which arise as a time-2π maps for the Duffing equation and the forced damped pendulum equation.

  4. Chaos control and synchronization in Bragg acousto-optic bistable systems driven by a separate chaotic system.

    Science.gov (United States)

    Wang, Rong; Gao, Jin-Yue

    2005-09-01

    In this paper we propose a new scheme to achieve chaos control and synchronization in Bragg acousto-optic bistable systems. In the scheme, we use the output of one system to drive two identical chaotic systems. Using the maximal conditional Lyapunov exponent (MCLE) as the criterion, we analyze the conditions for realizing chaos synchronization. Numerical calculation shows that the two identical systems in chaos with negative MCLEs and driven by a chaotic system can go into chaotic synchronization whether or not they were in chaos initially. The two systems can go into different periodic states from chaos following an inverse period-doubling bifurcation route as well when driven by a periodic system.

  5. Augmented chaos-multiple linear regression approach for prediction of wave parameters

    Directory of Open Access Journals (Sweden)

    M.A. Ghorbani

    2017-06-01

    The inter-comparisons demonstrated that the Chaos-MLR and pure MLR models yield almost the same accuracy in predicting the significant wave heights and the zero-up-crossing wave periods. Whereas, the augmented Chaos-MLR model is performed better results in term of the prediction accuracy vis-a-vis the previous prediction applications of the same case study.

  6. Anti-control of chaos of single time-scale brushless DC motor.

    Science.gov (United States)

    Ge, Zheng-Ming; Chang, Ching-Ming; Chen, Yen-Sheng

    2006-09-15

    Anti-control of chaos of single time-scale brushless DC motors is studied in this paper. In order to analyse a variety of periodic and chaotic phenomena, we employ several numerical techniques such as phase portraits, bifurcation diagrams and Lyapunov exponents. Anti-control of chaos can be achieved by adding an external constant term or an external periodic term.

  7. Secure communications of CAP-4 and OOK signals over MMF based on electro-optic chaos.

    Science.gov (United States)

    Ai, Jianzhou; Wang, Lulu; Wang, Jian

    2017-09-15

    Chaos-based secure communication can provide a high level of privacy in data transmission. Here, we experimentally demonstrate secure signal transmission over two kinds of multimode fiber (MMF) based on electro-optic intensity chaos. High-quality synchronization is achieved in an electro-optic feedback configuration. Both 5  Gbit/s carrier-less amplitude/phase (CAP-4) modulation and 10  Gbit/s on-off key (OOK) signals are recovered efficiently in electro-optic chaos-based communication systems. Degradations of chaos synchronization and communication system due to mismatch of various hardware keys are also discussed.

  8. 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

  9. The Chaos Theory of Careers

    Science.gov (United States)

    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…

  10. Meso-structures of dynamical chaos and E-infinity theory

    International Nuclear Information System (INIS)

    Mukhamedov, A.M.

    2009-01-01

    A novel proposal is made to develop a unified theory of dynamical chaos using an idea of extra-coordinates. It is supposed that chaos is capable to translate influences from quantum level of description to the classical macroscopic one and vise versa. The notion of macroscopically prepared microstates is proposed to determine a special case of extra-coordinates induced by cooperative effects at quantum resolution of dynamical events. Meso-structures mediating quantum and classical appearances of chaotic motion are studied in the light of E-infinity theory.

  11. Controlling chaos in permanent magnet synchronous motor based on finite-time stability theory

    International Nuclear Information System (INIS)

    Du-Qu, Wei; Bo, Zhang

    2009-01-01

    This paper reports that the performance of permanent magnet synchronous motor (PMSM) degrades due to chaos when its systemic parameters fall into a certain area. To control the undesirable chaos in PMSM, a nonlinear controller, which is simple and easy to be constructed, is presented to achieve finite-time chaos control based on the finite-time stability theory. Computer simulation results show that the proposed controller is very effective. The obtained results may help to maintain the industrial servo driven system's security operation. (general)

  12. Dynamical Chaos Rise in the System of Large Number of Nonlinear Coupled Oscillators

    International Nuclear Information System (INIS)

    Buts, V.A.; Koval'chuk, I.K.; Tarasov, D.V.

    2007-01-01

    The problem of dynamical chaos arising in distributed systems is considered. It was shown that in many cases it is possible to allocate relatively isolated subsystem which may be simpler for investigation. We suppose that chaos in this subsystem leads to chaotic behaviour of all system. Besides, the allocated subsystem may be used for describing complex dynamics of nonlinear three-wave interaction, in particular, in plasma systems. The analytical criterion of arising dynamics chaos in distributed system was obtained. This criterion was confirmed by numerical simulation

  13. Leveraging Chaos in Continuous Thrust Trajectory Design

    Data.gov (United States)

    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...

  14. 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)

  15. 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

  16. Chaos as a psychological construct: historical roots, principal findings, and current growth directions.

    Science.gov (United States)

    Guastello, Stephen J

    2009-07-01

    The landmarks in the use of chaos and related constructs in psychology were entwined with the growing use of other nonlinear dynamical constructs, especially catastrophes and self-organization. The growth in substantive applications of chaos in psychology is partially related to the development of methodologies that work within the constraints of psychological data. The psychological literature includes rigorous theory with testable propositions, lighter-weight metaphorical uses of the construct, and colloquial uses of "chaos" with no particular theoretical intent. The current state of the chaos construct and supporting empirical research in psychological theory is summarized in neuroscience, psychophysics, psychomotor skill and other learning phenomena, clinical and abnormal psychology, and group dynamics and organizational behavior. Trends indicate that human systems do not remain chaotic indefinitely; they eventually self-organize, and the concept of the complex adaptive system has become prominent. Chaotic turbulence is generally higher in healthy systems compared to unhealthy systems, although opposite appears true in mood disorders. Group dynamics research shows trends consistent with the complex adaptive system, whereas organizational behavior lags behind in empirical studies relative to the quantity of its theory. Future directions for research involving the chaos construct and other nonlinear dynamics are outlined.

  17. Shil'nikov chaos control using homoclinic orbits and the Newhouse region

    International Nuclear Information System (INIS)

    Furui, Sadataka; Niiya, Shohei

    2007-01-01

    A method of controlling Shil'nikov's type chaos using windows that appear in the 1-dimensional bifurcation diagram when perturbations are applied, and using existence of stable homoclinic orbits near the unstable one is presented and applied to the electronic Chua's circuit. A demonstration of the chaos control in the electronic circuit experiments and their simulations and bifurcation analyses are given

  18. 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

  19. Chaos and fractals an elementary introduction

    CERN Document Server

    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.

  20. Taming Chaos by Linear Regulation with Bound Estimation

    Directory of Open Access Journals (Sweden)

    Jiqiang Wang

    2015-01-01

    Full Text Available Chaos control has become an important area of research and consequently many approaches have been proposed to control chaos. This paper proposes a linear regulation method. Different from the existing approaches is that it can provide region of attraction while estimating the bounding behaviour of the norm of the states. The proposed method also possesses design flexibility and can be easily used to cater for special requirement such that control signal should be generated via single input, single state, static feedback and so forth. The applications to the Tigan system, the Genesio chaotic system, the novel chaotic system, and the Lorenz chaotic system justify the above claims.

  1. Counterintuitive Constraints on Chaos Formation Set by Heat Flux through Europa's Ocean

    Science.gov (United States)

    Goodman, J. C.

    2013-12-01

    Models for the formation of disruptive chaos features on the icy surface of Europa fall into two broad categories: either chaos is formed when basal heating causes localized melting and thinning of the ice shell, or basal heating drives diapiric convection within the ice shell. We argue that in both of these cases, heating of the ice shell from below does not lead to chaos formation at the location of heating. If chaos is formed when a localized oceanic heat source, such as a hydrothermal plume, "melts through" the ice crust, we must consider what happens to the melted liquid. If Europa's ocean is salty, the melt will form a buoyant pool inside the melted cavity, leading to a stable interface between cold fresh meltwater and warm salty seawater. This stable interface acts like an ablative heat shield, protecting the ice from further damage. Some heat can be transferred across the stable layer by double diffusion, but this transfer is very inefficient. We calculate that local ocean heating cannot be balanced by local flux through the stable layer: instead, the warm ocean water must spread laterally until it is delivering heat to the ice base on a regional or global scale (a heating zone hundreds or thousands of km across, for conservative parameters.) If chaos is formed by diapiric solid-state convection within the ice shell, many investigators have assumed that diapirism and chaos should be most prevalent where the basal heat flux is strongest. We argue that this is not the case. In Rayleigh-Benard convection, increasing the heat flux will make convection more vigorous --- if and only if the convecting layer thickness does not change. We argue that increased basal heat flux will thin the ice shell, reducing its Rayleigh number and making convection less likely, not more. This insight allows us to reverse the logic of recent discussions of the relationship between ocean circulation and chaos (for instance, Soderlund et al, 2013 LPSC). We argue that global oceanic

  2. 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...

  3. Routes to spatiotemporal chaos in Kerr optical frequency combs.

    Science.gov (United States)

    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.

  4. 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

  5. Phase Locking and Chaos in a Josephson Junction Array Shunted by a Common Resistance

    International Nuclear Information System (INIS)

    Tie-Ge, Zhou; Jing, Mao; Ting-Shu, Liu; Yue, Lai; Shao-Lin, Yan

    2009-01-01

    The dynamics of a Josephson junction array shunted by a common resistance are investigated by using numerical methods. Coexistence of phase locking and chaos is observed in the system when the resistively and capacitively shunted junction model is adopted. The corresponding parameter ranges for phase locking and chaos are presented. When there are three resistively shunted junctions in the array, chaos is found for the first time and the parameter range for chaos is also presented. According to the theory of Chernikov and Schmidt, when there are four or more junctions in the array, the system exhibits chaotic behavior. Our results indicate that the theory of Chernikov and Schmidt is not exactly appropriate. (condensed matter: electronicstructure, electrical, magnetic, and opticalproperties)

  6. Frequency locking, quasiperiodicity, subharmonic bifurcations and chaos in high frequency modulated stripe geometry DH semiconductor lasers

    International Nuclear Information System (INIS)

    Zhao Yiguang

    1991-01-01

    The method of obtaining self-consistent solutions of the field equation and the rate equations of photon density and carrier concentration has been used to study frequecny locking, quasiperiodicity, subharmonic bifurcations and chaos in high frequency modulated stripe geometry DH semiconductor lasers. The results show that the chaotic behavior arises in self-pulsing stripe geometry semiconductor lasers. The route to chaos is not period-double, but quasiperiodicity to chaos. All of the results agree with the experiments. Some obscure points in previous theory about chaos have been cleared up

  7. Applied Chaos Level Test for Validation of Signal Conditions Underlying Optimal Performance of Voice Classification Methods

    Science.gov (United States)

    Liu, Boquan; Polce, Evan; Sprott, Julien C.; Jiang, Jack J.

    2018-01-01

    Purpose: The purpose of this study is to introduce a chaos level test to evaluate linear and nonlinear voice type classification method performances under varying signal chaos conditions without subjective impression. Study Design: Voice signals were constructed with differing degrees of noise to model signal chaos. Within each noise power, 100…

  8. CHAOS THEORY OF LAW: PENJELASAN ATAS KETERATURAN DAN KETIDAKTERATURAN DALAM HUKUM

    Directory of Open Access Journals (Sweden)

    . Sudjito

    2015-02-01

    Full Text Available It is of no posibilitiy to understand the complex reality of law by means of linear-mechanistic approach used to be ulitilized in rechtsdogmatiek or legal-positivism which is still dominant in the teaching of law. It needs our readiness to see the world of law not as in order but in chaos; and this is the basic reason to present the Chaos theory of law. It is hoped that this theory will enable us to explore and explain the law throroughly. Thus the law science will be the total science which does not limit itself to the positive law, the state law or the lawyer’s law. Furthermore this chaos theory is expected to give better description and comprehension of law. Order and disorder are not opposant, or white-black dichotomy, but they are interrelated, interwoven and having mutual fulfilment in a sustainably and continually change process. The Chaos theory of law, thus, constitutes a theory which is qualified to give good explanation of the complex reality of law and provide the best solution to the critical condition of law in our country.

  9. In Command And Out Of Control: Leaders Developing Teams That Thrive In Chaos And Ambiguity

    Science.gov (United States)

    2016-05-26

    In Command and Out of Control: Leaders Developing Teams that Thrive in Chaos and Ambiguity A Monograph by...TITLE AND SUBTITLE Sa. CONTRACT NUMBER In Command and Out of Control: Leaders Developing Teams that Thrive in Chaos and Ambiguity Sb. GRANT NUMBER...the chaos and ambiguity associated with war. Teams must provide the innovative and creative solutions formerly left to the individual leader. This

  10. Solitons and chaos in plasma

    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

  11. General definitions of chaos for continuous and discrete-time processes

    OpenAIRE

    Vieru, Andrei

    2008-01-01

    A precise definition of chaos for discrete processes based on iteration already exists. We shall first reformulate it in a more general frame, taking into account the fact that discrete chaotic behavior is neither necessarily based on iteration nor strictly related to compact metric spaces or to bounded functions. Then we shall apply the central idea of this definition to continuous processes. We shall try to see what chaos is, regardless of the way it is generated.

  12. La théorie du chaos vers une nouvelle science

    CERN Document Server

    Gleick, James

    1989-01-01

    Là où commence le chaos s'arrêtait jusqu'ici la science. Or, dans les années 70, quelques scientifiques français et américains ont commencé à explorer le chaos. A la surprise générale celui-ci s'est révélé gouverné par un ordre dynamique qui a permis d'expliquer bien des phénomènes naturels jusqu'ici totalement incompréhensibles.

  13. Chaos: Challenges from and to socio-spatial form and policy

    Directory of Open Access Journals (Sweden)

    Dimitrios S. Dendrinos

    1997-01-01

    Full Text Available A brief assessment is given of the major accomplishments made through the mathematics of chaos to the understanding of socio-spatial dynamics to date. Certain shortfalls are also presented, mostly associated with model testing and falsifiability which transcend socio-spatial dynamics. Beyond such shortcomings, lie an array of challenges for chaotic dynamics involving specifically socio-spatial form and policy. A few directions on meeting these challenges are suggested including the case of limited chaos.

  14. Aureum Chaos

    Science.gov (United States)

    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.

  15. A novel image encryption scheme based on spatial chaos map

    International Nuclear Information System (INIS)

    Sun Fuyan; Liu Shutang; Li Zhongqin; Lue Zongwang

    2008-01-01

    In recent years, the chaos-based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques, but the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. In this paper, spatial chaos system are used for high degree security image encryption while its speed is acceptable. The proposed algorithm is described in detail. The basic idea is to encrypt the image in space with spatial chaos map pixel by pixel, and then the pixels are confused in multiple directions of space. Using this method one cycle, the image becomes indistinguishable in space due to inherent properties of spatial chaotic systems. Several experimental results, key sensitivity tests, key space analysis, and statistical analysis show that the approach for image cryptosystems provides an efficient and secure way for real time image encryption and transmission from the cryptographic viewpoint

  16. Family CHAOS is associated with glycaemic control in children and adolescents with type 1 diabetes mellitus.

    Science.gov (United States)

    Chae, M; Taylor, B J; Lawrence, J; Healey, D; Reith, D M; Gray, A; Wheeler, B J

    2016-02-01

    Despite advances in the medical management of type 1 diabetes mellitus (T1DM), for many, glycaemic control remains substandard. Other factors are clearly important in determining success, or lack thereof, with diabetes management. With this in mind, we have investigated whether family CHAOS may provide a novel tool to identify when environmental confusion could impact on diabetes management and subsequent glycaemic control. A case-control study of children and adolescents with established T1DM and age-/sex-matched controls was conducted. Demographic information, both maternal and paternal CHAOS scores, and HbA1c were collected. Statistical analysis was undertaken to explore associations between T1DM and CHAOS and between CHAOS and HbA1c. Data on 65 children with T1DM and 60 age-/sex-matched controls were obtained. There was no evidence of group differences for maternal CHAOS (p = 0.227), but paternal CHAOS scores were higher for the T1DM group (p = 0.041). Greater maternal and paternal CHAOS scores were both associated with higher HbA1c (p ≤ 0.027). The maternal association remained after controlling for diabetes duration, SMBG frequency, and insulin therapy. In children with T1DM, there appears to be a negative association between increased environmental confusion, as rated by CHAOS, and glycaemic control. In addition, when compared to controls, fathers of children and adolescents with T1DM appear to experience CHAOS differently to mothers. These findings contribute to the growing body of literature exploring psychosocial factors in T1DM. Continuing efforts are required to fully understand how the family and psychosocial environment interact with diabetes to impact on long-term health outcomes.

  17. Interactions between neural networks: a mechanism for tuning chaos and oscillations.

    Science.gov (United States)

    Wang, Lipo

    2007-06-01

    We show that chaos and oscillations in a higher-order binary neural network can be tuned effectively using interactions between neural networks. Our results suggest that network interactions may be useful as a means of adjusting the level of dynamic activities in systems that employ chaos and oscillations for information processing, or as a means of suppressing oscillatory behaviors in systems that require stability.

  18. Western Eos Chaos on Mars: A Potential Site for Future Landing and Returning Samples

    Science.gov (United States)

    Asif Iqbal Kakkassery; Rajesh, V. J.

    2018-04-01

    Introducing Eos Chaos as a potential area for collecting samples. Eos Chaos contains a number of aqueous minerals. We have detected zoisite — a least reported low-grade metamorphic mineral from this area.

  19. Cryptology transmitted message protection from deterministic chaos up to optical vortices

    CERN Document Server

    Izmailov, Igor; Romanov, Ilia; Smolskiy, Sergey

    2016-01-01

    This book presents methods to improve information security for protected communication. It combines and applies interdisciplinary scientific engineering concepts, including cryptography, chaos theory, nonlinear and singular optics, radio-electronics and self-changing artificial systems. It also introduces additional ways to improve information security using optical vortices as information carriers and self-controlled nonlinearity, with nonlinearity playing a key "evolving" role. The proposed solutions allow the universal phenomenon of deterministic chaos to be discussed in the context of information security problems on the basis of examples of both electronic and optical systems. Further, the book presents the vortex detector and communication systems and describes mathematical models of the chaos oscillator as a coder in the synchronous chaotic communication and appropriate decoders, demonstrating their efficiency both analytically and experimentally. Lastly it discusses the cryptologic features of analyze...

  20. Doubly excited helium. From strong correlation to chaos

    International Nuclear Information System (INIS)

    Jiang, Yuhai

    2006-03-01

    In the present dissertation, the double excitation states of helium including the autoionization decay of these states were studied experimentally and theoretically in a broad energy region, which includes the transition from strong correlation below the low single ionization thresholds (SIT) to the region of quantum chaos at energies very close to the double-ionization threshold. Two kind of experiments were performed, namely total-ion-yield measurements with the aim to observe total cross sections (TCS) and electron time-of-flight (TOF) measurements to obtain partial cross sections (PCS) as well as angular distribution parameters (ADP). Both types of measurements were performed at the third generation synchrotron radiation facility BESSY II in Berlin. The TCSs were recorded up to the SIT I 15 , and they were found to be in in excellent agreement with state-of-the-art complex-rotation calculations performed recently by D. Delande. These experimental and theoretical data on the TCSs were analyzed in order to study quantum chaos in doubly excited helium, and interesting signatures of quantum chaos were found. The TOF technique allowed to measure PCSs and ADPs in the energy regions from I 5 to I 9 and I 7 , respectively. These experimental data provide a critical assessment of theoretical models that can be used to explore the dynamics of strong correlation as well as quantum chaos in helium. In the theoretical part of this dissertation, the n- and l-specific PCSs and ADPs below I 4 were calculated employing the R-matrix method. The present theoretical results agree well with a recent experimental study of l-specific PCSs below I 4 by J.R. Harries et al. An analysis of patterns in the PCSs and ADPs on the basis of the present experimental and theoretical l-specific data allowed to improve the present understanding of autoionization decay dynamics in this two-electron atom. (orig.)

  1. Sparse grid-based polynomial chaos expansion for aerodynamics of an airfoil with uncertainties

    Directory of Open Access Journals (Sweden)

    Xiaojing WU

    2018-05-01

    Full Text Available The uncertainties can generate fluctuations with aerodynamic characteristics. Uncertainty Quantification (UQ is applied to compute its impact on the aerodynamic characteristics. In addition, the contribution of each uncertainty to aerodynamic characteristics should be computed by uncertainty sensitivity analysis. Non-Intrusive Polynomial Chaos (NIPC has been successfully applied to uncertainty quantification and uncertainty sensitivity analysis. However, the non-intrusive polynomial chaos method becomes inefficient as the number of random variables adopted to describe uncertainties increases. This deficiency becomes significant in stochastic aerodynamic analysis considering the geometric uncertainty because the description of geometric uncertainty generally needs many parameters. To solve the deficiency, a Sparse Grid-based Polynomial Chaos (SGPC expansion is used to do uncertainty quantification and sensitivity analysis for stochastic aerodynamic analysis considering geometric and operational uncertainties. It is proved that the method is more efficient than non-intrusive polynomial chaos and Monte Carlo Simulation (MSC method for the stochastic aerodynamic analysis. By uncertainty quantification, it can be learnt that the flow characteristics of shock wave and boundary layer separation are sensitive to the geometric uncertainty in transonic region. The uncertainty sensitivity analysis reveals the individual and coupled effects among the uncertainty parameters. Keywords: Non-intrusive polynomial chaos, Sparse grid, Stochastic aerodynamic analysis, Uncertainty sensitivity analysis, Uncertainty quantification

  2. From archaic narcissism to empathy for the self: the evolution of new capacities in psychoanalysis.

    Science.gov (United States)

    Gehrie, Mark J

    2011-04-01

    The concept of the selfobject was central to Heinz Kohut's psychology of the self. With an eye to studying the development of narcissism and its implications for the growth of new psychic structure, this concept is reviewed and reassessed. Post-Kohutian complexities regarding its definition and use extend our consideration of the development of narcissism beyond archaic configurations toward further evolution of the self and the nature of mature narcissism. The hypothesis is offered that developing narcissism and the growth of self-regulation impact the acquisition of new structure and new capacities through the emergence of newly potentiated aspects of the self. The implications of these emergent qualities of the self are examined in the context of our understanding of self-esteem regulation, the state of the self, and the goals of psychoanalysis. A clinical example illustrates how technique and process in an analysis may be organized around the development of such new capacities.

  3. Role of nonlinear dynamics and chaos in applied sciences

    International Nuclear Information System (INIS)

    Lawande, Quissan V.; Maiti, Nirupam

    2000-02-01

    Nonlinear dynamics manifests itself in a number of phenomena in both laboratory and day to day dealings. However, little attention was being paid to this dynamically rich field. With the advent of high speed computers with visual graphics, the field has proliferated over past few years. One of the most rewarding realization from nonlinear dynamics is the universally acclaimed field of chaos. Chaos has brought in order and has broken the disciplinary boundaries that existed until recently. With its universal phenomena, almost all disciplines following an evolutionary character can be treated on same footing. Chaotic dynamics has its grounding in the multidisciplinary field of synergetics founded by Professor Hermann Haken. In this report, we address some of the basics related to the field of chaos. We have discussed simple mechanisms for generating chaotic trajectories, ways and means of characterizing such systems and the manifestation of their signatures in the evolutions. We have mentioned the links of this field with other existing theories. We have outlined the topics on bifurcation and stability of dynamical systems. Information theoretic aspects and notions on fractal geometry are reviewed in the light of dynamical characterization of chaotic systems. Application oriented views of this novel dynamical phenomena are discussed through examples on simple nonlinear electronic circuits and a BWR reactor. Some ideas relating to control and synchronization in chaotic systems also addressed. In conclusion, we have explored the possibilities of exploiting nonlinear dynamics and chaos in the context of multidisciplinary character of BARC. (author)

  4. Chaos - a new degree of freedom in nuclear physics

    International Nuclear Information System (INIS)

    Besliu, Calin.; Jipa, Alexandru; Felea, Daniel

    2002-01-01

    Before 1985 the chaos representation and its dynamics was known as a mathematical construction generated by the solution instability for the coupled nonlinear differential equations. A number of important needs (the temporal scenarios, a stochastic time scale for nuclear processes, separation between the breakup and statistical processes, nuclear phase transitions at high and very high energies, etc.) determines a focused effort to adapt the chaos theory as a tool for the nuclear physics. In this list, essentially is the distinction between the nonequilibrium and equilibrium states and its general and local balance. The authors report an attempt to introduce the chaos representation in the first stage of the nuclear fragmentation. The trajectories lead to a chaotic behavior at the resonance regime in all cases analyzed. A number of stochastic functions (the Lyapunov exponents, the power functions, the autocorrelation coefficients and the Shannon and Kolmogorov informational entropies) verified the main conclusion. This model, usually called as the 'game of billiards', as studied in the resonance regime, is more realistic than the adiabatic case studied by the Catania-Grenoble group (Burgio, Baldo, Rapisarda, Schuck) which represents the first step for this kind of analysis. A number of properties connected to the chaotic behaviour were related, among them, the influence of the multipolarity of the nuclear barrier on the time required in order to notice the onset of the chaotic behaviour. Also, the connections between the Shannon entropy and chaos suggest the existence of a number of quasi-equilibrium states. (authors)

  5. Tuning quantum measurements to control chaos.

    Science.gov (United States)

    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.

  6. Is there chaos in the Spanish labour market?

    International Nuclear Information System (INIS)

    Olmedo, Elena

    2011-01-01

    Highlights: We consider Spanish unemployment time series. We apply a number of nonlinearity tests and chaoticity measures. We establish the presence of nonlinearity and chaos, which disappears when the data are shuffled. Abstract: One could argue that there is a resurgence of the non-linear modelling in economics. Some instruments have been developed to measure the complexity or instability of the analysed systems. At the present work some of these developed techniques are applied to verify the non-linearity present in the time series of Spanish unemployment, as well as to quantify the degree of complexity of the system that has generated the series. Using these techniques we find evidence of chaos in Spanish unemployment time series.

  7. Chaos M-ary modulation and demodulation method based on Hamilton oscillator and its application in communication.

    Science.gov (United States)

    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.

  8. Viewing Eye Movements During Reading through the Lens of Chaos Theory: How Reading Is Like the Weather

    Science.gov (United States)

    Paulson, Eric J.

    2005-01-01

    This theoretical article examines reading processes using chaos theory as an analogy. Three principles of chaos theory are identified and discussed, then related to reading processes as revealed through eye movement research. Used as an analogy, the chaos theory principle of sensitive dependence contributes to understanding the difficulty in…

  9. Stochastic resonance based on modulation instability in spatiotemporal chaos.

    Science.gov (United States)

    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.

  10. Applications of chaos and nonlinear dynamics in science and engineering

    CERN Document Server

    Rondoni, Lamberto; Mitra, Mala

    Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever the quantitative modeling and analysis of complex, nonlinear phenomena are required, chaos theory and its methods can play a key role.    This second volume concentrates on reviewing further relevant, contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. This encompasses, but is not limited to, topics such as the spread of epidemics; electronic circuits; chaos control in mechanical devices; secure communication; and digital watermarking. Featuring contributions from active and leading research groups, this collection is ideal both as a reference work and as a ‘recipe book’ full of tried and tested, successf...

  11. An Improved Chaos Genetic Algorithm for T-Shaped MIMO Radar Antenna Array Optimization

    Directory of Open Access Journals (Sweden)

    Xin Fu

    2014-01-01

    Full Text Available In view of the fact that the traditional genetic algorithm easily falls into local optimum in the late iterations, an improved chaos genetic algorithm employed chaos theory and genetic algorithm is presented to optimize the low side-lobe for T-shaped MIMO radar antenna array. The novel two-dimension Cat chaotic map has been put forward to produce its initial population, improving the diversity of individuals. The improved Tent map is presented for groups of individuals of a generation with chaos disturbance. Improved chaotic genetic algorithm optimization model is established. The algorithm presented in this paper not only improved the search precision, but also avoids effectively the problem of local convergence and prematurity. For MIMO radar, the improved chaos genetic algorithm proposed in this paper obtains lower side-lobe level through optimizing the exciting current amplitude. Simulation results show that the algorithm is feasible and effective. Its performance is superior to the traditional genetic algorithm.

  12. Revisitation of chaos in Bianchi IX Universe and in generalized scalar-tensor cosmologies

    International Nuclear Information System (INIS)

    Lehner, Thierry; Di Menza, Laurent

    2003-01-01

    We show that there is a threshold for the onset of chaos in cosmology for the Universe described as a dynamical system derived from the Einstein equations of general relativity (GR). In the case of the mixmaster model (homogeneous and anisotropic cosmology with a Bianchi IX metric) the chaos occurs precisely at the prescribed necessary value H vac =0 of the GR for the energy of the Universe while the system is found regular for H vac >0 and chaotic for H vac <0 with respect to its pure vacuum part. In the case of generalized scalar tensor theories within the Bianchi IX model we show using the ADM formalism and a conformal transformation that the energy of the dynamical system as compared to vacuum lies below the threshold thus the system is not exhibiting chaos and the conclusion still holds in the presence of ordinary matter as well. The suppression of chaos occurs in a similar way for stiff matter alone

  13. Dermoscopic 'Chaos and Clues' in the diagnosis of melanoma in situ.

    Science.gov (United States)

    Ramji, Rajan; Valdes-Gonzalez, Guillermo; Oakley, Amanda; Rademaker, Marius

    2017-11-02

    To describe the dermoscopic features of melanoma in situ using the Chaos and Clues method. Histologically proven primary melanoma in situ (MIS) diagnosed through a specialist teledermoscopy clinic were reviewed by three dermatologists. By consensus they agreed on the global dermoscopic pattern, colours, presence of chaos (asymmetry of colour and structure and more than one pattern), and each of the nine clues described for malignancy. One hundred MIS in 92 patients of European ethnicity (45 males) were assessed. Mean age was 67.3 years (range 20-95). The mean dimensions of the lesions were 11.1 × 12.0 mm (range 2.5-31.3 × 2.3-32.3 mm). Using pattern analysis, 82% of the lesions had three or more patterns (multicomponent) and the rest had 2 patterns. Colours included light brown (100%), dark brown (98%) and grey (75%). All MIS demonstrated chaos. The most prevalent clues were thick lines (88%), eccentric structureless areas (88%), and grey or blue structures (75%). Dermoscopy can be very helpful in the early diagnosis of melanoma and MIS. The Chaos and Clues method is simple to use. Its unambiguous descriptors can be successfully used to describe MIS. The presence of chaos and clues to malignancy (including thick lines, eccentric structureless areas, and blue/grey structures) should raise a red flag and lead to referral or excision. © 2017 The Australasian College of Dermatologists.

  14. 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...

  15. Weak and strong chaos in Fermi-Pasta-Ulam models and beyond

    Science.gov (United States)

    Pettini, Marco; Casetti, Lapo; Cerruti-Sola, Monica; Franzosi, Roberto; Cohen, E. G. D.

    2005-03-01

    We briefly review some of the most relevant results that our group obtained in the past, while investigating the dynamics of the Fermi-Pasta-Ulam (FPU) models. The first result is the numerical evidence of the existence of two different kinds of transitions in the dynamics of the FPU models: (i) A stochasticity threshold (ST), characterized by a value of the energy per degree of freedom below which the overwhelming majority of the phase space trajectories are regular (vanishing Lyapunov exponents). It tends to vanish as the number N of degrees of freedom is increased. (ii) A strong stochasticity threshold (SST), characterized by a value of the energy per degree of freedom at which a crossover appears between two different power laws of the energy dependence of the largest Lyapunov exponent, which phenomenologically corresponds to the transition between weak and strong chaotic regimes. It is stable with N. The second result is the development of a Riemannian geometric theory to explain the origin of Hamiltonian chaos. Starting this theory has been motivated by the inadequacy of the approach based on homoclinic intersections to explain the origin of chaos in systems of arbitrarily large N, or arbitrarily far from quasi-integrability, or displaying a transition between weak and strong chaos. Finally, the third result stems from the search for the transition between weak and strong chaos in systems other than FPU. Actually, we found that a very sharp SST appears as the dynamical counterpart of a thermodynamic phase transition, which in turn has led, in the light of the Riemannian theory of chaos, to the development of a topological theory of phase transitions.

  16. Information processing in echo state networks at the edge of chaos.

    Science.gov (United States)

    Boedecker, Joschka; Obst, Oliver; Lizier, Joseph T; Mayer, N Michael; Asada, Minoru

    2012-09-01

    We investigate information processing in randomly connected recurrent neural networks. It has been shown previously that the computational capabilities of these networks are maximized when the recurrent layer is close to the border between a stable and an unstable dynamics regime, the so called edge of chaos. The reasons, however, for this maximized performance are not completely understood. We adopt an information-theoretical framework and are for the first time able to quantify the computational capabilities between elements of these networks directly as they undergo the phase transition to chaos. Specifically, we present evidence that both information transfer and storage in the recurrent layer are maximized close to this phase transition, providing an explanation for why guiding the recurrent layer toward the edge of chaos is computationally useful. As a consequence, our study suggests self-organized ways of improving performance in recurrent neural networks, driven by input data. Moreover, the networks we study share important features with biological systems such as feedback connections and online computation on input streams. A key example is the cerebral cortex, which was shown to also operate close to the edge of chaos. Consequently, the behavior of model systems as studied here is likely to shed light on reasons why biological systems are tuned into this specific regime.

  17. Chaos control in the cerium-catalyzed Belousov–Zhabotinsky reaction using recurrence quantification analysis measures

    International Nuclear Information System (INIS)

    Fatoorehchi, Hooman; Zarghami, Reza; Abolghasemi, Hossein; Rach, Randolph

    2015-01-01

    Highlights: •Theoretical and experimental chaos control for the Belousov–Zhabotinsky-CSTR system. •Application of recurrence analysis quantification for chaos control by feedback loops. •Optimization of determinism and recurrence rate as RQA-based measures. •Accurate solution of the Montanator model by the multi-stage Adomian decomposition method. -- Abstract: Chaos control in the Belousov–Zhabotinsky-CSTR system was investigated theoretically and experimentally by reconstructing the phase space of the cerium (IV) ions concentration time series and then optimizing recurrence quantification analysis measures. The devised feedback loop acting on the reactor inlet flow rate was able to experimentally suppress chaos and drive the system to an almost predictable state with approximately 93% determinism. Similar theoretical results have also been demonstrated in numerical simulations using the four-variable Montanator model as solved by the multistage Adomian decomposition method

  18. Chaos and The Changing Nature of Science and Medicine. Proceedings

    International Nuclear Information System (INIS)

    Herbert, D.E.; Croft, P.; Silver, D.S.; Williams, S.G.; Woodall, M.

    1996-01-01

    These proceedings represent the lectures given at the workshop on chaos and the changing nature of science and medicine. The workshop was sponsored by the University of South Alabama and the American Association of Physicists in Medicine. The topics discussed covered nonlinear dynamical systems, complexity theory, fractals, chaos in biology and medicine and in fluid dynamics. Applications of chaotic dynamics in climatology were also discussed. There were 8 lectures at the workshop and all 8 have been abstracted for the Energy Science and Technology database

  19. 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

  20. 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.

  1. Chaos-based wireless communication resisting multipath effects

    Science.gov (United States)

    Yao, Jun-Liang; Li, Chen; Ren, Hai-Peng; Grebogi, Celso

    2017-09-01

    In additive white Gaussian noise channel, chaos has been shown to be the optimal coherent communication waveform in the sense of using a very simple matched filter to maximize the signal-to-noise ratio. Recently, Lyapunov exponent spectrum of the chaotic signals after being transmitted through a wireless channel has been shown to be unaltered, paving the way for wireless communication using chaos. In wireless communication systems, inter-symbol interference caused by multipath propagation is one of the main obstacles to achieve high bit transmission rate and low bit-error rate (BER). How to resist the multipath effect is a fundamental problem in a chaos-based wireless communication system (CWCS). In this paper, a CWCS is built to transmit chaotic signals generated by a hybrid dynamical system and then to filter the received signals by using the corresponding matched filter to decrease the noise effect and to detect the binary information. We find that the multipath effect can be effectively resisted by regrouping the return map of the received signal and by setting the corresponding threshold based on the available information. We show that the optimal threshold is a function of the channel parameters and of the information symbols. Practically, the channel parameters are time-variant, and the future information symbols are unavailable. In this case, a suboptimal threshold is proposed, and the BER using the suboptimal threshold is derived analytically. Simulation results show that the CWCS achieves a remarkable competitive performance even under inaccurate channel parameters.

  2. CHAOS-2-a geomagnetic field model derived from one decade of continuous satellite data

    DEFF Research Database (Denmark)

    Olsen, Nils; Mandea, M.; Sabaka, T.J.

    2009-01-01

    We have derived a model of the near-Earth's magnetic field using more than 10 yr of high-precision geomagnetic measurements from the three satellites Orsted, CHAMP and SAC-C. This model is an update of the two previous models, CHAOS (Olsen et al. 2006) and xCHAOS (Olsen & Mandea 2008). Data...... by minimizing the second time derivative of the squared magnetic field intensity at the core-mantle boundary. The CHAOS-2 model describes rapid time changes, as monitored by the ground magnetic observatories, much better than its predecessors....

  3. Invoking the muse: Dada's chaos.

    Science.gov (United States)

    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.

  4. 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

  5. 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

  6. Hybrid electronic/optical synchronized chaos communication system.

    Science.gov (United States)

    Toomey, J P; Kane, D M; Davidović, A; Huntington, E H

    2009-04-27

    A hybrid electronic/optical system for synchronizing a chaotic receiver to a chaotic transmitter has been demonstrated. The chaotic signal is generated electronically and injected, in addition to a constant bias current, to a semiconductor laser to produce an optical carrier for transmission. The optical chaotic carrier is photodetected to regenerate an electronic signal for synchronization in a matched electronic receiver The system has been successfully used for the transmission and recovery of a chaos masked message that is added to the chaotic optical carrier. Past demonstrations of synchronized chaos based, secure communication systems have used either an electronic chaotic carrier or an optical chaotic carrier (such as the chaotic output of various nonlinear laser systems). This is the first electronic/optical hybrid system to be demonstrated. We call this generation of a chaotic optical carrier by electronic injection.

  7. 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.

  8. Bifurcations and chaos of classical trajectories in a deformed nuclear potential

    International Nuclear Information System (INIS)

    Carbonell, J.; Arvieu, R.

    1983-01-01

    The organization of the phase space of a classical nucleon in an axially symmetric deformed potential with the restriction Lsub(z)=0 is studied by drawing the Poincare surfaces of section. In the limit of small deformations three simple limits help to understand this organization. Moreover important bifurcations of periodic trajectories occur. At higher deformations multifurcations and chaos are observed. Chaos is developed to a larger extent in the heavier nuclei. (author)

  9. Order in large and chaos in small components of nuclear wave functions

    International Nuclear Information System (INIS)

    Soloviev, V.G.

    1992-06-01

    An investigation of the order and chaos of the nuclear excited states has shown that there is order in the large and chaos in the small quasiparticle or phonon components of the nuclear wave functions. The order-to-chaos transition is treated as a transition from the large to the small components of the nuclear wave function. The analysis has shown that relatively large many-quasiparticle components of the wave function at an excitation energy (4-8)MeV may exist. The large many-quasiparticle components of the wave functions of the neutron resonances are responsible for enhanced E1-, M1- and E2-transition probabilities from neutron resonance to levels lying (1-2)MeV below them. (author)

  10. Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science.

    Science.gov (United States)

    Ecke, Robert E

    2015-09-01

    The paradigms of nonlinear science were succinctly articulated over 25 years ago as deterministic chaos, pattern formation, coherent structures, and adaptation/evolution/learning. For chaos, the main unifying concept was universal routes to chaos in general nonlinear dynamical systems, built upon a framework of bifurcation theory. Pattern formation focused on spatially extended nonlinear systems, taking advantage of symmetry properties to develop highly quantitative amplitude equations of the Ginzburg-Landau type to describe early nonlinear phenomena in the vicinity of critical points. Solitons, mathematically precise localized nonlinear wave states, were generalized to a larger and less precise class of coherent structures such as, for example, concentrated regions of vorticity from laboratory wake flows to the Jovian Great Red Spot. The combination of these three ideas was hoped to provide the tools and concepts for the understanding and characterization of the strongly nonlinear problem of fluid turbulence. Although this early promise has been largely unfulfilled, steady progress has been made using the approaches of nonlinear science. I provide a series of examples of bifurcations and chaos, of one-dimensional and two-dimensional pattern formation, and of turbulence to illustrate both the progress and limitations of the nonlinear science approach. As experimental and computational methods continue to improve, the promise of nonlinear science to elucidate fluid turbulence continues to advance in a steady manner, indicative of the grand challenge nature of strongly nonlinear multi-scale dynamical systems.

  11. Breaking a chaos-based secure communication scheme designed by an improved modulation method

    Energy Technology Data Exchange (ETDEWEB)

    Li Shujun [Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong (China)]. E-mail: hooklee@mail.com; Alvarez, Gonzalo [Instituto de Fisica Aplicada, Consejo Superior de Investigaciones Cientificas, Serrano 144-28006 Madrid (Spain); Chen Guanrong [Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong (China)

    2005-07-01

    Recently Bu and Wang [Bu S, Wang B-H. Chaos, Solitons and Fractals 2004;19(4):919-24] proposed a simple modulation method aiming to improve the security of chaos-based secure communications against return-map-based attacks. Soon this modulation method was independently cryptanalyzed by Chee et al. [Chee CY, Xu D, Bishop SR. Chaos, Solitons and Fractals 2004;21(5):1129-34], Wu et al. [Wu X, Hu H, Zhang B. Chaos, Solitons and Fractals 2004;22(2):367-73], and Alvarez et al. [Alvarez G, Montoya F, Romera M, Pastor G. Chaos, Solitons and Fractals, in press, arXiv:nlin/0406065] via different attacks. As an enhancement to the Bu-Wang method, an improving scheme was suggested by Wu et al. by removing the relationship between the modulating function and the zero-points. The present paper points out that the improved scheme proposed by Wu et al. is still insecure against a new attack. Compared with the existing attacks, the proposed attack is more powerful and can also break the original Bu-Wang scheme. Furthermore, it is pointed out that the security of the modulation-based schemes proposed by Wu et al. is not so satisfactory from a pure cryptographical point of view. The synchronization performance of this class of modulation-based schemes is also discussed.

  12. Breaking a chaos-based secure communication scheme designed by an improved modulation method

    International Nuclear Information System (INIS)

    Li Shujun; Alvarez, Gonzalo; Chen Guanrong

    2005-01-01

    Recently Bu and Wang [Bu S, Wang B-H. Chaos, Solitons and Fractals 2004;19(4):919-24] proposed a simple modulation method aiming to improve the security of chaos-based secure communications against return-map-based attacks. Soon this modulation method was independently cryptanalyzed by Chee et al. [Chee CY, Xu D, Bishop SR. Chaos, Solitons and Fractals 2004;21(5):1129-34], Wu et al. [Wu X, Hu H, Zhang B. Chaos, Solitons and Fractals 2004;22(2):367-73], and Alvarez et al. [Alvarez G, Montoya F, Romera M, Pastor G. Chaos, Solitons and Fractals, in press, arXiv:nlin/0406065] via different attacks. As an enhancement to the Bu-Wang method, an improving scheme was suggested by Wu et al. by removing the relationship between the modulating function and the zero-points. The present paper points out that the improved scheme proposed by Wu et al. is still insecure against a new attack. Compared with the existing attacks, the proposed attack is more powerful and can also break the original Bu-Wang scheme. Furthermore, it is pointed out that the security of the modulation-based schemes proposed by Wu et al. is not so satisfactory from a pure cryptographical point of view. The synchronization performance of this class of modulation-based schemes is also discussed

  13. Chaos in a complex plasma

    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

  14. Effect of correction of aberration dynamics on chaos in human ocular accommodation.

    Science.gov (United States)

    Hampson, Karen M; Cufflin, Matthew P; Mallen, Edward A H

    2013-11-15

    We used adaptive optics to determine the effect of monochromatic aberration dynamics on the level of chaos in the accommodation control system. Four participants viewed a stationary target while the dynamics of their aberrations were either left uncorrected, defocus was corrected, or all aberrations except defocus were corrected. Chaos theory analysis was used to discern changes in the accommodative microfluctuations. We found a statistically significant reduction in the chaotic nature of the accommodation microfluctuations during correction of defocus, but not when all aberrations except defocus were corrected. The Lyapunov exponent decreased from 0.71 ± 0.07 D/s (baseline) to 0.55 ± 0.03 D/s (correction of defocus fluctuations). As the reduction of chaos in physiological signals is indicative of stress to the system, the results indicate that for the participants included in this study, fluctuations in defocus have a more profound effect than those of the other aberrations. There were no changes in the power spectrum between experimental conditions. Hence chaos theory analysis is a more subtle marker of changes in the accommodation control system and will be of value in the study of myopia onset and progression.

  15. Chaos resulting from nonlinear relations between different variables

    International Nuclear Information System (INIS)

    Dohtani, Akitaka

    2011-01-01

    Research highlights: → We prove a general result on the existence of chaos. → We focus on the cyclic composites of interdependent relations between different variables. → By considering several examples, we conclude that the cyclic composites play an important role in detecting chaotic dynamics. - Abstract: In this study, we further develop the perturbation method of Marotto and investigate the general mechanisms responsible for nonlinear dynamics, which are typical of multidimensional systems. We focus on the composites of interdependent relations between different variables. First, we prove a general result on chaos, which shows that the cyclic composites of nonlinear interdependent relations are sources of chaotic dynamics in multidimensional systems. By considering several examples, we conclude that the cyclic composites play an important role in detecting chaotic dynamics.

  16. Dynamical control of chaos by slave-master feedback

    International Nuclear Information System (INIS)

    Behnia, S.; Akhshani, A.

    2009-01-01

    Techniques for stabilizing unstable state in nonlinear dynamical systems using small perturbations fall into three general categories: feedback, non-feedback schemes, and a combination of feedback and non-feedback. However, the general problem of finding conditions for creation or suppression of chaos still remains open. We describe a method for dynamical control of chaos. This method is based on a definition of the hierarchy of solvable chaotic maps with dynamical parameter as a control parameter. In order to study the new mechanism of control of chaotic process, Kolmogorov-Sinai entropy of the chaotic map with dynamical parameter based on discussion the properties of invariant measure have been calculated and confirmed by calculation of Lyapunov exponents. The introduced chaotic maps can be used as dynamical control.

  17. In the Wake of Chaos Unpredictable Order in Dynamical Systems

    CERN Document Server

    Kellert, Stephen H

    1993-01-01

    Chaos theory has captured scientific and popular attention. What began as the discovery of randomness in simple physical systems has become a widespread fascination with "chaotic" models of everything from business cycles to brainwaves to heart attacks. But what exactly does this explosion of new research into chaotic phenomena mean for our understanding of the world? In this timely book, Stephen Kellert takes the first sustained look at the broad intellectual and philosophical questions raised by recent advances in chaos theory—its implications for science as a source of knowledge a

  18. Analysis and improvement of a chaos-based image encryption algorithm

    International Nuclear Information System (INIS)

    Xiao Di; Liao Xiaofeng; Wei Pengcheng

    2009-01-01

    The security of digital image attracts much attention recently. In Guan et al. [Guan Z, Huang F, Guan W. Chaos-based image encryption algorithm. Phys Lett A 2005; 346: 153-7.], a chaos-based image encryption algorithm has been proposed. In this paper, the cause of potential flaws in the original algorithm is analyzed in detail, and then the corresponding enhancement measures are proposed. Both theoretical analysis and computer simulation indicate that the improved algorithm can overcome these flaws and maintain all the merits of the original one.

  19. Investigation of Chinese archaic jade by PIXE and μRaman spectrometry

    International Nuclear Information System (INIS)

    Chen, T.H.; Calligaro, T.; Pages-Camagna, S.; Menu, M.

    2004-01-01

    External-beam particle-induced X-ray emission (PIXE) and μRaman spectrometry were used for elemental and structural studies of Chinese archaic nephrite jades of the Guimet Asian Museum in Paris in a non-destructive way. Nephrite is a variety of tremolite-actinolite of the amphibole group, with variable iron and magnesium contents. In the present work, in addition to identification of materials, the cation distribution in nephrite was investigated. Cation order-disorder is related to thermodynamic properties of minerals, and hence associated with geological conditions of the mineral formation. Besides, it plays an important role in the mechanism of coloration. So far, little work has been done on the cation distribution in nephrite. We thus initiated this research expecting to answer open questions concerning art and archaeological issues such as jade provenance and colour. The OH stretching vibration band of nephrite, depending on the electronegativity of the bonded cations, presents a fine structure. The study of this fine structure, together with the total cation content obtained by PIXE, allows estimation of the cation distribution in nephrite. In this study, six jade artefacts, dated from the Neolithic period to the Han dynasty (about 3000 BC to 220 AD), with diverse colours including white, yellow-green, green, dark green and black, were analysed. The data obtained permits establishing a geological database for determination of nephrite provenance and explaining the correlation between colour and cation distribution. (orig.)

  20. 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