Intrinsically localized chaos in discrete nonlinear extended systems
Martínez, P J; Falo, F; Mazo, J J
1999-01-01
The phenomenon of intrinsic localization in discrete nonlinear extended systems, i.e. the (generic) existence of discrete breathers, is shown to be not restricted to periodic solutions but it also extends to more complex (chaotic) dynamical behaviour. We illustrate this with two different forced and damped systems exhibiting this type of solutions: In an anisotropic Josephson junction ladder, we obtain intrinsically localized chaotic solutions by following periodic rotobreather solutions through a cascade of period-doubling bifurcations. In an array of forced and damped van der Pol oscillators, they are obtained by numerical continuation (path-following) methods from the uncoupled limit, where its existence is trivially ascertained, following the ideas of the anticontinuum limit.
Energy Technology Data Exchange (ETDEWEB)
Zhou, T G; Yan, S L; Fang, L; He, M; Zhao, X J [Department of Electronics, Nankai University, Tianjin 300071 (China)], E-mail: zhoutg@nankai.edu.cn
2009-05-15
The dynamics of capacitively coupled intrinsic Josephson junction arrays with a McCumber parameter {beta}{sub c}<1 driven by a dc current are investigated by using numerical simulations. For the first time, spatiotemporal chaotic behaviors are found. Analysis of the dynamics of individual junctions shows that the chaos is caused by the strong diffusive coupling between the junctions in the array. The chaotic regions of different parameters are also presented, from which the conditions for chaos are deduced. The properties of the array shunted by an LCR series resonance circuit are also investigated. The results show that the spatiotemporal chaos can be effectively controlled by the shunted LCR circuit. This presents a new spatiotemporal chaos control method.
2012-01-01
In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in the system through application of the Thurston-Nielsen classification theorem (TNCT). We expand upon earlier work that introduced the application of the TNCT to braiding of almost-cyclic sets, which are individual components of almost-invariant sets [Stremler et al., "Topological chaos and periodic braiding of almost-cyclic sets," Phys. Rev. Lett. 106, 114101 (2011)]. In this co...
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...
Physical white chaos generation
Wang, Anbang; Wang, Bingjie; Li, Lei; Zhang, Mingjiang; Zhang, Wendong
2014-01-01
Physical chaos is a fascinating prospect for high-speed data security by serving as a masking carrier or a key source, but suffers from a colored spectrum that divulges system's intrinsic oscillations and degrades randomness. Here, we demonstrate that physical chaos with a white spectrum can be achieved by the optical heterodyning of two delayed-feedback lasers. A white chaotic spectrum with 1-dB fluctuation in a band of 11 GHz is experimentally obtained. The white chaos also has a perfect delta-like autocorrelation function and a high dimensionality of greater than 10, which makes chaos reconstruction extremely difficult and thus improves security.
Authenticity and autochthonous traditions in archaic and Hellenistic poetry
Klooster, Julia
2016-01-01
J.J.H. Klooster, ‘Authenticity and autochthonous traditions in archaic and Hellenistic poetry’. In E. Bakker (ed): Authorship, Authority and Authenticity in Archaic and Classical Greek Song. Proceedings of the Network for the Study of Archaic and Classical Greek Song, Vol. 2, Leiden: Brill
Archaic introjects and the cosmology of H.G. Wells.
Parkin, A
1982-01-01
The roles of the archaic loving and hating introjects are traced in the early scientific romances and the life work of H.G. Wells. The preambivalent polarization of the early loving introjects of an archaic ego ideal (giving rise to utopian fantasies and, later, to promulgations of a new world state) and the early hostile introjects of an archaic superego (giving rise to fears of death and, later, to fears of cosmic dissolution) is represented in eschatological preoccupations with death, the Last Judgment, heaven and hell. These religious preoccupations are derivatives of wishes for maternal union and bliss on the one hand, and of castration anxiety and fears of personal annihilation on the other. Further transformations of the archaic introjects are traced through an indentification with the role of redeemer, and later, through his scientific studies, to an espousal of T.H. Huxley's teachings of organic evolution and to the development of cosmological themes in his work.
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.
Zhang, Rui; Cavalcante, Hugo L. D. de S.; Gao, Zheng; Gauthier, Daniel J.; Socolar, Joshua E. S.; Adams, Matthew M.; Lathrop, Daniel P.
2009-01-01
We observe deterministic chaos in a simple network of electronic logic gates that are not regulated by a clocking signal. The resulting power spectrum is ultra-wide-band, extending from dc to beyond 2 GHz. The observed behavior is reproduced qualitatively using an autonomously updating Boolean model with signal propagation times that depend on the recent history of the gates and filtering of pulses of short duration, whose presence is confirmed experimentally. Electronic Boolean chaos may fin...
Wireless communication with chaos.
Ren, Hai-Peng; Baptista, Murilo S; Grebogi, Celso
2013-05-03
The modern world fully relies on wireless communication. Because of intrinsic physical constraints of the wireless physical media (multipath, damping, and filtering), signals carrying information are strongly modified, preventing information from being transmitted with a high bit rate. We show that, though a chaotic signal is strongly modified by the wireless physical media, its Lyapunov exponents remain unaltered, suggesting that the information transmitted is not modified by the channel. For some particular chaotic signals, we have indeed proved that the dynamic description of both the transmitted and the received signals is identical and shown that the capacity of the chaos-based wireless channel is unaffected by the multipath propagation of the physical media. These physical properties of chaotic signals warrant an effective chaos-based wireless communication system.
Analysis of Human Accelerated DNA Regions Using Archaic Hominin Genomes
Burbano, Hernán A.; Green, Richard E.; Maricic, Tomislav; Lalueza-Fox, Carles; de la Rasilla, Marco; Rosas, Antonio; Kelso, Janet; Pollard, Katherine S.; Lachmann, Michael; Pääbo, Svante
2012-01-01
Several previous comparisons of the human genome with other primate and vertebrate genomes identified genomic regions that are highly conserved in vertebrate evolution but fast-evolving on the human lineage. These human accelerated regions (HARs) may be regions of past adaptive evolution in humans. Alternatively, they may be the result of non-adaptive processes, such as biased gene conversion. We captured and sequenced DNA from a collection of previously published HARs using DNA from an Iberian Neandertal. Combining these new data with shotgun sequence from the Neandertal and Denisova draft genomes, we determine at least one archaic hominin allele for 84% of all positions within HARs. We find that 8% of HAR substitutions are not observed in the archaic hominins and are thus recent in the sense that the derived allele had not come to fixation in the common ancestor of modern humans and archaic hominins. Further, we find that recent substitutions in HARs tend to have come to fixation faster than substitutions elsewhere in the genome and that substitutions in HARs tend to cluster in time, consistent with an episodic rather than a clock-like process underlying HAR evolution. Our catalog of sequence changes in HARs will help prioritize them for functional studies of genomic elements potentially responsible for modern human adaptations. PMID:22412940
Banerjee, S; Grebogi, C; Banerjee, Soumitro; Yorke, James A.; Grebogi, Celso
1998-01-01
It has been proposed to make practical use of chaos in communication, in enhancing mixing in chemical processes and in spreading the spectrum of switch-mode power suppies to avoid electromagnetic interference. It is however known that for most smooth chaotic systems, there is a dense set of periodic windows for any range of parameter values. Therefore in practical systems working in chaotic mode, slight inadvertent fluctuation of a parameter may take the system out of chaos. We say a chaotic attractor is robust if, for its parameter values there exists a neighborhood in the parameter space with no periodic attractor and the chaotic attractor is unique in that neighborhood. In this paper we show that robust chaos can occur in piecewise smooth systems and obtain the conditions of its occurrence. We illustrate this phenomenon with a practical example from electrical engineering.
Some archaic traits in social life of Brskuceans: Ethnographical notes
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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
Waelbroeck, H
1999-01-01
We propose a theory of deterministic chaos for discrete systems, based on their representations in symbolic history spaces Ømega. These are spaces of semi-infinite sequences, as the one-sided shift spaces, but endowed with a more general topology which we call a semicausal topology. We show that define metrical properties, including the correlation dimension of the attractor. Examples are considered: Asymmetric neural networks and random cellular automata are not chaotic. A neural network model with memory, on the other hand, does appear to be an example of discrete chaos.
Stochastic Chaos with Its Control and Synchronization
Institute of Scientific and Technical Information of China (English)
Zhang Ying; Xu Wei; Zhang Tianshu; Yang Xiaoli; Wu Cunli; Fang Tong
2008-01-01
The discovery of chaos in the sixties of last century was a breakthrough in concept,revealing the truth that some disorder behavior, called chaos, could happen even in a deterministic nonlinear system under barely deterministic disturbance. After a series of serious studies, people begin to acknowledge that chaos is a specific type of steady state motion other than the conventional periodic and quasi-periodic ones, featuring a sensitive dependence on initial conditions, resulting from the intrinsic randomness of a nonlinear system itself. In fact, chaos is a collective phenomenon consisting of massive individual chaotic responses, corresponding to different initial conditions in phase space. Any two adjacent individual chaotic responses repel each other, thus causing not only the sensitive dependence on initial conditions but also the existence of at least one positive top Lyapunov exponent (TLE) for chaos. Meanwhile, all the sample responses share one common invariant set on the Poincaré map, called chaotic attractor,which every sample response visits from time to time ergodically. So far, the existence of at least one positive TLE is a commonly acknowledged remarkable feature of chaos. We know that there are various forms of uncertainties in the real world. In theoretical studies, people often use stochastic models to describe these uncertainties, such as random variables or random processes.Systems with random variables as their parameters or with random processes as their excitations are often called stochastic systems. No doubt, chaotic phenomena also exist in stochastic systems, which we call stochastic chaos to distinguish it from deterministic chaos in the deterministic system. Stochastic chaos reflects not only the intrinsic randomness of the nonlinear system but also the external random effects of the random parameter or the random excitation.Hence, stochastic chaos is also a collective massive phenomenon, corresponding not only to different initial
Relation of Origins of Primitive Chaos
Ogasawara, Yoshihito
2014-01-01
A new concept, primitive chaos, was proposed, as a concept closely related to the fundamental problems of sciences themselves such as determinism, causality, free will, predictability, and time asymmetry [{\\em J. Phys. Soc. Jpn.} {\\bf 2014}, {\\em 83}, 1401]. This concept is literally a primitive chaos in such a sense that it leads to the characteristic properties of the conventional chaos under natural conditions. Then, two contrast concepts, nondegenerate Peano continuum and Cantor set, are known as the origins of the primitive chaos. In this study, the relation of these origins is investigated with the aid of a mathematical method, topology. Then, we can see the emergence of interesting concepts such as the relation of whole and part, and coarse graining, which imply the essence of our intrinsic recognition for phenomena.
Some chaotic features of intrinsically coupled Josephson junctions
Energy Technology Data Exchange (ETDEWEB)
Kolahchi, M.R., E-mail: kolahchi@iasbs.ac.ir [Institute for Advanced Studies in Basic Sciences, Zanjan 45195-1159 (Iran, Islamic Republic of); Shukrinov, Yu.M. [BLTP, JINR, Dubna, Moscow Region 141980 (Russian Federation); Max-Planck-Institute for the Physics of Complex Systems, 01187 Dresden (Germany); Hamdipour, M. [Institute for Advanced Studies in Basic Sciences, Zanjan 45195-1159 (Iran, Islamic Republic of); BLTP, JINR, Dubna, Moscow Region 141980 (Russian Federation); Botha, A.E. [Department of Physics, University of South Africa, P.O. Box 392, Pretoria 0003 (South Africa); Suzuki, M. [Photonics and Electronics Science and Engineering Center and Department of Electronic Science and Engineering, Kyoto University, Kyoto 615-8510 (Japan)
2013-08-15
Highlights: ► Intrinsically coupled Josephson junctions model a high-T{sub 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{sub c} resonators which require coherence amongst the junctions.
Chaos Control in Mechanical Systems
Directory of Open Access Journals (Sweden)
Marcelo A. Savi
2006-01-01
Full Text Available Chaos has an intrinsically richness related to its structure and, because of that, there are benefits for a natural system of adopting chaotic regimes with their wide range of potential behaviors. Under this condition, the system may quickly react to some new situation, changing conditions and their response. Therefore, chaos and many regulatory mechanisms control the dynamics of living systems, conferring a great flexibility to the system. Inspired by nature, the idea that chaotic behavior may be controlled by small perturbations of some physical parameter is making this kind of behavior to be desirable in different applications. Mechanical systems constitute a class of system where it is possible to exploit these ideas. Chaos control usually involves two steps. In the first, unstable periodic orbits (UPOs that are embedded in the chaotic set are identified. After that, a control technique is employed in order to stabilize a desirable orbit. This contribution employs the close-return method to identify UPOs and a semi-continuous control method, which is built up on the OGY method, to stabilize some desirable UPO. As an application to a mechanical system, a nonlinear pendulum is considered and, based on parameters obtained from an experimental setup, analyses are carried out. Signals are generated by numerical integration of the mathematical model and two different situations are treated. Firstly, it is assumed that all state variables are available. After that, the analysis is done from scalar time series and therefore, it is important to evaluate the effect of state space reconstruction. Delay coordinates method and extended state observers are employed with this aim. Results show situations where these techniques may be used to control chaos in mechanical systems.
Manifestation of resonance-related chaos in coupled Josephson junctions
Energy Technology Data Exchange (ETDEWEB)
Shukrinov, Yu.M. [BLTP, JINR, Dubna, Moscow Region, 141980 (Russian Federation); Hamdipour, M. [BLTP, JINR, Dubna, Moscow Region, 141980 (Russian Federation); Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-1159, Zanjan (Iran, Islamic Republic of); Kolahchi, M.R. [Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-1159, Zanjan (Iran, Islamic Republic of); Botha, A.E., E-mail: bothaae@unisa.ac.za [Department of Physics, University of South Africa, P.O. Box 392, Pretoria 0003 (South Africa); Suzuki, M. [Photonics and Electronics Science and Engineering Center and Department of Electronic Science and Engineering, Kyoto University, Kyoto 615-8510 (Japan)
2012-11-01
Manifestation of chaos in the temporal dependence of the electric charge is demonstrated through the calculation of the maximal Lyapunov exponent, phase–charge and charge–charge Lissajous diagrams and correlation functions. It is found that the number of junctions in the stack strongly influences the fine structure in the current–voltage characteristics and a strong proximity effect results from the nonperiodic boundary conditions. The observed resonance-related chaos exhibits intermittency. The criteria for a breakpoint region with no chaos are obtained. Such criteria could clarify recent experimental observations of variations in the power output from intrinsic Josephson junctions in high temperature superconductors.
Manifestation of resonance-related chaos in coupled Josephson junctions
Shukrinov, Yu. M.; Hamdipour, M.; Kolahchi, M. R.; Botha, A. E.; Suzuki, M.
2012-11-01
Manifestation of chaos in the temporal dependence of the electric charge is demonstrated through the calculation of the maximal Lyapunov exponent, phase-charge and charge-charge Lissajous diagrams and correlation functions. It is found that the number of junctions in the stack strongly influences the fine structure in the current-voltage characteristics and a strong proximity effect results from the nonperiodic boundary conditions. The observed resonance-related chaos exhibits intermittency. The criteria for a breakpoint region with no chaos are obtained. Such criteria could clarify recent experimental observations of variations in the power output from intrinsic Josephson junctions in high temperature superconductors.
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.
Quantum Chaos and Statistical Mechanics
Srednicki, Mark
1994-01-01
We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics.
Cosmology, Epistemology and Chaos
Unno, Wasaburo
1992-03-01
We may consider the following three fundamental epistemological questions concerning cosmology. Can cosmology at last understand the origin of the universe? Can computers at last create? Can life be formed at last synthetically? These questions are in some sense related to the liar paradox containing the self-reference and, therefore, may not be answered by recursive processes in finite time. There are, however, various implications such that the chaos may break the trap of the self- reference paradox. In other words, Goedel's incompleteness theorem would not apply to chaos, even if the chaos can be generated by recursive processes. Internal relations among cosmology, epistemology and chaos must be investigated in greater detail
Spano, Mark
1997-04-01
The publication by Ott, Grebogi and Yorke(E. Ott, C. Grebogi and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).) of their theory of chaos control in 1990 led to an explosion of experimental work applying their theory to mechanical systems and electronic circuits, lasers and chemical reactors, and heart and brain tissue, to name only a few. In this talk the basics of chaos control as implemented in a simple mechanical system will be described, as well as extensions of the method to biological applications. Finally, current advances in the field, including the maintenance of chaos and the control of high dimensional chaos, will be discussed.
Harnessing quantum transport by transient chaos.
Yang, Rui; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso; Pecora, Louis M
2013-03-01
Chaos has long been recognized to be generally advantageous from the perspective of control. In particular, the infinite number of unstable periodic orbits embedded in a chaotic set and the intrinsically sensitive dependence on initial conditions imply that a chaotic system can be controlled to a desirable state by using small perturbations. Investigation of chaos control, however, was largely limited to nonlinear dynamical systems in the classical realm. In this paper, we show that chaos may be used to modulate or harness quantum mechanical systems. To be concrete, we focus on quantum transport through nanostructures, a problem of considerable interest in nanoscience, where a key feature is conductance fluctuations. We articulate and demonstrate that chaos, more specifically transient chaos, can be effective in modulating the conductance-fluctuation patterns. Experimentally, this can be achieved by applying an external gate voltage in a device of suitable geometry to generate classically inaccessible potential barriers. Adjusting the gate voltage allows the characteristics of the dynamical invariant set responsible for transient chaos to be varied in a desirable manner which, in turn, can induce continuous changes in the statistical characteristics of the quantum conductance-fluctuation pattern. To understand the physical mechanism of our scheme, we develop a theory based on analyzing the spectrum of the generalized non-Hermitian Hamiltonian that includes the effect of leads, or electronic waveguides, as self-energy terms. As the escape rate of the underlying non-attracting chaotic set is increased, the imaginary part of the complex eigenenergy becomes increasingly large so that pointer states are more difficult to form, making smoother the conductance-fluctuation pattern.
Chaos applications in telecommunications
Stavroulakis, Peter
2005-01-01
IntroductionPeter StavroulakisChaotic Signal Generation and Transmission Antonio Cândido Faleiros,Waldecir João Perrella,TâniaNunes Rabello,Adalberto Sampaio Santos, andNeiYoshihiro SomaChaotic Transceiver Design Arthur Fleming-DahlChaos-Based Modulation and DemodulationTechniques Francis C.M. Lau and Chi K. TseA Chaos Approach to Asynchronous DS-CDMASystems S. Callegari, G. Mazzini, R. Rovatti, and G. SettiChannel Equalization in Chaotic CommunicationSystems Mahmut CiftciOptical Communications using ChaoticTechniques Gregory D. VanWiggerenAPPENDIX AFundamental Concepts of the Theory ofChaos a
Maldacena, Juan; Stanford, Douglas
2015-01-01
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 $\\lambda_L \\le 2 \\pi k_B T/\\hbar$. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.
Directory of Open Access Journals (Sweden)
David Murphy
2011-11-01
Full Text Available About 20 years ago, while lost in the midst of my PhD research, I mused over proposed titles for my thesis. I was pretty pleased with myself when I 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. I used the then-emerging theories of chaos and complexity to underpin my analysis. So it was with more than a little excitement that I read the call for contributions to this special issue of IRRODL. What follows is a walk-through of my thesis with an emphasis on the contribution of chaos and complexity theory.
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.
Global genetic variation at OAS1 provides evidence of archaic admixture in Melanesian populations.
Mendez, Fernando L; Watkins, Joseph C; Hammer, Michael F
2012-06-01
Recent analysis of DNA extracted from two Eurasian forms of archaic human shows that more genetic variants are shared with humans currently living in Eurasia than with anatomically modern humans in sub-Saharan Africa. Although these genome-wide average measures of genetic similarity are consistent with the hypothesis of archaic admixture in Eurasia, analyses of individual loci exhibiting the signal of archaic introgression are needed to test alternative hypotheses and investigate the admixture process. Here, we provide a detailed sequence analysis of the innate immune gene OAS1, a locus with a divergent Melanesian haplotype that is very similar to the Denisova sequence from the Altai region of Siberia. We resequenced a 7-kb region encompassing the OAS1 gene in 88 individuals from six Old World populations (San, Biaka, Mandenka, French Basque, Han Chinese, and Papua New Guineans) and discovered previously unknown and ancient genetic variation. The 5' region of this gene has unusual patterns of diversity, including 1) higher levels of nucleotide diversity in Papuans than in sub-Saharan Africans, 2) very deep ancestry with an estimated time to the most recent common ancestor of >3 myr, and 3) a basal branching pattern with Papuan individuals on either side of the rooted network. A global geographic survey of >1,500 individuals showed that the divergent Papuan haplotype is nearly restricted to populations from eastern Indonesia and Melanesia. Polymorphic sites within this haplotype are shared with the draft Denisova genome over a span of ∼90 kb and are associated with an extended block of linkage disequilibrium, supporting the hypothesis that this haplotype introgressed from an archaic source that likely lived in Eurasia.
Wild Goat style ceramics at Troy and the impact of Archaic period colonisation on the Troad
Aslan, Carolyn C.; Pernicka, Ernst
2013-01-01
The establishment of colonies along the Hellespont by inhabitants of Ionia, Athens and Lesbos is well-known from historical texts. Recently, stratified contexts at Troy as well as other surveys and excavations have yielded new information about the chronology and material markers of Archaic period settlements in the Troad and the Gallipoli peninsula. The archaeological evidence for colonisation in this region is not clearly seen until the late seventh to early sixth century BC when there is a...
Fractal Patterns and Chaos Games
Devaney, Robert L.
2004-01-01
Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.
Introducing chaos a graphic guide
Sardar, Ziauddin; Abrams, Iwona
2014-01-01
Explains how chaos makes its presence felt in many varieties of event, from the fluctuation of animal populations to the ups and downs of the stock market. This book also examines the roots of chaos in modern mathematics and physics, and explores the relationship between chaos and complexity.
Dissipative structures and chaos
Mori, Hazime
1998-01-01
This monograph consists of two parts and gives an approach to the physics of open nonequilibrium systems. Part I derives the phenomena of dissipative structures on the basis of reduced evolution equations and includes Bénard convection and Belousov-Zhabotinskii chemical reactions. Part II discusses the physics and structures of chaos. While presenting a construction of the statistical physics of chaos, the authors unify the geometrical and statistical descriptions of dynamical systems. The shape of chaotic attractors is characterized, as are the mixing and diffusion of chaotic orbits and the fluctuation of energy dissipation exhibited by chaotic systems.
Shigehara, T; Mishima, T; Cheon, T; Shigehara, Takaomi; Mizoguchi, Hiroshi; Mishima, Taketoshi; Cheon, Taksu
1998-01-01
In this paper, we show that two-dimensional billiards with point interactions inside exhibit a chaotic nature in the microscopic world, although their classical counterpart is non-chaotic. After deriving the transition matrix of the system by using the self-adjoint extension theory of functional analysis, we deduce the general condition for the appearance of chaos. The prediction is confirmed by numerically examining the statistical properties of energy spectrum of rectangular billiards with multiple point interactions inside. The dependence of the level statistics on the strength as well as the number of the scatterers is displayed. KEYWORDS: wave chaos, quantum mechanics, pseudointegrable billiard, point interaction, functional analysis
A Description of Quantum Chaos
Inoue, K; Ohya, M; Inoue, Kei; Kossakowski, Andrzej; Ohya, Masanori
2004-01-01
A measure describing the chaos of a dynamics was introduced by two complexities in information dynamics, and it is called the chaos degree. In particular, the entropic chaos degree has been used to characterized several dynamical maps such that logistis, Baker's, Tinckerbel's in classical or quantum systems. In this paper, we give a new treatment of quantum chaos by defining the entropic chaos degree for quantum transition dynamics, and we prove that every non-chaotic quantum dynamics, e.g., dissipative dynamics, has zero chaos degree. A quantum spin 1/2 system is studied by our chaos degree, and it is shown that this degree well describes the chaotic behavior of the spin system.
Inverse anticipating chaos synchronization.
Shahverdiev, E M; Sivaprakasam, S; Shore, K A
2002-07-01
We derive conditions for achieving inverse anticipating synchronization where a driven time-delay chaotic system synchronizes to the inverse future state of the driver. The significance of inverse anticipating chaos in delineating synchronization regimes in time-delay systems is elucidated. The concept is extended to cascaded time-delay systems.
Akhmet, Marat
2012-01-01
Morphogenesis, as it is understood in a wide sense by Ren\\'e Thom, is considered for various types of chaos. That is, those, obtained by period-doubling cascade, Devaney's and Li-Yorke chaos. Moreover, in discussion form we consider inheritance of intermittency, the double-scroll Chua's attractor and quasiperiodical motions as a possible skeleton of a chaotic attractor. To make our introduction of the paper more clear, we have to say that one may consider other various accompanying concepts of chaos such that a structure of the chaotic attractor, its fractal dimension, form of the bifurcation diagram, the spectra of Lyapunov exponents, etc. We make comparison of the main concept of our paper with Turing's morphogenesis and John von Neumann automata, considering that this may be not only formal one, but will give ideas for the chaos development in the morphogenesis of Turing and for self-replicating machines. To provide rigorous study of the subject, we introduce new definitions such as chaotic sets of functio...
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.
Chaos induced by coupling between Josephson junctions
Shukrinov, Yu. M.; Azemtsa-Donfack, H.; Botha, A. E.
2015-02-01
It is found that, in a stack of intrinsic Josephson junctions in layered high temperature superconductors under external electromagnetic radiation, the chaotic features are triggered by interjunction coupling, i.e., the coupling between different junctions in the stack. While the radiation is well known to produce chaotic effects in the single junction, the effect of interjunction coupling is fundamentally different and it can lead to the onset of chaos via a different route to that of the single junction. A precise numerical study of the phase dynamics of intrinsic Josephson junctions, as described by the CCJJ+DC model, is performed. We demonstrate the charging of superconducting layers, in a bias current interval corresponding to a Shapiro step subharmonic, due to the creation of a longitudinal plasma wave along the stack of junctions. With increase in radiation amplitude chaotic behavior sets in. The chaotic features of the coupled Josephson junctions are analyzed by calculations of the Lyapunov exponents. We compare results for a stack of junctions to the case of a single junction and prove that the observed chaos is induced by the coupling between the junctions. The use of Shapiro step subharmonics may allow longitudinal plasma waves to be excited at low radiation power.
Converting transient chaos into sustained chaos by feedback control
Lai, Ying-Cheng; Grebogi, Celso
1994-02-01
A boundary crisis is a catastrophic event in which a chaotic attractor is suddenly destroyed, leaving a nonattracting chaotic saddle in its place in the phase space. Based on the controlling-chaos idea [E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990)], we present a method for stabilizing chaotic trajectories on the chaotic saddle by applying only small parameter perturbations. This strategy enables us to convert transient chaos into sustained chaos, thereby restoring attracting chaotic motion.
Fuzzy controller based on chaos optimal design and its application
Institute of Scientific and Technical Information of China (English)
邹恩; 李祥飞; 张泰山
2004-01-01
In order to overcome difficulty of tuning parameters of fuzzy controller, a chaos optimal design method based on annealing strategy is proposed. First, apply the chaotic variables to search for parameters of fuzzy controller, and transform the optimal variables into chaotic variables by carrier-wave method. Making use of the intrinsic stochastic property and ergodicity of chaos movement to escape from the local minimum and direct optimization searching within global range, an approximate global optimal solution is obtained. Then, the chaos local searching and optimization based on annealing strategy are cited, the parameters are optimized again within the limits of the approximate global optimal solution, the optimization is realized by means of combination of global and partial chaos searching, which can converge quickly to global optimal value. Finally, the third order system and discrete nonlinear system are simulated and compared with traditional method of fuzzy control. The results show that the new chaos optimal design method is superior to fuzzy control method, and that the control results are of high precision, with no overshoot and fast response.
Bishop, Paul
2008-09-01
In 1930 Jung gave a lecture entitled 'Archaic Man' to the Lesezirkel in Hottingen. Following recent work on this text by two commentators, this article uses their interpretations as a springboard for a complementary reading, which emphasizes the fundamental significance of this paper as bridging the earlier and later stages in the development of analytical psychology, and examines closely the opposition between 'archaic'-'modern' in Jung's paper; indeed, in his work as a whole. In contrast to Lévy-Bruhl, Jung rejects the label of 'mysticism' as applied to the 'primitive' point of view, and his anti-mystical stance can be explained in terms of his dialectical conception of the relationship between Self and World. On this account, the subject and the object--the psyche and the external world--are more closely (inter)related than conventional (modern) epistemology and ontology generally believe. This conception of the relation between the subjective and the objective foreshadows his later, and controversial, concept of synchronicity, which is, Jung insists, a way of apprehending the world in terms of its meaning. Concluding with a survey of the status of the 'primordial' in some other texts by Jung, this article aims to foster further debate on one of Jung's most complex and fascinating texts.
Interpolity exchange of basalt tools facilitated via elite control in Hawaiian archaic states.
Kirch, Patrick V; Mills, Peter R; Lundblad, Steven P; Sinton, John; Kahn, Jennifer G
2012-01-24
Ethnohistoric accounts of late precontact Hawaiian archaic states emphasize the independence of chiefly controlled territories (ahupua'a) based on an agricultural, staple economy. However, elite control of unevenly distributed resources, such as high-quality volcanic rock for adze production, may have provided an alternative source of economic power. To test this hypothesis we used nondestructive energy-dispersive X-ray fluorescence (ED-XRF) analysis of 328 lithic artifacts from 36 archaeological features in the Kahikinui district, Maui Island, to geochemically characterize the source groups. This process was followed by a limited sampling using destructive wavelength-dispersive X-ray fluorescence (WD-XRF) analysis to more precisely characterize certain nonlocal source groups. Seventeen geochemical groups were defined, eight of which represent extra-Maui Island sources. Although the majority of stone tools were derived from Maui Island sources (71%), a significant quantity (27%) of tools derived from extraisland sources, including the large Mauna Kea quarry on Hawai'i Island as well as quarries on O'ahu, Moloka'i, and Lāna'i islands. Importantly, tools quarried from extralocal sources are found in the highest frequency in elite residential features and in ritual contexts. These results suggest a significant role for a wealth economy based on the control and distribution of nonagricultural goods and resources during the rise of the Hawaiian archaic states.
Wu, Miaomiao; Xu, Shihui; Zhu, Wei; Mao, Xiaohua
2014-10-01
Subunit-subunit interactions of the classical and alternate chaperone-usher (CU) systems have been shown to proceed through a donor strand exchange (DSE) mechanism. However, it is not known whether DSE is required for intersubunit interactions in the archaic CU system. We have previously shown that the Myxococcus xanthus Mcu system, a member of the archaic CU family that functions in spore coat formation, is likely to use the principle of donor strand complementation to medicate chaperone-subunit interactions analogous to the classical CU pathway. Here we describe the results of studies on Mcu subunit-subunit interactions. We constructed a series of N-terminal-deleted, single amino acid-mutated and donor strand-complemented Mcu subunits, and characterized their abilities to participate in subunit-subunit interactions. It appears that certain residues in both the N and C termini of McuA, a subunit of the Mcu system, play a critical role in intersubunit interactions and these interactions may involve the general principle of DSE of the classical and alternate CU systems. In addition, the specificity of the M. xanthus CU system for Mcu subunits over other spore coat proteins is demonstrated.
Chaos control of cardiac arrhythmias.
Garfinkel, A; Weiss, J N; Ditto, W L; Spano, M L
1995-01-01
Chaos theory has shown that many disordered and erratic phenomena are in fact deterministic, and can be understood causally and controlled. The prospect that cardiac arrhythmias might be instances of deterministic chaos is therefore intriguing. We used a recently developed method of chaos control to stabilize a ouabain-induced arrhythmia in rabbit ventricular tissue in vitro. Extension of these results to clinically significant arrhythmias such as fibrillation will require overcoming the additional obstacles of spatiotemporal complexity.
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.
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
Chaos detection and predictability
Gottwald, Georg; Laskar, Jacques
2016-01-01
Distinguishing chaoticity from regularity in deterministic dynamical systems and specifying the subspace of the phase space in which instabilities are expected to occur is of utmost importance in as disparate areas as astronomy, particle physics and climate dynamics. To address these issues there exists a plethora of methods for chaos detection and predictability. The most commonly employed technique for investigating chaotic dynamics, i.e. the computation of Lyapunov exponents, however, may suffer a number of problems and drawbacks, for example when applied to noisy experimental data. In the last two decades, several novel methods have been developed for the fast and reliable determination of the regular or chaotic nature of orbits, aimed at overcoming the shortcomings of more traditional techniques. This set of lecture notes and tutorial reviews serves as an introduction to and overview of modern chaos detection and predictability techniques for graduate students and non-specialists. The book cover...
Marklof, J
2005-01-01
The central objective in the study of quantum chaos is to characterize universal properties of quantum systems that reflect the regular or chaotic features of the underlying classical dynamics. Most developments of the past 25 years have been influenced by the pioneering models on statistical properties of eigenstates (Berry 1977) and energy levels (Berry and Tabor 1977; Bohigas, Giannoni and Schmit 1984). Arithmetic quantum chaos (AQC) refers to the investigation of quantum system with additional arithmetic structures that allow a significantly more extensive analysis than is generally possible. On the other hand, the special number-theoretic features also render these systems non-generic, and thus some of the expected universal phenomena fail to emerge. Important examples of such systems include the modular surface and linear automorphisms of tori (`cat maps') which will be described below.
Hosur, Pavan; Roberts, Daniel A; Yoshida, Beni
2015-01-01
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.
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.
Noise tolerant spatiotemporal chaos computing
Energy Technology Data Exchange (ETDEWEB)
Kia, Behnam; Kia, Sarvenaz; Ditto, William L. [Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, Hawaii 96822 (United States); Lindner, John F. [Physics Department, The College of Wooster, Wooster, Ohio 44691 (United States); Sinha, Sudeshna [Indian Institute of Science Education and Research (IISER), Mohali, Punjab 140306 (India)
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.
Noise tolerant spatiotemporal chaos computing.
Kia, Behnam; Kia, Sarvenaz; Lindner, John F; Sinha, Sudeshna; Ditto, William L
2014-12-01
We introduce and design a noise tolerant chaos computing system based on a coupled map lattice (CML) and the noise reduction capabilities inherent in coupled dynamical systems. The resulting spatiotemporal chaos computing system is more robust to noise than a single map chaos computing system. In this CML based approach to computing, under the coupled dynamics, the local noise from different nodes of the lattice diffuses across the lattice, and it attenuates each other's effects, resulting in a system with less noise content and a more robust chaos computing architecture.
Tailoring wavelets for chaos control.
Wei, G W; Zhan, Meng; Lai, C-H
2002-12-31
Chaos is a class of ubiquitous phenomena and controlling chaos is of great interest and importance. In this Letter, we introduce wavelet controlled dynamics as a new paradigm of dynamical control. We find that by modifying a tiny fraction of the wavelet subspaces of a coupling matrix, we could dramatically enhance the transverse stability of the synchronous manifold of a chaotic system. Wavelet controlled Hopf bifurcation from chaos is observed. Our approach provides a robust strategy for controlling chaos and other dynamical systems in nature.
Voglis, Nikos
2003-01-01
Galaxies and Chaos examines the application of tools developed for Nonlinear Dynamical Systems to Galactic Dynamics and Galaxy Formation, as well as to related issues in Celestial Mechanics. The contributions collected in this volume have emerged from selected presentations at a workshop on this topic and key chapters have been suitably expanded in order to be accessible to nonspecialist researchers and postgraduate students wishing to enter this exciting field of research.
DEFF Research Database (Denmark)
Lindberg, Erik
1996-01-01
Can we believe in the results of our circuit simulators ? Is it possible to distinguish between results due to numerical chaos and resultsdue to the eventual chaotic nature of our modelsof physical systems ?. Three experiments with SPICE are presented: (1) A "stable" active RCcircuit with poles i...... in the models of the circuits to be analyzed. If trimmed properly SPICE normally gives the correct result....
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...
van De Water W; de Weger J
2000-11-01
We study the control of chaos in an experiment on a parametrically excited pendulum whose excitation mechanism is not perfect. This imperfection leads to a weakly excited degree of freedom with an associated small eigenvalue. Although the state of the pendulum could be characterized well and although the perturbation is weak, we fail to control chaos. From a numerical model we learn that the small eigenvalue cannot be ignored when attempting control. However, the estimate of this eigenvalue from an (experimental) time series is elusive. The reason is that points in an experimental time series are distributed according to the natural measure. It is this extremely uneven distribution of points that thwarts attempts to measure eigenvalues that are very different. Another consequence of the phase-space distribution of points for control is the occurrence of logarithmic-oscillations in the waiting time before control can be attempted. We come to the conclusion that chaos needs to be destroyed before the information needed for its control can be obtained.
Chaos Theory and Post Modernism
Snell, Joel
2009-01-01
Chaos theory is often associated with post modernism. However, one may make the point that both terms are misunderstood. The point of this article is to define both terms and indicate their relationship. Description: Chaos theory is associated with a definition of a theory dealing with variables (butterflies) that are not directly related to a…
Kaszás, Bálint; Feudel, Ulrike; Tél, Tamás
2016-12-01
We investigate the death and revival of chaos under the impact of a monotonous time-dependent forcing that changes its strength with a non-negligible rate. Starting on a chaotic attractor it is found that the complexity of the dynamics remains very pronounced even when the driving amplitude has decayed to rather small values. When after the death of chaos the strength of the forcing is increased again with the same rate of change, chaos is found to revive but with a different history. This leads to the appearance of a hysteresis in the complexity of the dynamics. To characterize these dynamics, the concept of snapshot attractors is used, and the corresponding ensemble approach proves to be superior to a single trajectory description, that turns out to be nonrepresentative. The death (revival) of chaos is manifested in a drop (jump) of the standard deviation of one of the phase-space coordinates of the ensemble; the details of this chaos-nonchaos transition depend on the ratio of the characteristic times of the amplitude change and of the internal dynamics. It is demonstrated that chaos cannot die out as long as underlying transient chaos is present in the parameter space. As a condition for a "quasistatically slow" switch-off, we derive an inequality which cannot be fulfilled in practice over extended parameter ranges where transient chaos is present. These observations need to be taken into account when discussing the implications of "climate change scenarios" in any nonlinear dynamical system.
Pakharukova, Natalia; Garnett, J.A.; Tuittila, Minna; Paavilainen, Sari; Diallo, Mamou; Xu, Yingqi; Matthews, S.J.; Zavialov, A.V.
2015-01-01
Gram-negative pathogens express fibrous adhesive organelles that mediate targeting to sites of infection. The major class of these organelles is assembled via the classical, alternative and archaic chaperone-usher pathways. Although non-classical systems share a wider phylogenetic distribution an
From archaic narcissism to empathy for the self: the evolution of new capacities in psychoanalysis.
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.
Chaos Criminology: A critical analysis
McCarthy, Adrienne L.
There has been a push since the early 1980's for a paradigm shift in criminology from a Newtonian-based ontology to one of quantum physics. Primarily this effort has taken the form of integrating Chaos Theory into Criminology into what this thesis calls 'Chaos Criminology'. However, with the melding of any two fields, terms and concepts need to be translated properly, which has yet to be done. In addition to proving a translation between fields, this thesis also uses a set of criteria to evaluate the effectiveness of the current use of Chaos Theory in Criminology. While the results of the theory evaluation reveal that the current Chaos Criminology work is severely lacking and in need of development, there is some promise in the development of Marx's dialectical materialism with Chaos Theory.
Institute of Scientific and Technical Information of China (English)
方锦清; 罗晓曙; 陈关荣; 翁甲强
2001-01-01
Beam halo-chaos is essentially a complex spatiotemporal chaotic motion in a periodic-focusing channel of a highpower linear proton accelerator. The controllability condition for beam halo-chaos is analysed qualitatively. A special nonlinear control method, i.e. the wavelet-based function feedback, is proposed for controlling beam halochaos. Particle-in-cell simulations are used to explore the nature of halo-chaos formation, which has shown that the beam hMo-chaos is suppressed effectively after using nonlinear control for the proton beam with an initial full Gaussian distribution. The halo intensity factor Hav is reduced from 14%o to zero, and the other statistical physical quantities of beam halo-chaos are more than doubly reduced. The potential applications of such nonlinear control in experiments are briefly pointed out.
Baran, V; Baran, Virgil; Bonasera, Aldo
1998-01-01
The asymptotic distance between trajectories $d_{\\infty}$, is studied in detail to characterize the occurrence of chaos. We show that this quantity is quite distinct and complementary to the Lyapunov exponents, and it allows for a quantitave estimate for the folding mechanism which keeps the motion bounded in phase space. We study the behaviour of $d_{\\infty}$ in simple unidimensional maps. Near a critical point $d_{\\infty}$ has a power law dependence on the control parameter. Furthermore, at variance with the Lyapunov exponents, it shows jumps when there are sudden changes on the available phase-space.
Dembiński, S. T.; Makowski, A. J.; Pepłowski, P.
1993-02-01
We report for the first time quantum calculations for the so-called bouncer model, the classical analog of which is well known to manifest a chaotic behavior. Three versions of our model are fully tractable quantum mechanically and are potentially a rich source of data for establishing properties of a quantum system of which the classical mechanics can be chaotic. Among the results presented here, consequences of the varying bandwidth of infinite-dimensional transition matrices on the use of the correspondence between classical chaos and non-Poissonian quasienergy statistics are discussed.
2004-01-01
15 May 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows the results of a small landslide off of a hillslope in the Aureum Chaos region of Mars. Mass movement occurred from right (the slope) to left (the lobate feature pointed left). Small dark dots in the landslide area are large boulders. This feature is located near 2.6oS, 24.5oW. This picture covers an area approximately 3 km (1.9 mi) across and is illuminated by sunlight from the left/upper left.
Nonhyperbolic homoclinic chaos
Cicogna, G
1999-01-01
Homoclinic chaos is usually examined with the hypothesis of hyperbolicity of the critical point. We consider here, following a (suitably adjusted) classical analytic method, the case of non-hyperbolic points and show that, under a Melnikov-type condition plus an additional assumption, the negatively and positively asymptotic sets persist under periodic perturbations, together with their infinitely many intersections on the Poincaré section. We also examine, by means of essentially the same procedure, the case of (heteroclinic) orbits tending to the infinity; this case includes in particular the classical Sitnikov 3--body problem.
Chaos a very short introduction
Smith, Leonard
2007-01-01
Chaos: A Very Short Introduction shows that we all have an intuitive understanding of chaotic systems. It uses accessible maths and physics (replacing complex equations with simple examples like pendulums, railway lines, and tossing coins) to explain the theory, and points to numerous examples in philosophy and literature (Edgar Allen Poe, Chang-Tzu, and Arthur Conan Doyle) that illuminate the problems. The beauty of fractal patterns and their relation to chaos, as well as the history of chaos, and its uses in the real world and implications for the philosophy of science are all discussed in this Very Short Introduction.
Stalling chaos control accelerates convergence
Bick, Christian; Kolodziejski, Christoph; Timme, Marc
2013-06-01
Since chaos control has found its way into many applications, the development of fast, easy-to-implement and universally applicable chaos control methods is of crucial importance. Predictive feedback control has been widely applied but suffers from a speed limit imposed by highly unstable periodic orbits. We show that this limit can be overcome by stalling the control, thereby taking advantage of the stable directions of the uncontrolled chaotic map. This analytical finding is confirmed by numerical simulations, giving a chaos-control method that is capable of successfully stabilizing periodic orbits of high period.
Schmidt, Britney E.
2013-10-01
A critical question for the habitability of Europa remains: how does the ice shell work? The detection of shallow subsurface lenses below Europa’s chaos implies that the ice shell is recycled rapidly and that Europa may be currently active. While this is not the first time liquid water has been implicated for Europa, the location of these features combined with new perspective on their dynamics frames the question in a new way. Melt lenses are intriguing potential habitats. Moreover, their formation requires the existence of impurities within the upper ice shell that may be sources of energy for microorganisms. Geomorphic evidence also exists for hydraulic redistribution of fluids both vertically and horizontally through pores and fractures. This process, observed in terrestrial ice shelves, may preserve liquid water within the ice matrix over many kilometers from the source. Horizontal transport of material may produce interconnectivity between distinct regions of Europa, thus preserving habitable conditions within the ice over a longer duration. At a surface age of 40-90 Myr, with 25-50% covered by chaos terrain, Europa's resurfacing rate is very high and water likely plays a significant role. Because of the vigor of overturn implied by this new work, it is likely that surface and subsurface materials are well-mixed within the largest and deepest lenses, providing a mechanism for bringing oxidants and other surface contaminants to the deeper ice shell where it can reach the ocean by convective or compositional effects. The timescales over which large lenses refreeze are large compared to the timescales for vertical transport, while the timescales for smaller lenses are comparable to or shorter than convective timescales. Moreover, marine ice accretion at the bottom of the ice shell may be contributing to a compositional buoyancy engine that would change the makeup of the ice shell. From this point of view, we evaluate the habitability of Europa’s ice and
Chaos and complexity by design
Roberts, Daniel A
2016-01-01
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 $k$th 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.
Ercsey-Ravasz, Maria
2012-01-01
The mathematical structure of the widely popular Sudoku puzzles is akin to typical hard constraint satisfaction problems that lie at the heart of many applications, including protein folding and the general problem of finding the ground state of a glassy spin system. Via an exact mapping of Sudoku into a deterministic, continuous-time dynamical system, here we show that the difficulty of Sudoku translates into transient chaotic behavior exhibited by the dynamical system. In particular, we show that the escape rate $\\kappa$, an invariant characteristic of transient chaos, provides a single scalar measure of the puzzle's hardness, which correlates well with human difficulty level ratings. Accordingly, $\\eta = -\\log_{10}{\\kappa}$ can be used to define a "Richter"-type scale for puzzle hardness, with easy puzzles falling in the range $0 3$. To our best knowledge, there are no known puzzles with $\\eta > 4$.
Mitchener, W Garrett; Nowak, Martin A
2004-04-01
Human language is a complex communication system with unlimited expressibility. Children spontaneously develop a native language by exposure to linguistic data from their speech community. Over historical time, languages change dramatically and unpredictably by accumulation of small changes and by interaction with other languages. We have previously developed a mathematical model for the acquisition and evolution of language in heterogeneous populations of speakers. This model is based on game dynamical equations with learning. Here, we show that simple examples of such equations can display complex limit cycles and chaos. Hence, language dynamical equations mimic complicated and unpredictable changes of languages over time. In terms of evolutionary game theory, we note that imperfect learning can induce chaotic switching among strict Nash equilibria.
Wernecke, Hendrik; Gros, Claudius
2016-01-01
For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation is split into an initial decrease characterized by the maximal Lyapunov exponent and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. The time scales of both processes can be either of the same or of very different orders of magnitude. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall size of the attractor) for exceedingly long times and therefore remain partially predictable. We introduce a 0-1 indicator for chaos capable of describing this scenario, arguing, in addition, that the chaotic closed braids found close to a period-doubling transition are generically partially predictable.
Boundary condition may change chaos
Energy Technology Data Exchange (ETDEWEB)
Itoh, Sanae-I.; Yagi, Masatoshi [Kyushu Univ., RIAM, Kasuga, Fukuoka (Japan); Kawai, Yoshinobu [Kyushu Univ., Interdisciplinary Graduate School of Engineering Sciences, Kasuga, Fukuoka (Japan)
2001-07-01
Role of boundary condition for the appearance of chaos is examined. Imposition of the boundary condition is interpreted as the reduction of the system size L. For a demonstration, Rayleigh-Benard instability is considered and the shell model analysis is applied. It is shown that the reduction of L reduces the number of positive Lyapunov exponent of the system, hence opens the route from the turbulence, to the chaos and to the limit cycle/fixed point. (author)
Stochastic Estimation via Polynomial Chaos
2015-10-01
TΨ is a vector with P+1 elements. With these dimensions, (29) is solvable by standard numerical linear algebra techniques. The specific matrix...initial conditions for partial differential equations. Here, the elementary theory of the polynomial chaos is presented followed by the details of a...the elementary theory of the polynomial chaos is presented followed by the details of a number of example calculations where the statistical mean and
Granular chaos and mixing: Whirled in a grain of sand
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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.
Utilizing nonlinearity of transistors for reconfigurable chaos computation
Ditto, William; Kia, Behnam
2014-03-01
A VLSI circuit design for chaos computing is presented that exploits the intrinsic nonlinearity of transistors to implement a novel approach for conventional and chaotic computing circuit design. In conventional digital circuit design and implementation, transistors are simply switched on or off. We argue that by using the full range of nonlinear dynamics of transistors, we can design and build more efficient computational elements and logic blocks. Furthermore, the nonlinearity of these transistor circuits can be used to program the logic block to implement different types of computational elements that can be reconfigured. Because the intrinsic nonlinear dynamics of the transistors are utilized the resulting circuits typically require fewer transistors compared to conventional digital circuits as we exploit the intrinsic nonlinearity of the transistors to realize computations. This work was done with support from ONR grant N00014-12-1-0026 and from an ONR STTR and First Pass Engineering.
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.
Directory of Open Access Journals (Sweden)
Kasianenko O.G.
2009-10-01
Full Text Available The author has realized the historical analysis of one of the information sources about Ancient Olympic games, namely lists of winners. Had presented the description of geographical information, characterizing the sportsmen's place of origin, and also social origin of afore-named, allows to conduct parallels in consideration of the studied information with political and cultural changes in Greek civilization in archaic and classic periods which had a direct influence on the Olympic Games.
Investigation of Chinese archaic jade by PIXE and {mu}Raman spectrometry
Energy Technology Data Exchange (ETDEWEB)
Chen, T.H. [UMR 171 du CNRS, Centre de Recherche et de Restauration des Musees de France, Palais du Louvre, Porte des Lions, 14 Quai Francois Mitterrand, 75001, Paris (France); Ecole Doctorale MMRMM, Universite de Versailles - St Quentin en Yvelines, 45 Avenue des Etats Unis, 78035, Versailles Cedex (France); Calligaro, T.; Pages-Camagna, S.; Menu, M. [UMR 171 du CNRS, Centre de Recherche et de Restauration des Musees de France, Palais du Louvre, Porte des Lions, 14 Quai Francois Mitterrand, 75001, Paris (France)
2004-07-01
External-beam particle-induced X-ray emission (PIXE) and {mu}Raman 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.)
Investigation of Chinese archaic jade by PIXE and μRaman spectrometry
Chen, T.-H.; Calligaro, T.; Pagès-Camagna, S.; Menu, M.
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.
Directory of Open Access Journals (Sweden)
Yang Liu
Full Text Available Mitochondrial genomes have maintained some bacterial features despite their residence within eukaryotic cells for approximately two billion years. One of these features is the frequent presence of polycistronic operons. In land plants, however, it has been shown that all sequenced vascular plant chondromes lack large polycistronic operons while bryophyte chondromes have many of them. In this study, we provide the completely sequenced mitochondrial genome of a lycophyte, from Huperzia squarrosa, which is a member of the sister group to all other vascular plants. The genome, at a size of 413,530 base pairs, contains 66 genes and 32 group II introns. In addition, it has 69 pseudogene fragments for 24 of the 40 protein- and rRNA-coding genes. It represents the most archaic form of mitochondrial genomes of all vascular plants. In particular, it has one large conserved gene cluster containing up to 10 ribosomal protein genes, which likely represents a polycistronic operon but has been disrupted and greatly reduced in the chondromes of other vascular plants. It also has the least rearranged gene order in comparison to the chondromes of other vascular plants. The genome is ancestral in vascular plants in several other aspects: the gene content resembling those of charophytes and most bryophytes, all introns being cis-spliced, a low level of RNA editing, and lack of foreign DNA of chloroplast or nuclear origin.
2012 Symposium on Chaos, Complexity and Leadership
Erçetin, Şefika
2014-01-01
These proceedings from the 2012 symposium on "Chaos, complexity and leadership" reflect current research results from all branches of Chaos, Complex Systems and their applications in Management. Included are the diverse results in the fields of applied nonlinear methods, modeling of data and simulations, as well as theoretical achievements of Chaos and Complex Systems. Also highlighted are Leadership and Management applications of Chaos and Complexity Theory.
Hashimoto, Koji; Yoshida, Kentaroh
2016-01-01
Assigning a chaos index for vacua of generic quantum field theories is a challenging problem. We find chaotic behavior of chiral condensates of a quantum gauge theory at strong coupling limit, by using the AdS/CFT correspondence. We evaluate the time evolution of homogeneous quark condensates and in an N=2 supersymmetric QCD with the SU(N_c) gauge group at large N_c and at large 't Hooft coupling lambda. At an equivalent classical gravity picture, a Lyapunov exponent is readily defined. We show that the condensates exhibit chaotic behavior for energy density E > (6x10^2) (N_c/lambda^2) (m_q)^4 where m_q is the quark mass. The energy region of the chaotic vacua of the N=2 supersymmetric QCD increases for smaller N_c or larger lambda. The Lyapunov exponent is calculated as a function of the theory (N_c,lambda,E), showing that the N=2 supersymmetric QCD is more chaotic for smaller N_c.
Barrow, John D; Barrow, John D.; Dabrowski, Mariusz P.
1998-01-01
We investigate Bianchi type IX ''Mixmaster'' universes within the framework of the low-energy tree-level effective action for string theory, which (when the ''stringy'' 2-form axion potential vanishes) is formally the same as the Brans-Dicke action with $\\omega =-1$. We show that, unlike the case of general relativity in vacuum, there is no Mixmaster chaos in these string cosmologies. In the Einstein frame an infinite sequence of chaotic oscillations of the scale factors on approach to the initial singularity is impossible, as it was in general relativistic Mixmaster universes in the presence of stiff -fluid matter (or a massless scalar field). A finite sequence of oscillations of the scale factors approximated by Kasner metrics is possible, but it always ceases when all expansion rates become positive. In the string frame the evolution through Kasner epochs changes to a new form which reflects the duality symmetry of the theory. Again, we show that chaotic oscillations must end after a finite time. The need ...
Contopoulos, George
2008-01-01
We distinguish two types of stickiness in systems of two degrees of freedom (a) stickiness around an island of stability and (b) stickiness in chaos, along the unstable asymptotic curves of unstable periodic orbits. We studied these effects in the standard map with a rather large nonlinearity K=5, and we emphasized the role of the asymptotic curves U, S from the central orbit O and the asymptotic curves U+U-S+S- from the simplest unstable orbit around the island O1. We calculated the escape times (initial stickiness times) for many initial points outside but close to the island O1. The lines that separate the regions of the fast from the slow escape time follow the shape of the asymptotic curves S+,S-. We explained this phenomenon by noting that lines close to S+ on its inner side (closer to O1) approach a point of the orbit 4/9, say P1, and then follow the oscillations of the asymptotic curve U+, and escape after a rather long time, while the curves outside S+ after their approach to P1 follow the shape of t...
Chaos theory for the biomedical engineer.
Eberhart, R C
1989-01-01
A brief introduction to chaos theory is provided. Definitions of chaos and attributes of chaos and fractals are discussed. Several general examples are examined, and fractals are introduced with a brief look at the Mandelbrot and Julia sets. Biomedical examples of chaotic behaviour and fractals are presented.
Directory of Open Access Journals (Sweden)
V. B. Okorokov
2016-06-01
Full Text Available Purpose. The purpose of research consists in that: having plunged into depths of primitive consciousness (using the recipe of many thinkers of non-classical philosophy, to reveal contradiction of the European thought (at its sources in Ancient Greek thought and show resources of mythological thinking on the way of overcoming of these contradictions. Methodology. All methodological installations, using possibilities, borderlines and effects of non-classical consciousness, have appeared insufficiently effective for adequate understanding of essence of the person. The generalised method, which is used by us, leans on deep resources of high-energy consciousness and on decoding of possibilities of anthropological time that it presumes to open new horizons of human existence. Originality. Addressing to modern representations about the changed conditions of consciousness, we have tried to see the historically generated discursive practices of understanding reality by the consciousness (including the historical one. Thus, using the consistently conducted destruction we are aimed at reaching the first sources of consciousness and revealing the deep historical mechanisms of temporal consciousnesses formation (as far as it possible in the modern conditions. Conclusions. It is shown that the use of the basic ideas of Ancient Greek thought leads scientific consciousness to deadlocks of contradictions, which were consistently revealed during subsequent history of philosophy and culture. The analysis of ancient mythological texts allows concluding, that the Greek thought is not a source of modern scientific thought. That is to understand the scientific thought one should address to the more ancient archaic thinking. Thus, to overcome the contradictions of modern scientific and philosophical thought it is necessary to search new alternative (more ancient sources of understanding of the historical reality, first of all, connected with deepening into ancient
Directory of Open Access Journals (Sweden)
Mónica Díaz
2011-01-01
Full Text Available Introduction: Ancient DNA (aDNAstudies can support hypotheses regarding ancient populations; molecular studies can analyze the local population’s genetic composition, minimizing biases introduced by later migrations, demographic expansions, mutations, and bottleneck effects. These analyses must be performed with special care because of the low DNA concentrations and contamination risk; therefore, it is necessary to establish protocols to guarantee the reproducibility and veracity of results. Objective: The present study aims to establish a protocol to obtain ancient DNA from 16 pre-Columbian bone samples found in an excavation performed in the area «Candelaria La Nueva» in Bogota, Colombia, dated in the period «Muisca Tardio». Methods: Four founder mitochondrial DNA Amerindian haplotypes were analyzed by high resolution restriction enzyme analyses, obtaining fragments between 121 and 186 base pairs (bp. Different analyses were performed following a strict control of authenticity criteria regarding laboratory conditions, including: positive and negative controls, reproducibility of results, and verification of particular characteristics present in ancient DNA. Results: Results obtained from the bone samples showed the exclusive presence of haplogroup A in the population studied. This data support the statement of the archaeologists of a single biological population in space and time. The distribution of this haplogroup in a 100% frequency supports the hypothesis of Chibcha genetic affiliation. Conclusion: The present study is a contribution to the study of genetic diversity in archaic American populations, allowing the integration of geographic and historic data with genetic characterization techniques associated with linguistic, ethnographic, and glottochronology patterns. Following the protocol proposed in the present study allows fulfilling authenticity criteria for ancient samples with the available techniques.
Directory of Open Access Journals (Sweden)
Roger B.J. Benson
2015-12-01
Full Text Available Rhomaleosaurid plesiosaurians were a common and ecologically significant component of Early Jurassic marine faunas, primarily as large-bodied predators. They declined in abundance and made their last fossil appearance in the Middle Jurassic. However, the geographic pattern of rhomaleosaurid extinction has thus far been obscured by spatial bias in the Middle Jurassic marine reptile fossil record, which is strongly focussed on low-latitude European assemblages. We report two rhomaleosaurid specimens from the Callovian (late Middle Jurassic of the UK and Russia. Along with Borealonectes from Arctic Canada, these are the youngest-known occurrences of rhomaleosaurids. The UK specimen is the first identified from the Callovian of Europe, despite intensive fossil sampling over almost 200 years and the recovery of hundreds of other plesiosaurian specimens. Its discovery indicates that rhomaleosaurids were present, but extremely rare, at low palaeolatitudes of the Callovian. The Russian specimen is one of relatively few marine reptile specimens from its mid-palaeolatitude assemblage, as is also true of Borealonectes, which occurs in a high-palaeolatitude marine assemblage. Furthermore, we suggest that a mid latitude southern hemisphere occurrence from the Callovian of Argentina, previously referred to Pliosauridae, in fact represents a rhomaleosaurid. These findings suggest that rhomaleosaurids were actually common elements of mid-high palaeolatitude marine faunas, indicating a geographically staggered pattern of declining rhomaleosaurid abundance, and demonstrating the apparent persistence of an archaic marine reptile group in cool, mid–high latitude environments of the Middle Jurassic. It is therefore possible that sustained Middle–Late Jurassic global warming accelerated the ultimate extinction of rhomaleosaurids. Our findings suggest that widening the geographical breadth of fossil exploration could considerably enhance current knowledge of
Turiaci, Gustavo J.; Verlinde, Herman
2016-12-01
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.
Turiaci, Gustavo
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.
The information geometry of chaos
Cafaro, Carlo
2008-10-01
In this Thesis, we propose a new theoretical information-geometric framework (IGAC, Information Geometrodynamical Approach to Chaos) suitable to characterize chaotic dynamical behavior of arbitrary complex systems. First, the problem being investigated is defined; its motivation and relevance are discussed. The basic tools of information physics and the relevant mathematical tools employed in this work are introduced. The basic aspects of Entropic Dynamics (ED) are reviewed. ED is an information-constrained dynamics developed by Ariel Caticha to investigate the possibility that laws of physics---either classical or quantum---may emerge as macroscopic manifestations of underlying microscopic statistical structures. ED is of primary importance in our IGAC. The notion of chaos in classical and quantum physics is introduced. Special focus is devoted to the conventional Riemannian geometrodynamical approach to chaos (Jacobi geometrodynamics) and to the Zurek-Paz quantum chaos criterion of linear entropy growth. After presenting this background material, we show that the ED formalism is not purely an abstract mathematical framework, but is indeed a general theoretical scheme from which conventional Newtonian dynamics is obtained as a special limiting case. The major elements of our IGAC and the novel notion of information geometrodynamical entropy (IGE) are introduced by studying two "toy models". To illustrate the potential power of our IGAC, one application is presented. An information-geometric analogue of the Zurek-Paz quantum chaos criterion of linear entropy growth is suggested. Finally, concluding remarks emphasizing strengths and weak points of our approach are presented and possible further research directions are addressed. At this stage of its development, IGAC remains an ambitious unifying information-geometric theoretical construct for the study of chaotic dynamics with several unsolved problems. However, based on our recent findings, we believe it already
Distributed chaos and isotropic turbulence
Bershadskii, A
2015-01-01
Power spectrum of the distributed chaos can be represented by a weighted superposition of the exponential functions which is converged to a stretched exponential $\\exp-(k/k_{\\beta})^{\\beta }$. An asymptotic theory has been developed in order to estimate the value of $\\beta$ for the isotropic turbulence. This value has been found to be $\\beta =3/4$. Excellent agreement has been established between this theory and the data of direct numerical simulations not only for the velocity field but also for the passive scalar and energy dissipation fields. One can conclude that the isotropic turbulence emerges from the distributed chaos.
Enhancing chaoticity of spatiotemporal chaos.
Li, Xiaowen; Zhang, Heqiao; Xue, Yu; Hu, Gang
2005-01-01
In some practical situations strong chaos is needed. This introduces the task of chaos control with enhancing chaoticity rather than suppressing chaoticity. In this paper a simple method of linear amplifications incorporating modulo operations is suggested to make spatiotemporal systems, which may be originally chaotic or nonchaotic, strongly chaotic. Specifically, this control can eliminate periodic windows, increase the values and the number of positive Lyapunov exponents, make the probability distributions of the output chaotic sequences more homogeneous, and reduce the correlations of chaotic outputs for different times and different space units. The applicability of the method to practical tasks, in particular to random number generators and secure communications, is briefly discussed.
Controlling chaos with simple limiters
Corron; Pethel; Hopper
2000-04-24
New experimental results demonstrate that chaos control can be accomplished using controllers that are very simple relative to the system being controlled. Chaotic dynamics in a driven pendulum and a double scroll circuit are controlled using an adjustable, passive limiter-a weight for the pendulum and a diode for the circuit. For both experiments, multiple unstable periodic orbits are selectively controlled using minimal perturbations. These physical examples suggest that chaos control can be practically applied to a much wider array of important problems than initially thought possible.
Sprott, J C
2013-04-01
This paper demonstrates that an artificial neural network training on time-series data from the logistic map at the onset of chaos trains more effectively when it is weakly chaotic. This suggests that a modest amount of chaos in the brain in addition to the ever present random noise might be beneficial for learning. In such a case, human subjects might exhibit an increased Lyapunov exponent in their EEG recordings during the performance of creative tasks, suggesting a possible line of future research.
Universal quantification for deterministic chaos in dynamical systems
Selvam, A M
1993-01-01
A cell dynamical system model for deterministic chaos enables precise quantification of the round-off error growth,i.e., deterministic chaos in digital computer realizations of mathematical models of continuum dynamical systems. The model predicts the following: (a) The phase space trajectory (strange attractor) when resolved as a function of the computer accuracy has intrinsic logarithmic spiral curvature with the quasiperiodic Penrose tiling pattern for the internal structure. (b) The universal constant for deterministic chaos is identified as the steady-state fractional round-off error k for each computational step and is equal to 1 /sqr(tau) (=0.382) where tau is the golden mean. (c) The Feigenbaum's universal constants a and d are functions of k and, further, the expression 2(a**2) = (pie)*d quantifies the steady-state ordered emergence of the fractal geometry of the strange attractor. (d) The power spectra of chaotic dynamical systems follow the universal and unique inverse power law form of the statist...
Deterministic polarization chaos from a laser diode
Virte, Martin; Thienpont, Hugo; Sciamanna, Marc
2014-01-01
Fifty years after the invention of the laser diode and fourty years after the report of the butterfly effect - i.e. the unpredictability of deterministic chaos, it is said that a laser diode behaves like a damped nonlinear oscillator. Hence no chaos can be generated unless with additional forcing or parameter modulation. Here we report the first counter-example of a free-running laser diode generating chaos. The underlying physics is a nonlinear coupling between two elliptically polarized modes in a vertical-cavity surface-emitting laser. We identify chaos in experimental time-series and show theoretically the bifurcations leading to single- and double-scroll attractors with characteristics similar to Lorenz chaos. The reported polarization chaos resembles at first sight a noise-driven mode hopping but shows opposite statistical properties. Our findings open up new research areas that combine the high speed performances of microcavity lasers with controllable and integrated sources of optical chaos.
Yoneda, Minoru; Abe-Ouchi, Ayako; Oguchi, Takashi; Kawahata, Hodaka; Yokoyama, Yusuke
2013-04-01
The impact of climate change is an intriguing focus to invest the replacement of archaic humans, including Neanderthals in Europe, by the modern humans. On the other hand, our ancestor survived in the same/similar environmental settings sharing with archaic human species. The reason why only homo sapience can survive is the important but still challenging task for anthropologists and archaeologists. In the project "Replacement of Neanderthal by Modern Humans: Testing Evolutionary Models of Learning" supported by MEXT, Japan, we have tried to establish more reliable maps of human distribution and climatic zones by developing some new techniques. New data-set for calibrating conventional radiocarbon dates, IntCAl09, makes it possible to compare the archaeological events dated by radiocarbon and the history of climate changes recorded in annual rings in ice cores from the Antarctic and Greenland. Because the replacement was a process ongoing in time and space, however, it is not easy to evaluate the impact of climate change on the extinction of archaic humans. Hence, we are applying several different methods to extract quantitative relationship between the changes in human activities and past climate. Our methods include (1) the development of geoscientific and informatics methodology such as the meta-analysis of large data-set of radiocarbon dating, (2) the reconstruction of climate and vegetation maps in higher resolution based on a global circulation model, (3) reconstructing history of regional environments based on geochemical proxies from land, and (4) the combination and comparison between environmental factors and human distribution using the eco-cultural niche modeling. Each branch of our project has established methods to evaluate the more concrete distribution of past climate and human species in time and space. We would like to discuss the current status of our project and the problems we have to overcome.
Chaos Behaviour of Molecular Orbit
Institute of Scientific and Technical Information of China (English)
LIU Shu-Tang; SUN Fu-Yan; SHEN Shu-Lan
2007-01-01
Based on H(u)ckel's molecular orbit theory,the chaos and;bifurcation behaviour of a molecular orbit modelled by a nonlinear dynamic system is studied.The relationship between molecular orbit and its energy level in the nonlinear dynamic system is obtained.
Distributed chaos in turbulent wakes
Bershadskii, A
2016-01-01
Soft and hard spontaneous breaking of space translational symmetry (homogeneity) have been studied in turbulent wakes by means of distributed chaos. In the case of the soft translational symmetry breaking the vorticity correlation integral $\\int_{V} \\langle {\\boldsymbol \\omega} ({\\bf x},t) \\cdot {\\boldsymbol \\omega} ({\\bf x} + {\\bf r},t) \\rangle_{V} d{\\bf r}$ dominates the distributed chaos and the chaotic spectra $\\exp-(k/k_{\\beta})^{\\beta }$ have $\\beta =1/2$. In the case of the hard translational symmetry breaking, control on the distributed chaos is switched from one type of fundamental symmetry to another (in this case to Lagrangian relabeling symmetry). Due to the Noether's theorem the relabeling symmetry results in the inviscid helicity conservation and helicity correlation integral $I=\\int \\langle h({\\bf x},t)~h({\\bf x}+{\\bf r}, t)\\rangle d{\\bf r}$ (Levich-Tsinober invariant) dominates the distributed chaos with $\\beta =1/3$. Good agreement with the experimatal data has been established for turbulent ...
Wang, Frank Y
2009-01-01
The general public has been made aware of the research field of "chaos" by the book of that title by James Gleick. This paper will focus on the achievements of Sonya Kovalevskaya, Mary Cartwright, and Mary Tsingou, whose pioneer works were not mentioned in Gleick's book.
Lecar, M; Holman, M; Murray, N
2002-01-01
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-period'' 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 10^{12} 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 10^9 times the age of the solar ...
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.
Does chaos assist localization or delocalization?
Energy Technology Data Exchange (ETDEWEB)
Tan, Jintao; 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); Lu, Gengbiao [Department of Physics and Electronic Science, Changsha University of Science and Technology, Changsha 410004 (China)
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.
Controlling neuronal noise using chaos control
Christini, D J; Christini, David J; Collins, James J
1995-01-01
Chaos control techniques have been applied to a wide variety of experimental systems, including magneto-elastic ribbons, lasers, chemical reactions, arrhythmic cardiac tissue, and spontaneously bursting neuronal networks. An underlying assumption in all of these studies is that the system being controlled is chaotic. However, the identification of chaos in experimental systems, particularly physiological systems, is a difficult and often misleading task. Here we demonstrate that the chaos criteria used in a recent study can falsely classify a noise-driven, non-chaotic neuronal model as being chaotic. We apply chaos control, periodic pacing, and anticontrol to the non-chaotic model and obtain results which are similar to those reported for apparently chaotic, {\\em in vitro} neuronal networks. We also obtain similar results when we apply chaos control to a simple stochastic system. These novel findings challenge the claim that the aforementioned neuronal networks were chaotic and suggest that chaos control tech...
Advances in chaos theory and intelligent control
Vaidyanathan, Sundarapandian
2016-01-01
The book reports on the latest advances in and applications of chaos theory and intelligent control. Written by eminent scientists and active researchers and using a clear, matter-of-fact style, it covers advanced theories, methods, and applications in a variety of research areas, and explains key concepts in modeling, analysis, and control of chaotic and hyperchaotic systems. Topics include fractional chaotic systems, chaos control, chaos synchronization, memristors, jerk circuits, chaotic systems with hidden attractors, mechanical and biological chaos, and circuit realization of chaotic systems. The book further covers fuzzy logic controllers, evolutionary algorithms, swarm intelligence, and petri nets among other topics. Not only does it provide the readers with chaos fundamentals and intelligent control-based algorithms; it also discusses key applications of chaos as well as multidisciplinary solutions developed via intelligent control. The book is a timely and comprehensive reference guide for graduate s...
Robust chaos in smooth unimodal maps
Andrecut, M.; Ali, M. K.
2001-08-01
Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhood of the parameter space. It has been conjectured that robust chaos cannot occur in smooth systems [E. Barreto, B. Hunt, and C. Grebogi, Phys. Rev. Lett. 78, 4561 (1997); 80, 3049 (1998)]. Contrary to this conjecture, we describe a general procedure for generating robust chaos in smooth unimodal maps.
How Can We Observe and Describe Chaos?
Kossakowski, A; Togawa, Y; Kossakowski, Andrzej; Ohya, Masanori; Togawa, Yosio
2003-01-01
We propose a new approach to define chaos in dynamical systems from the point of view of Information Dynamics. Observation of chaos in reality depends upon how to observe it, for instance, how to take the scale in space and time. Therefore it is natural to abandon taking several mathematical limiting procedures. We take account of them, and chaos degree previously introduced is redefined in this paper.
Olsen, L F; Degn, H
1977-05-12
Dynamic systems are usually thought to have either monotonic or periodic behaviour. Although the possibility of other types of behaviour has been recognised for many years, the existence of non-monotonic, non-periodic behaviour in dynamic systems has been firmly established only recently. It is termed chaotic behaviour. A review on the rapidly expanding literature on chaos in discrete model systems described by difference equations has been published by May. Rössler, on the other hand, has discussed a few published works on systems of differential equations with chaotic solutions, and he has proposed a three-component chemical model system which he argues has chaotic solutions [figure see text]. The argument is based on a theorem by Li and Yorke. Here we report the finding of chaotic behaviour as an experimental result in an enzyme system (peroxidase). Like Rössler we base our identification of chaos on the theorem by Li and Yorke.
Fitzpatrick, A Liam
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 $\\lambda_L$, which is a diagnostic for the early onset of chaos, receives $1/c$ corrections that may be interpreted as $\\lambda_L = \\frac{2 \\pi}{\\beta} \\left( 1 + \\frac{12}{c} \\right)$. 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 $\\lambda_L$ 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.
The chaos cookbook a practical programming guide
Pritchard, Joe
2014-01-01
The Chaos Cookbook: A Practical Programming Guide discusses the use of chaos in computer programming. The book is comprised of 11 chapters that tackle various topics relevant to chaos and programming. Chapter 1 reviews the concept of chaos, and Chapter 2 discusses the iterative functions. Chapters 3 and 4 cover differential and Lorenz equations. Chapter 5 talks about strange attractors, while Chapter 6 deals with the fractal link. The book also discusses the Mandelbrot set, and then covers the Julia sets. The other fractal systems and the cellular automata are also explained. The last chapter
Random Behaviour in Quantum Chaos
Garbaczewski, P
2001-01-01
We demonstrate that a family of radial Ornstein-Uhlenbeck stochastic processes displays an ergodic behaviour appropriate for known quantum chaos universality classes of nearest neighbour spacing distributions. A common feature of those parametric processes is an asymptotic balance between the radial (Bessel-type) repulsion and the harmonic attraction, as manifested in the general form of forward drifts $b(x) = {{N-1}\\over {2x}} - x$, ($N = 2,3,5$ correspond respectively to the familiar GOE, GUE and GSE cases).
Polynomial-Chaos-based Kriging
Schöbi, R; Sudret, B.; Wiart, J.
2015-01-01
International audience; Computer simulation has become the standard tool in many engineering fields for designing and optimizing systems, as well as for assessing their reliability. Optimization and uncertainty quantification problems typically require a large number of runs of the computational model at hand, which may not be feasible with high-fidelity models directly. Thus surrogate models (a.k.a metamodels) have been increasingly investigated in the last decade. Polynomial Chaos Expansion...
Analysis of FBC deterministic chaos
Energy Technology Data Exchange (ETDEWEB)
Daw, C.S.
1996-06-01
It has recently been discovered that the performance of a number of fossil energy conversion devices such as fluidized beds, pulsed combustors, steady combustors, and internal combustion engines are affected by deterministic chaos. It is now recognized that understanding and controlling the chaotic elements of these devices can lead to significantly improved energy efficiency and reduced emissions. Application of these techniques to key fossil energy processes are expected to provide important competitive advantages for U.S. industry.
Temperature chaos and quenched heterogeneities
Barucca, Paolo; Parisi, Giorgio; Rizzo, Tommaso
2014-03-01
We present a treatable generalization of the Sherrington-Kirkpatrick (SK) model which introduces correlations in the elements of the coupling matrix through multiplicative disorder on the single variables and investigate the consequences on the phase diagram. We define a generalized qEA parameter and test the structural stability of the SK results in this correlated case evaluating the de Almeida-Thouless line of the model. As a main result we demonstrate the increase of temperature chaos effects due to heterogeneities.
Hamiltonian chaos and fractional dynamics
Zaslavsky, George M
2008-01-01
The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology. The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. The book does not follow the traditional scheme of most of today's literature on chaos. The intention of the author has been to put together some of the most complex and yet open problems on the general theory of chaotic systems. The importance of the discussed issues and an understanding of their origin should inspire students and researchers to touch upon some of the deepest aspects of nonlinear dynamics. The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others. It presents a new and realistic image ...
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.
Directory of Open Access Journals (Sweden)
Camilo Rubén Fernández-Cozman
2016-07-01
Full Text Available This article holds that there is a radical ethnocentrism in two essays of Mario Vargas Llosa, Archaic Utopia and Civilization of the Show. In this regard, the Peruvian writer does not recognize a mythical rationality and conceived that legal culture is superior to oral culture.
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 resolut...
Weak chaos in the asymmetric heavy top
Barrientos, M; Ranada, A F
1995-01-01
We consider the dynamics of the slightly asymmetric heavy top, a non-integrable system obtained from the Lagrange top by breaking the symmetry of its inertia tensor. It shows signs of weak chaos, which we study numerically. We argue that it is a good example for introducing students to non-integrability and chaos. (author)
Radio lighting based on dynamic chaos generators
Dmitriev, Alexander; Gerasimov, Mark; Itskov, Vadim
2016-01-01
A problem of lighting objects and surfaces with artificial sources of noncoherent microwave radiation with the aim to observe them using radiometric equipment is considered. Transmitters based on dynamic chaos generators are used as sources of noncoherent wideband microwave radiation. An experimental sample of such a device, i.e., a radio lighting lamp based on a chaos microgenerator and its performance are presented.
"Chaos" Theory: Implications for Educational Research.
Lindsay, Jean S.
"Chaos" theory is a revolutionary new paradigm developed by scientists to study the behavior of natural systems. "Chaos" refers to the tendency of dynamic non-linear systems toward irregular, sometimes unpredictable, yet deterministic behavior. Major tenets of the theory are presented. The precedent for use of models developed in the natural…
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 deter...
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 a...
Chaos in nonlinear oscillations controlling and synchronization
Lakshamanan, M
1996-01-01
This book deals with the bifurcation and chaotic aspects of damped and driven nonlinear oscillators. The analytical and numerical aspects of the chaotic dynamics of these oscillators are covered, together with appropriate experimental studies using nonlinear electronic circuits. Recent exciting developments in chaos research are also discussed, such as the control and synchronization of chaos and possible technological applications.
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 inter...
Unusual biophysics of intrinsically disordered proteins.
Uversky, Vladimir N
2013-05-01
Research of a past decade and a half leaves no doubt that complete understanding of protein functionality requires close consideration of the fact that many functional proteins do not have well-folded structures. These intrinsically disordered proteins (IDPs) and proteins with intrinsically disordered protein regions (IDPRs) are highly abundant in nature and play a number of crucial roles in a living cell. Their functions, which are typically associated with a wide range of intermolecular interactions where IDPs possess remarkable binding promiscuity, complement functional repertoire of ordered proteins. All this requires a close attention to the peculiarities of biophysics of these proteins. In this review, some key biophysical features of IDPs are covered. In addition to the peculiar sequence characteristics of IDPs these biophysical features include sequential, structural, and spatiotemporal heterogeneity of IDPs; their rough and relatively flat energy landscapes; their ability to undergo both induced folding and induced unfolding; the ability to interact specifically with structurally unrelated partners; the ability to gain different structures at binding to different partners; and the ability to keep essential amount of disorder even in the bound form. IDPs are also characterized by the "turned-out" response to the changes in their environment, where they gain some structure under conditions resulting in denaturation or even unfolding of ordered proteins. It is proposed that the heterogeneous spatiotemporal structure of IDPs/IDPRs can be described as a set of foldons, inducible foldons, semi-foldons, non-foldons, and unfoldons. They may lose their function when folded, and activation of some IDPs is associated with the awaking of the dormant disorder. It is possible that IDPs represent the "edge of chaos" systems which operate in a region between order and complete randomness or chaos, where the complexity is maximal. This article is part of a Special Issue
4th international interdisciplinary chaos symposium
Banerjee, Santo; Caglar, Suleyman; Ozer, Mehmet; Chaos and complex systems
2013-01-01
Complexity Science and Chaos Theory are fascinating areas of scientific research with wide-ranging applications. The interdisciplinary nature and ubiquity of complexity and chaos are features that provides scientists with a motivation to pursue general theoretical tools and frameworks. Complex systems give rise to emergent behaviors, which in turn produce novel and interesting phenomena in science, engineering, as well as in the socio-economic sciences. The aim of all Symposia on Chaos and Complex Systems (CCS) is to bring together scientists, engineers, economists and social scientists, and to discuss the latest insights and results obtained in the area of corresponding nonlinear-system complex (chaotic) behavior. Especially for the “4th International Interdisciplinary Chaos Symposium on Chaos and Complex Systems,” which took place April 29th to May 2nd, 2012 in Antalya, Turkey, the scope of the symposium had been further enlarged so as to encompass the presentation of work from circuits to econophysic...
Chaos the science of predictable random motion
Kautz, Richard
2011-01-01
Based on only elementary mathematics, this engaging account of chaos theory bridges the gap between introductions for the layman and college-level texts. It develops the science of dynamics in terms of small time steps, describes the phenomenon of chaos through simple examples, and concludes with a close look at a homoclinic tangle, the mathematical monster at the heart of chaos. The presentation is enhanced by many figures, animations of chaotic motion (available on a companion CD), and biographical sketches of the pioneers of dynamics and chaos theory. To ensure accessibility to motivated high school students, care has been taken to explain advanced mathematical concepts simply, including exponentials and logarithms, probability, correlation, frequency analysis, fractals, and transfinite numbers. These tools help to resolve the intriguing paradox of motion that is predictable and yet random, while the final chapter explores the various ways chaos theory has been put to practical use.
Semiconductor Lasers Stability, Instability and Chaos
Ohtsubo, Junji
2013-01-01
This third edition of “Semiconductor Lasers, Stability, Instability and Chaos” was significantly extended. In the previous edition, the dynamics and characteristics of chaos in semiconductor lasers after the introduction of the fundamental theory of laser chaos and chaotic dynamics induced by self-optical feedback and optical injection was discussed. Semiconductor lasers with new device structures, such as vertical-cavity surface-emitting lasers and broad-area semiconductor lasers, are interesting devices from the viewpoint of chaotic dynamics since they essentially involve chaotic dynamics even in their free-running oscillations. These topics are also treated with respect to the new developments in the current edition. Also the control of such instabilities and chaos control are critical issues for applications. Another interesting and important issue of semiconductor laser chaos in this third edition is chaos synchronization between two lasers and the application to optical secure communication. One o...
Prediction based chaos control via a new neural network
Energy Technology Data Exchange (ETDEWEB)
Shen Liqun [School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001 (China)], E-mail: liqunshen@gmail.com; Wang Mao [Space Control and Inertia Technology Research Center, Harbin Institute of Technology, Harbin 150001 (China); Liu Wanyu [School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001 (China); Sun Guanghui [Space Control and Inertia Technology Research Center, Harbin Institute of Technology, Harbin 150001 (China)
2008-11-17
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.
Energy Technology Data Exchange (ETDEWEB)
Bunimovich, Leonid A., E-mail: bunimovh@math.gatech.edu [ABC Program, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States); School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States); Vela-Arevalo, Luz V., E-mail: luzvela@math.gatech.edu [School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States)
2015-09-15
A 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.
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......Chaotic systems are observed everywhere. Electronic circuit analogues based on the differential equations of the models for the chaotic systems are often used to study the nature of chaotic systems. This tutorial is an attempt to classify electronic chaotic oscillators according to the mechanism...
A. Fitzpatrick; 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 = 2 π β 1 + 12 c $$ {\\lambda}_L=\\frac{2\\pi }{\\beta}\\left(1+\\frac{12}{c}\\right) $$ . 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 ...
Critical states of transient chaos
Kaufmann, Z; Szépfalusy, P
1999-01-01
One-dimensional maps exhibiting transient chaos and defined on two preimages of the unit interval [0,1] are investigated. It is shown that such maps have continuously many conditionally invariant measures $\\mu_{\\sigma}$ scaling at the fixed point at $x=0$ as $x^{\\sigma}$, but smooth elsewhere. Here $\\sigma$ should be smaller than a critical value $\\sigma_{c}$ that is related to the spectral properties of the Frobenius-Perron operator. The corresponding natural measures are proven to be entirely concentrated on the fixed point.
Chaos control in duffing system
Energy Technology Data Exchange (ETDEWEB)
Wang Ruiqi [Department of Electrical Engineering and Electronics, Osaka Sangyo University, Nakagaito 3-1-1, Daito, Osaka 574-8530 (Japan); Deng Jin [Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080 (China); Graduate School of the Chinese Academy of Sciences, Beijing 100039 (China); Jing Zhujun [Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080 (China); Department of Mathematics, Hunan Normal University, Hunan, Changsha 410081 (China); E-mail: jingzj@math.ac.cn
2006-01-01
Analytical and numerical results concerning the inhibition of chaos in Duffing's equation with two weak forcing excitations are presented. We theoretically give parameter-space regions by using Melnikov's function, where chaotic states can be suppressed. The intervals of initial phase difference between the two excitations for which chaotic dynamics can be eliminated are given. Meanwhile, the influence of the phase difference on Lyapunov exponents for different frequencies is investigated. Numerical simulation results show the consistence with the theoretical analysis and the chaotic motions can be controlled to period-motions by adjusting parameter of suppressing excitation.
Institute of Scientific and Technical Information of China (English)
2001-01-01
In this work, we proposed the wavelet-based feedback controller is as follows: G = -g{fab(rrms)-fab(am)} (1)where the master wavelet function is in a simplified form(2)where a and b are scaling and translation constants, respectively. C is a selected constant. The main reason of using wavelet function for controller design is that it has strong nonlinearity and excellent localization property. It turns out that for halo-chaos control purpose, the translation b can be very small, so for simplicity one may let b = 0 . Our goal of control is rms→am, in this
Global Optimal Trajectory in Chaos and NP-Hardness
Latorre, Vittorio; Gao, David Yang
This paper presents an unconventional theory and method for solving general nonlinear dynamical systems. Instead of the direct iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. A newly developed canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by linear iterative methods are mainly due to the intrinsic numerical error accumulations. Otherwise, the global optimization problem could be NP-hard and the nonlinear system can be really chaotic. A conjecture is proposed, which reveals the connection between chaos in nonlinear dynamics and NP-hardness in computer science. The methodology and the conjecture are verified by applications to the well-known logistic equation, a forced memristive circuit and the Lorenz system. Computational results show that the canonical duality theory can be used to identify chaotic systems and to obtain realistic global optimal solutions in nonlinear dynamical systems. The method and results presented in this paper should bring some new insights into nonlinear dynamical systems and NP-hardness in computational complexity theory.
Delay driven spatiotemporal chaos in single species population dynamics models.
Jankovic, Masha; Petrovskii, Sergei; Banerjee, Malay
2016-08-01
Questions surrounding the prevalence of complex population dynamics form one of the central themes in ecology. Limit cycles and spatiotemporal chaos are examples that have been widely recognised theoretically, although their importance and applicability to natural populations remains debatable. The ecological processes underlying such dynamics are thought to be numerous, though there seems to be consent as to delayed density dependence being one of the main driving forces. Indeed, time delay is a common feature of many ecological systems and can significantly influence population dynamics. In general, time delays may arise from inter- and intra-specific trophic interactions or population structure, however in the context of single species populations they are linked to more intrinsic biological phenomena such as gestation or resource regeneration. In this paper, we consider theoretically the spatiotemporal dynamics of a single species population using two different mathematical formulations. Firstly, we revisit the diffusive logistic equation in which the per capita growth is a function of some specified delayed argument. We then modify the model by incorporating a spatial convolution which results in a biologically more viable integro-differential model. Using the combination of analytical and numerical techniques, we investigate the effect of time delay on pattern formation. In particular, we show that for sufficiently large values of time delay the system's dynamics are indicative to spatiotemporal chaos. The chaotic dynamics arising in the wake of a travelling population front can be preceded by either a plateau corresponding to dynamical stabilisation of the unstable equilibrium or by periodic oscillations.
An Experimental Investigation of Secure Communication With Chaos Masking
Dhar, Sourav
2007-01-01
The most exciting recent development in nonlinear dynamics is realization that chaos can be useful. One application involves "Secure Communication". Two piecewise linear systems with switching nonlinearities have been taken as chaos generators. In the present work the phenomenon of secure communication with chaos masking has been investigated experimentally. In this investigation chaos which is generated from two chaos generators is masked with the massage signal to be transmitted, thus makes communication is more secure.
Nonlinear Dynamics and Chaos: Applications in Atmospheric Sciences
Selvam, A M
2010-01-01
Atmospheric flows, an example of turbulent fluid flows, exhibit fractal fluctuations of all space-time scales ranging from turbulence scale of mm - sec to climate scales of thousands of kilometers - years and may be visualized as a nested continuum of weather cycles or periodicities, the smaller cycles existing as intrinsic fine structure of the larger cycles. The power spectra of fractal fluctuations exhibit inverse power law form signifying long - range correlations identified as self - organized criticality and are ubiquitous to dynamical systems in nature and is manifested as sensitive dependence on initial condition or 'deterministic chaos' in finite precision computer realizations of nonlinear mathematical models of real world dynamical systems such as atmospheric flows. Though the self-similar nature of atmospheric flows have been widely documented and discussed during the last three to four decades, the exact physical mechanism is not yet identified. There now exists an urgent need to develop and inco...
Markov transitions and the propagation of chaos
Energy Technology Data Exchange (ETDEWEB)
Gottlieb, Alexander David [Univ. of California, Berkeley, CA (United States)
1998-12-01
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 s how 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.
Chaos dynamic characteristics during mine fires
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Mine fires break out and continue in confmed scopes, studying mine fire dynamics characteristics is very usefulto prevent and control fire. The judgement index of fire chaos characteristics was introduced, chaos analysis of mine Fireprocess was described, and the reconstruction of phase space was also presented. An example of mine fire was calculated.The computations show that it is feasible to analyze mine fire dynamic characteristics with chaos theory, and indicate thatfire preoeas is a catastrophe, that is to say, the fire system changes from one state to another during mine fire
Physics and Applications of Laser Diode Chaos
Sciamanna, Marc
2015-01-01
An overview of chaos in laser diodes is provided which surveys experimental achievements in the area and explains the theory behind the phenomenon. The fundamental physics underpinning this behaviour and also the opportunities for harnessing laser diode chaos for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient test-bed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.
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...
Chua's circuit a paradigm for chaos
1993-01-01
For uninitiated researchers, engineers, and scientists interested in a quick entry into the subject of chaos, this book offers a timely collection of 55 carefully selected papers covering almost every aspect of this subject. Because Chua's circuit is endowed with virtually every bifurcation phenomena reported in the extensive literature on chaos, and because it is the only chaotic system which can be easily built by a novice, simulated in a personal computer, and tractable mathematically, it has become a paradigm for chaos, and a vehicle for illustrating this ubiquitous phenomenon. Its supreme
Semiconductor Lasers Stability, Instability and Chaos
Ohtsubo, Junji
2008-01-01
This monograph describes fascinating recent progress in the field of chaos, stability and instability of semiconductor lasers. Applications and future prospects are discussed in detail. The book emphasizes the various dynamics induced in semiconductor lasers by optical and electronic feedback, optical injection, and injection current modulation. Recent results of both theoretical and experimental investigations are presented. Demonstrating applications of semiconductor laser chaos, control and noise, Semiconductor Lasers describes suppression and chaotic secure communications. For those who are interested in optics but not familiar with nonlinear systems, a brief introduction to chaos analysis is presented.
Chaos from simple models to complex systems
Cencini, Massimo; Vulpiani, Angelo
2010-01-01
Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theor
Uku Masingu luule arhailine kujundisüsteem / The Archaic Figurative System of Uku Masing’s
Directory of Open Access Journals (Sweden)
Külliki Kuusk
2016-01-01
This paper illustrates the importance of the linguistic role of the ”I“ speech act in the interpretation of Masing’s poetic figures, including parallelism, and relies partially on pragmatics, since poetic figures in his poetry refer not only to the individual speech act of the here and now, but also to the subjective mythological reality of the ”I“ in an utterance. To describe a speech event in Masing’s poetry, one must first assume that his poetry is understood as a dialogical sensory or communication act. Secondly, when observing referentiality, one must assume that different levels of language use (i.e., the differentiation of Saussure’s langue and parole also exist, which influence the semantic understanding of the sentence and utterance level of his work. Until recently, the hidden and repetitive patterns in Masing’s work have largely gone unnoticed. To many, his poetic language consists of a lexicon known only to him. When considering the basis of his creative process, I find that conceptual theory of metaphor, a cognitive linguistic approach popularized in the 1980s, helps to make sense of his poetic language system and, additionally, to differentiate the archaic boreal mentality and mytho-poetic symbols containing universal cultural meaning. The current article primarily uses material from Masing’s 1930s body of work, but also references later periods when necessary. I will show how Masing’s creative conscious is based on image schema, which in turn are based on archaic mythological patterns. These patterns form a corresponding system of concept formation in the text. The primary goal of this analysis is to observe Masing’s body of work, regardless of genre, be it poetry or prose, fact or fiction. Although many critics have analyzed Masing’s linguistic and theological ideas, mostly drawing from his essays and articles, this paper’s author finds that Masing’s poetry and essays are not two separate phenomena, but rather originate
Zaheer, Muhammad Hamad; Rehan, Muhammad; Mustafa, Ghulam; Ashraf, Muhammad
2014-11-01
This paper proposes a novel state feedback delay-range-dependent control approach for chaos synchronization in coupled nonlinear time-delay systems. The coupling between two systems is esteemed to be nonlinear subject to time-lags. Time-varying nature of both the intrinsic and the coupling delays is incorporated to broad scope of the present study for a better-quality synchronization controller synthesis. Lyapunov-Krasovskii (LK) functional is employed to derive delay-range-dependent conditions that can be solved by means of the conventional linear matrix inequality (LMI)-tools. The resultant control approach for chaos synchronization of the master-slave time-delay systems considers non-zero lower bound of the intrinsic as well as the coupling time-delays. Further, the delay-dependent synchronization condition has been established as a special case of the proposed LK functional treatment. Furthermore, a delay-range-dependent condition, independent of the delay-rate, has been provided to address the situation when upper bound of the delay-derivative is unknown. A robust state feedback control methodology is formulated for synchronization of the time-delay chaotic networks against the L2 norm bounded perturbations by minimizing the L2 gain from the disturbance to the synchronization error. Numerical simulation results are provided for the time-delay chaotic networks to show effectiveness of the proposed delay-range-dependent chaos synchronization methodologies.
Chaos concepts, control and constructive use
Bolotin, Yurii; Yanovsky, Vladimir
2017-01-01
This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interf...
Superfluid (quantum) turbulence and distributed chaos
Bershadskii, A
2016-01-01
Properties of distributed chaos in superfluid (quantum) turbulence have been studied using the data of recent direct numerical simulations (HVBK two-fluid model for He II, and a moving grid in the frames of Gross-Pitaevskii model of the Bose-Einstein condensates at low temperatures). It is found that for the viscous (normal) component of the velocity field in He II the viscosity dominates the distributed chaos with the stretched exponential spectrum $\\exp(-k/k_{\\beta})^{\\beta}$ and $\\beta = 2/3$. For the superfluid component the distributed chaos is dominated by the vorticity correlation integral with $\\beta =1/2$ (the soft spontaneous breaking of the space translational symmetry - homogeneity). For very low temperature the distributed chaos is tuned to the large-scale coherent motions: the viscous (normal) component is tuned to the fundamental mode, whereas the superfluid component is subharmonically tuned. For the Gross-Pitaevskii superfluid turbulence incompressible part of the energy spectrum (containing ...
Optimized chaos control with simple limiters.
Wagner, C; Stoop, R
2001-01-01
We present an elementary derivation of chaos control with simple limiters using the logistic map and the Henon map as examples. This derivation provides conditions for optimal stabilization of unstable periodic orbits of a chaotic attractor.
A simple method of chaos control
Shahverdiev, E M
1998-01-01
A simple method to perform chaos control without the need of complex numerical and analytical calculations is proposed. The method works for dynamical systems with bounded solutions and in the trivial case of constant Jacobians.
Compressive Sensing with Optical Chaos
Rontani, D.; Choi, D.; Chang, C.-Y.; Locquet, A.; Citrin, D. S.
2016-12-01
Compressive sensing (CS) is a technique to sample a sparse signal below the Nyquist-Shannon limit, yet still enabling its reconstruction. As such, CS permits an extremely parsimonious way to store and transmit large and important classes of signals and images that would be far more data intensive should they be sampled following the prescription of the Nyquist-Shannon theorem. CS has found applications as diverse as seismology and biomedical imaging. In this work, we use actual optical signals generated from temporal intensity chaos from external-cavity semiconductor lasers (ECSL) to construct the sensing matrix that is employed to compress a sparse signal. The chaotic time series produced having their relevant dynamics on the 100 ps timescale, our results open the way to ultrahigh-speed compression of sparse signals.
Detecting chaos from time series
Xiaofeng, Gong; Lai, C. H.
2000-02-01
In this paper, an entirely data-based method to detect chaos from the time series is developed by introducing icons/Journals/Common/epsilon" ALT="epsilon" ALIGN="TOP"/> p -neighbour points (the p -steps icons/Journals/Common/epsilon" ALT="epsilon" ALIGN="TOP"/> -neighbour points). We demonstrate that for deterministic chaotic systems, there exists a linear relationship between the logarithm of the average number of icons/Journals/Common/epsilon" ALT="epsilon" ALIGN="TOP"/> p -neighbour points, lnn p ,icons/Journals/Common/epsilon" ALT="epsilon" ALIGN="TOP"/> , and the time step, p . The coefficient can be related to the KS entropy of the system. The effects of the embedding dimension and noise are also discussed.
Chaos, Fractals and Their Applications
Thompson, J. Michael T.
2016-12-01
This paper gives an up-to-date account of chaos and fractals, in a popular pictorial style for the general scientific reader. A brief historical account covers the development of the subject from Newton’s laws of motion to the astronomy of Poincaré and the weather forecasting of Lorenz. Emphasis is given to the important underlying concepts, embracing the fractal properties of coastlines and the logistics of population dynamics. A wide variety of applications include: NASA’s discovery and use of zero-fuel chaotic “superhighways” between the planets; erratic chaotic solutions generated by Euler’s method in mathematics; atomic force microscopy; spontaneous pattern formation in chemical and biological systems; impact mechanics in offshore engineering and the chatter of cutting tools; controlling chaotic heartbeats. Reference is made to a number of interactive simulations and movies accessible on the web.
Control of collective network chaos
Energy Technology Data Exchange (ETDEWEB)
Wagemakers, Alexandre, E-mail: alexandre.wagemakers@urjc.es; Sanjuán, Miguel A. F., E-mail: miguel.sanjuan@urjc.es [Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid (Spain); Barreto, Ernest, E-mail: ebarreto@gmu.edu; So, Paul, E-mail: paso@gmu.edu [School of Physics, Astronomy, and Computational Sciences and The Krasnow Institute for Advanced Study, George Mason University, Fairfax, Virginia 22030 (United States)
2014-06-01
Under certain conditions, the collective behavior of a large globally-coupled heterogeneous network of coupled oscillators, as quantified by the macroscopic mean field or order parameter, can exhibit low-dimensional chaotic behavior. Recent advances describe how a small set of “reduced” ordinary differential equations can be derived that captures this mean field behavior. Here, we show that chaos control algorithms designed using the reduced equations can be successfully applied to imperfect realizations of the full network. To systematically study the effectiveness of this technique, we measure the quality of control as we relax conditions that are required for the strict accuracy of the reduced equations, and hence, the controller. Although the effects are network-dependent, we show that the method is effective for surprisingly small networks, for modest departures from global coupling, and even with mild inaccuracy in the estimate of network heterogeneity.
Control of collective network chaos
Wagemakers, Alexandre; Barreto, Ernest; Sanjuán, Miguel A. F.; So, Paul
2014-06-01
Under certain conditions, the collective behavior of a large globally-coupled heterogeneous network of coupled oscillators, as quantified by the macroscopic mean field or order parameter, can exhibit low-dimensional chaotic behavior. Recent advances describe how a small set of "reduced" ordinary differential equations can be derived that captures this mean field behavior. Here, we show that chaos control algorithms designed using the reduced equations can be successfully applied to imperfect realizations of the full network. To systematically study the effectiveness of this technique, we measure the quality of control as we relax conditions that are required for the strict accuracy of the reduced equations, and hence, the controller. Although the effects are network-dependent, we show that the method is effective for surprisingly small networks, for modest departures from global coupling, and even with mild inaccuracy in the estimate of network heterogeneity.
Sándor, Bulcsú; Tél, Tamás; Néda, Zoltán
2013-01-01
The dynamics of a spring-block train placed on a moving conveyor belt is investigated both by simple experiments and computer simulations. The first block is connected by spring to an external static point, and due to the dragging effect of the belt the blocks undergo complex stick-slip dynamics. A qualitative agreement with the experimental results can only be achieved by taking into account the spatial inhomogeneity of the friction force on the belt's surface, modeled as noise. As a function of the velocity of the conveyor belt and the noise strength, the system exhibits complex, self-organized critical, sometimes chaotic dynamics and phase transition-like behavior. Noise induced chaos and intermittency is also observed. Simulations suggest that the maximum complexity of the dynamical states is achieved for a relatively small number of blocks, around five.
Ergodic theory, randomness, and "chaos".
Ornstein, D S
1989-01-13
Ergodic theory is the theory of the long-term statistical behavior of dynamical systems. The baker's transformation is an object of ergodic theory that provides a paradigm for the possibility of deterministic chaos. It can now be shown that this connection is more than an analogy and that at some level of abstraction a large number of systems governed by Newton's laws are the same as the baker's transformation. Going to this level of abstraction helps to organize the possible kinds of random behavior. The theory also gives new concrete results. For example, one can show that the same process could be produced by a mechanism governed by Newton's laws or by a mechanism governed by coin tossing. It also gives a statistical analog of structural stability.
Engel, J
2006-01-01
The Hohenberg-Kohn theorem and Kohn-Sham procedure are extended to functionals of the localized intrinsic density of a self-bound system such as a nucleus. After defining the intrinsic-density functional, we modify the usual Kohn-Sham procedure slightly to evaluate the mean-field approximation to the functional, and carefully describe the construction of the leading corrections for a system of fermions in one dimension with a spin-degeneracy equal to the number of particles N. Despite the fact that the corrections are complicated and nonlocal, we are able to construct a local Skyrme-like intrinsic-density functional that, while different from the exact functional, shares with it a minimum value equal to the exact ground-state energy at the exact ground-state intrinsic density, to next-to-leading order in 1/N. We briefly discuss implications for real Skyrme functionals.
Terminal chaos for information processing in neurodynamics.
Zak, M
1991-01-01
New nonlinear phenomenon-terminal chaos caused by failure of the Lipschitz condition at equilibrium points of dynamical systems is introduced. It is shown that terminal chaos has a well organized probabilistic structure which can be predicted and controlled. This gives an opportunity to exploit this phenomenon for information processing. It appears that chaotic states of neurons activity are associated with higher level of cognitive processes such as generalization and abstraction.
Thiel, Marco; Kurths, Jürgen; Romano, M. Carmen; Moura, Alessandro; Károlyi, György
In the celebratory dinner honouring Celso Grebogi's 60th birthday, a number of scientists in the area of chaos were asked by James Yorke to tell the tale about how they got involved in the field. Since all the participants have played crucial roles in the development of the subject, their stories give unique insights into the historical development of dynamical systems and chaos. We have transcribed their tales here.
Detecting nonlinearity and chaos in epidemic data
Energy Technology Data Exchange (ETDEWEB)
Ellner, S.; Gallant, A.R. [North Carolina State Univ., Raleigh, NC (United States). Dept. of Statistics; Theiler, J. [Santa Fe Inst., NM (United States)]|[Los Alamos National Lab., NM (United States)
1993-08-01
Historical data on recurrent epidemics have been central to the debate about the prevalence of chaos in biological population dynamics. Schaffer and Kot who first recognized that the abundance and accuracy of disease incidence data opened the door to applying a range of methods for detecting chaos that had been devised in the early 1980`s. Using attractor reconstruction, estimates of dynamical invariants, and comparisons between data and simulation of SEIR models, the ``case for chaos in childhood epidemics`` was made through a series of influential papers beginning in the mid 1980`s. The proposition that the precise timing and magnitude of epidemic outbreaks are deterministic but chaotic is appealing, since it raises the hope of finding determinism and simplicity beneath the apparently stochastic and complicated surface of the data. The initial enthusiasm for methods of detecting chaos in data has been followed by critical re-evaluations of their limitations. Early hopes of a ``one size fits all`` algorithm to diagnose chaos vs. noise in any data set have given way to a recognition that a variety of methods must be used, and interpretation of results must take into account the limitations of each method and the imperfections of the data. Our goals here are to outline some newer methods for detecting nonlinearity and chaos that have a solid statistical basis and are suited to epidemic data, and to begin a re-evaluation of the claims for nonlinear dynamics and chaos in epidemics using these newer methods. We also identify features of epidemic data that create problems for the older, better known methods of detecting chaos. When we ask ``are epidemics nonlinear?``, we are not questioning the existence of global nonlinearities in epidemic dynamics, such as nonlinear transmission rates. Our question is whether the data`s deviations from an annual cyclic trend (which would reflect global nonlinearities) are described by a linear, noise-driven stochastic process.
Chaos control using sliding-mode theory
Energy Technology Data Exchange (ETDEWEB)
Nazzal, Jamal M. [Faculty of Engineering, Al-Ahliyya Amman University, Post Code 19328 Amman (Jordan)]. E-mail: jnazzal@ammanu.edu.jo; Natsheh, Ammar N. [Faculty of Engineering, Al-Ahliyya Amman University, Post Code 19328 Amman (Jordan)
2007-07-15
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.
Chaos control in traffic flow models
Shahverdiev, E M; Shahverdiev, Elman Mohammed; Tadaki, Shin-ichi
1998-01-01
Chaos control in some of the one- and two-dimensional traffic flow dynamical models in the mean field theory is studied.One dimensional model is investigated taking into account the effect of random delay. Two dimensional model takes into account the effects of overpasses, symmetric distribution of cars and blockages of cars moving in the same direction. Chaos synchronization is performed within both replica and nonreplica approaches, and using parameter perturbation method.
Yang, Melinda A; Harris, Kelley; Slatkin, Montgomery
2014-12-01
We introduce a method for comparing a test genome with numerous genomes from a reference population. Sites in the test genome are given a weight, w, that depends on the allele frequency, x, in the reference population. The projection of the test genome onto the reference population is the average weight for each x, [Formula: see text]. The weight is assigned in such a way that, if the test genome is a random sample from the reference population, then [Formula: see text]. Using analytic theory, numerical analysis, and simulations, we show how the projection depends on the time of population splitting, the history of admixture, and changes in past population size. The projection is sensitive to small amounts of past admixture, the direction of admixture, and admixture from a population not sampled (a ghost population). We compute the projections of several human and two archaic genomes onto three reference populations from the 1000 Genomes project-Europeans, Han Chinese, and Yoruba-and discuss the consistency of our analysis with previously published results for European and Yoruba demographic history. Including higher amounts of admixture between Europeans and Yoruba soon after their separation and low amounts of admixture more recently can resolve discrepancies between the projections and demographic inferences from some previous studies.
Chaos in World Politics: A Reflection
Ferreira, Manuel Alberto Martins; Filipe, José António Candeias Bonito; Coelho, Manuel F. P.; Pedro, Isabel C.
Chaos theory results from natural scientists' findings in the area of non-linear dynamics. The importance of related models has increased in the last decades, by studying the temporal evolution of non-linear systems. In consequence, chaos is one of the concepts that most rapidly have been expanded in what research topics respects. Considering that relationships in non-linear systems are unstable, chaos theory aims to understand and to explain this kind of unpredictable aspects of nature, social life, the uncertainties, the nonlinearities, the disorders and confusion, scientifically it represents a disarray connection, but basically it involves much more than that. The existing close relationship between change and time seems essential to understand what happens in the basics of chaos theory. In fact, this theory got a crucial role in the explanation of many phenomena. The relevance of this kind of theories has been well recognized to explain social phenomena and has permitted new advances in the study of social systems. Chaos theory has also been applied, particularly in the context of politics, in this area. The goal of this chapter is to make a reflection on chaos theory - and dynamical systems such as the theories of complexity - in terms of the interpretation of political issues, considering some kind of events in the political context and also considering the macro-strategic ideas of states positioning in the international stage.
Chaos and Quantumlike Mechanics in Atmospheric Flows A Superstring Theory for Supergravity
Selvam, A M
1997-01-01
The author has identified quantumlike mechanics in atmospheric flows with intrinsic nonlocal space-time connections manifested as the selfsimilar fractal geometry to the global cloud cover pattern concomitant with inverse power law form for power spectra of temporal fluctuations. Such long-range spatiotemporal correlations are generic to dynamical systems in nature and are recently identified as signatures of selforganized criticality, a field of study belonging to the newly emerging discipline of nonlinear dynamics and chaos. The author has presented a universal thory of chaos which postulates that spatial integration of enclosed small scale fluctuations result in the generation of a hierarchical scale invariant eddy continuum(network) with ordered two-way energy flow between the scales. The model concepts lead to the following results. (1) The eddy energy spectrum follows normal distribution characteristics,i.e.,the square of the eddy amplitude represents the probability density,a result which is observed i...
Cantorian Fractal Patterns, Quantum-Like Chaos and Prime Numbers in Atmospheric Flows
Selvam, A M; Fadnavis, Suvarna
1998-01-01
Atmospheric flows exhibit cantorian fractal space-time fluctuations signifying long-range spatiotemporal correlations. A recently developed cell dynamical system model shows that such non-local connections are intrinsic to quantum-like chaos governing flow dynamics. The dynamical evolution of fractal structures can be quantified in terms of ordered energy flow described by mathematical functions which occur in the field of number theory. The quantum-like chaos in atmospheric flows can be quantified in terms of the following mathematical functions / concepts: (1) The fractal structure of the flow pattern is resolved into an overall logarithmic spiral trajectory with the quasiperiodic Penrose tiling pattern for the internal structure and is equivalent to a hierarchy of vortices. The incorporation of Fibonacci mathematical series, representative of ramified bifurcations, indicates ordered growth of fractal patterns. (2) The steady state emergence of progressively larger fractal structures incorporates unique pri...
Chaos control applied to piezoelectric vibration-based energy harvesting systems
Barbosa, W. O. V.; De Paula, A. S.; Savi, M. A.; Inman, D. J.
2015-11-01
Chaotic behavior presents intrinsic richness due to the existence of an infinity number of unstable periodic orbits (UPOs). The possibility of stabilizing these periodic patterns with a small amount of energy makes this kind of response interesting to various dynamical systems. Energy harvesting has as a goal the use of available mechanical energy by promoting a conversion into electrical energy. The combination of these two approaches may establish autonomous systems where available environmental mechanical energy can be employed for control purposes. Two different goals can be defined as priority, allowing a change between them: vibration reduction and energy harvesting enhancement. This work deals with the use of harvested energy to perform chaos control. Both control actuation and energy harvesting are induced employing piezoelectric materials, in a simultaneous way. A bistable piezomagnetoelastic structure subjected to harmonic excitations is investigated as a case study. Numerical simulations show situations where it is possible to perform chaos control using only the energy generated by the harvesting system.
CHAOS III: Gas-Phase Abundances in NGC5457
Croxall, Kevin; Berg, Danielle A; Skillman, Evan D; Moustakas, John
2016-01-01
The CHemical Abundances of Spirals (CHAOS) project leverages the combined power of the Large Binocular Telescope with the broad spectral range and sensitivity of the Multi Object Double Spectrograph (MODS) to measure direct abundances in large samples of HII regions in spiral galaxies. We present LBT MODS observations of 109 Hii regions in NGC5457, of which 74 have robust measurements of key auroral lines, a factor of 3 larger than all previous published detections of auroral lines in the HII regions of NGC5457. Comparing the temperatures derived from the different ionic species we find: (1) strong correlations of T[NII] with T[SIII] and T[OIII], consistent with little or no intrinsic scatter; (2) a correlation of T[SIII] with T[OIII], but with significant intrinsic dispersion; (3) overall agreement between T[NII], T[SII], and T[OII], as expected, but with significant outliers; (4) the correlations of T[NII] with T[SIII] and T[OIII] match the predictions of photoionization modeling while the correlation of T[...
Genome chaos: survival strategy during crisis.
Liu, Guo; Stevens, Joshua B; Horne, Steven D; Abdallah, Batoul Y; Ye, Karen J; Bremer, Steven W; Ye, Christine J; Chen, David J; Heng, Henry H
2014-01-01
Genome chaos, a process of complex, rapid genome re-organization, results in the formation of chaotic genomes, which is followed by the potential to establish stable genomes. It was initially detected through cytogenetic analyses, and recently confirmed by whole-genome sequencing efforts which identified multiple subtypes including "chromothripsis", "chromoplexy", "chromoanasynthesis", and "chromoanagenesis". Although genome chaos occurs commonly in tumors, both the mechanism and detailed aspects of the process are unknown due to the inability of observing its evolution over time in clinical samples. Here, an experimental system to monitor the evolutionary process of genome chaos was developed to elucidate its mechanisms. Genome chaos occurs following exposure to chemotherapeutics with different mechanisms, which act collectively as stressors. Characterization of the karyotype and its dynamic changes prior to, during, and after induction of genome chaos demonstrates that chromosome fragmentation (C-Frag) occurs just prior to chaotic genome formation. Chaotic genomes seem to form by random rejoining of chromosomal fragments, in part through non-homologous end joining (NHEJ). Stress induced genome chaos results in increased karyotypic heterogeneity. Such increased evolutionary potential is demonstrated by the identification of increased transcriptome dynamics associated with high levels of karyotypic variance. In contrast to impacting on a limited number of cancer genes, re-organized genomes lead to new system dynamics essential for cancer evolution. Genome chaos acts as a mechanism of rapid, adaptive, genome-based evolution that plays an essential role in promoting rapid macroevolution of new genome-defined systems during crisis, which may explain some unwanted consequences of cancer treatment.
Lorentz invariant intrinsic decoherence
Milburn, G J
2003-01-01
Quantum decoherence can arise due to classical fluctuations in the parameters which define the dynamics of the system. In this case decoherence, and complementary noise, is manifest when data from repeated measurement trials are combined. Recently a number of authors have suggested that fluctuations in the space-time metric arising from quantum gravity effects would correspond to a source of intrinsic noise, which would necessarily be accompanied by intrinsic decoherence. This work extends a previous heuristic modification of Schr\\"{o}dinger dynamics based on discrete time intervals with an intrinsic uncertainty. The extension uses unital semigroup representations of space and time translations rather than the more usual unitary representation, and does the least violence to physically important invariance principles. Physical consequences include a modification of the uncertainty principle and a modification of field dispersion relations, in a way consistent with other modifications suggested by quantum grav...
Chaos in Black holes Surrounded by Electromagnetic Fields
Santoprete, Manuele; Cicogna, Giampaolo
2001-01-01
In this paper we prove the occurence of chaos for charged particles moving around a Schwarzshild black hole, perturbed by uniform electric and magnetic fields. The appearance of chaos is studied resorting to the Poincare'-Melnikov method.
Intrinsic Time Quantum Geometrodynamics
Ita, Eyo Eyo; Yu, Hoi-Lai
2015-01-01
Quantum Geometrodynamics with intrinsic time development and momentric variables is presented. An underlying SU(3) group structure at each spatial point regulates the theory. The intrinsic time behavior of the theory is analyzed, together with its ground state and primordial quantum fluctuations. Cotton-York potential dominates at early times when the universe was small; the ground state naturally resolves Penrose's Weyl Curvature Hypothesis, and thermodynamic and gravitational `arrows of time' point in the same direction. Ricci scalar potential corresponding to Einstein's General Relativity emerges as a zero-point energy contribution. A new set of fundamental canonical commutation relations without Planck's constant emerges from the unification of Gravitation and Quantum Mechanics.
Some Remarks on Distributional Chaos for Linear Operators
Institute of Scientific and Technical Information of China (English)
TIAN GENG; Hou BING-ZHE; Ji You-qing
2011-01-01
In this paper,we consider some properties for bounded linear operators concerning distributional chaos.Norm-unimodality of bounded linear operators implies distributional chaos.Some properties such as similarity and spectra description for norm-unimodal operators are considered.The existence of distributional chaos in nest algebra is also proved.In addition,we obtain a sufficient and necessary condition of distributional chaos for a class of operators,which contains unilateral backward weighted shift operators.
2nd International Symposium on Chaos, Complexity and Leadership
Banerjee, Santo
2015-01-01
These proceedings from the 2013 symposium on "Chaos, complexity and leadership" reflect current research results from all branches of Chaos, Complex Systems and their applications in Management. Included are the diverse results in the fields of applied nonlinear methods, modeling of data and simulations, as well as theoretical achievements of Chaos and Complex Systems. Also highlighted are Leadership and Management applications of Chaos and Complexity Theory.
Controlling Beam Halo-chaos Using a Special Nonlinear Method
Institute of Scientific and Technical Information of China (English)
2002-01-01
Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applications in industry,medicine, and national defense. Some general engineering methods for chaos control have been developedin recent years, but they generally are unsuccessful for beam halo-chaos suppression due to manytechnical constraints. Beam halo-chaos is essentially a spatotemporal chaotic motion within a high power
Regularly timed events amid chaos
Blakely, Jonathan N.; Cooper, Roy M.; Corron, Ned J.
2015-11-01
We show rigorously that the solutions of a class of chaotic oscillators are characterized by regularly timed events in which the derivative of the solution is instantaneously zero. The perfect regularity of these events is in stark contrast with the well-known unpredictability of chaos. We explore some consequences of these regularly timed events through experiments using chaotic electronic circuits. First, we show that a feedback loop can be implemented to phase lock the regularly timed events to a periodic external signal. In this arrangement the external signal regulates the timing of the chaotic signal but does not strictly lock its phase. That is, phase slips of the chaotic oscillation persist without disturbing timing of the regular events. Second, we couple the regularly timed events of one chaotic oscillator to those of another. A state of synchronization is observed where the oscillators exhibit synchronized regular events while their chaotic amplitudes and phases evolve independently. Finally, we add additional coupling to synchronize the amplitudes, as well, however in the opposite direction illustrating the independence of the amplitudes from the regularly timed events.
Energy Technology Data Exchange (ETDEWEB)
Dattani, Justine [Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath BA2 7AY (United Kingdom); Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA (United Kingdom); Blake, Jack C.H. [Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath BA2 7AY (United Kingdom); Hilker, Frank M., E-mail: f.hilker@bath.ac.uk [Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath BA2 7AY (United Kingdom)
2011-10-31
Designing intervention methods to control chaotic behavior in dynamical systems remains a challenging problem, in particular for systems that are difficult to access or to measure. We propose a simple, intuitive technique that modifies the values of the state variables directly toward a certain target. The intervention takes into account the difference to the target value, and is a combination of traditional proportional feedback and constant feedback methods. It proves particularly useful when the target corresponds to the equilibrium of the uncontrolled system, and is available or can be estimated from expert knowledge (e.g. in biology and economy). -- Highlights: → We propose a chaos control method that forces the system to a certain target. → The intervention takes into account the difference to the target value. → It can be seen as a combination of proportional and constant feedback methods. → The method is very robust and highly efficient in the long-term. → It is particularly applicable when suitable target values are known or available.
Generic superweak chaos induced by Hall effect.
Ben-Harush, Moti; Dana, Itzhack
2016-05-01
We introduce and study the "kicked Hall system" (KHS), i.e., charged particles periodically kicked in the presence of uniform magnetic (B) and electric (E) fields that are perpendicular to each other and to the kicking direction. We show that for resonant values of B and E and in the weak-chaos regime of sufficiently small nonintegrability parameter κ (the kicking strength), there exists a generic family of periodic kicking potentials for which the Hall effect from B and E significantly suppresses the weak chaos, replacing it by "superweak" chaos (SWC). This means that the system behaves as if the kicking strength were κ^{2} rather than κ. For E=0, SWC is known to be a classical fingerprint of quantum antiresonance, but it occurs under much less generic conditions, in particular only for very special kicking potentials. Manifestations of SWC are a decrease in the instability of periodic orbits and a narrowing of the chaotic layers, relative to the ordinary weak-chaos case. Also, for global SWC, taking place on an infinite "stochastic web" in phase space, the chaotic diffusion on the web is much slower than the weak-chaos one. Thus, the Hall effect can be relatively stabilizing for small κ. In some special cases, the effect is shown to cause ballistic motion for almost all parameter values. The generic global SWC on stochastic webs in the KHS appears to be the two-dimensional closest analog to the Arnol'd web in higher dimensional systems.
The Capabilities of Chaos and Complexity
Directory of Open Access Journals (Sweden)
David L. Abel
2009-01-01
Full Text Available To what degree could chaos and complexity have organized a Peptide or RNA World of crude yet necessarily integrated protometabolism? How far could such protolife evolve in the absence of a heritable linear digital symbol system that could mutate, instruct, regulate, optimize and maintain metabolic homeostasis? To address these questions, chaos, complexity, self-ordered states, and organization must all be carefully defined and distinguished. In addition their cause-and-effect relationships and mechanisms of action must be delineated. Are there any formal (non physical, abstract, conceptual, algorithmic components to chaos, complexity, self-ordering and organization, or are they entirely physicodynamic (physical, mass/energy interaction alone? Chaos and complexity can produce some fascinating self-ordered phenomena. But can spontaneous chaos and complexity steer events and processes toward pragmatic benefit, select function over non function, optimize algorithms, integrate circuits, produce computational halting, organize processes into formal systems, control and regulate existing systems toward greater efficiency? The question is pursued of whether there might be some yet-to-be discovered new law of biology that will elucidate the derivation of prescriptive information and control. Ã¢Â€ÂœSystemÃ¢Â€Â will be rigorously defined. Can a low-informational rapid succession of PrigogineÃ¢Â€Â™s dissipative structures self-order into bona fide organization?
Chaos Theory as a Model for Managing Issues and Crises.
Murphy, Priscilla
1996-01-01
Uses chaos theory to model public relations situations in which the salient feature is volatility of public perceptions. Discusses the premises of chaos theory and applies them to issues management, the evolution of interest groups, crises, and rumors. Concludes that chaos theory is useful as an analogy to structure image problems and to raise…
Chaos control and synchronization in a fractional neuron network system
Energy Technology Data Exchange (ETDEWEB)
Zhou Shangbo [Computer Department of Chongqing University, Chongqing 400044 (China); Li Hua [Department of Mathematics and Computer Science, University of Lethbridge, T1K 3M4 (Canada)], E-mail: hua.li@uleth.ca; Zhu Zhengzhou [Computer Department of Chongqing University, Chongqing 400044 (China)
2008-05-15
In this paper, an algorithm of numerical solution for fractional differential equations is presented. Chaos in a neuron network system is also illustrated. Moreover, chaos feedback control and synchronization systems are constructed. The study and experiment indicate that the chaos in fractional order neuron networks could be controlled and synchronized.
Predicting Intrinsic Motivation
Martens, Rob; Kirschner, Paul A.
2004-01-01
Intrinsic motivation can be predicted from participants' perceptions of the social environment and the task environment (Ryan & Deci, 2000)in terms of control, relatedness and competence. To determine the degree of independence of these factors 251 students in higher vocational education (physiotherapy and hotel management) indicated the extent to…
Controlling chaos in ecology: from deterministic to individual-based models.
Solé, R V; Gamarra, J G; Ginovart, M; López, D
1999-11-01
The possibility of chaos control in biological systems has been stimulated by recent advances in the study of heart and brain tissue dynamics. More recently, some authors have conjectured that such a method might be applied to population dynamics and even play a nontrivial evolutionary role in ecology. In this paper we explore this idea by means of both mathematical and individual-based simulation models. Because of the intrinsic noise linked to individual behavior, controlling a noisy system becomes more difficult but, as shown here, it is a feasible task allowed to be experimentally tested.
Nonlinear dynamics and quantum chaos an introduction
Wimberger, Sandro
2014-01-01
The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.
Hyperbolic Chaos A Physicist’s View
Kuznetsov, Sergey P
2012-01-01
"Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos. This book is designed as a reference work for university professors and researchers in the fields of physics, mechanics, and engineering. Dr. Sergey P. Kuznetsov is a professor at the Department of Nonlinear Processes, Saratov State University, Russia.
Avoiding Quantum Chaos in Quantum Computation
Berman, G P; Izrailev, F M; Tsifrinovich, V I
2001-01-01
We study a one-dimensional chain of nuclear $1/2-$spins in an external time-dependent magnetic field. This model is considered as a possible candidate for experimental realization of quantum computation. According to the general theory of interacting particles, one of the most dangerous effects is quantum chaos which can destroy the stability of quantum operations. According to the standard viewpoint, the threshold for the onset of quantum chaos due to an interaction between spins (qubits) strongly decreases with an increase of the number of qubits. Contrary to this opinion, we show that the presence of a magnetic field gradient helps to avoid quantum chaos which turns out to disappear with an increase of the number of qubits. We give analytical estimates which explain this effect, together with numerical data supporting
Nonlinear Physics Integrability, Chaos and Beyond
Lakshmanan, M
1997-01-01
Integrability and chaos are two of the main concepts associated with nonlinear physical systems which have revolutionized our understanding of them. Highly stable exponentially localized solitons are often associated with many of the important integrable nonlinear systems while motions which are sensitively dependent on initial conditions are associated with chaotic systems. Besides dramatically raising our perception of many natural phenomena, these concepts are opening up new vistas of applications and unfolding technologies: Optical soliton based information technology, magnetoelectronics, controlling and synchronization of chaos and secure communications, to name a few. These developments have raised further new interesting questions and potentialities. We present a particular view of some of the challenging problems and payoffs ahead in the next few decades by tracing the early historical events, summarizing the revolutionary era of 1950-70 when many important new ideas including solitons and chaos were ...
Nonlinear Dynamics and Chaos: Advances and Perspectives
Thiel, Marco; Romano, M. Carmen; Károlyi, György; Moura, Alessandro
2010-01-01
This book is a collection of contributions on various aspects of active frontier research in the field of dynamical systems and chaos. Each chapter examines a specific research topic and, in addition to reviewing recent results, also discusses future perspectives. The result is an invaluable snapshot of the state of the field by some of its most important researchers. The first contribution in this book, "How did you get into Chaos?", is actually a collection of personal accounts by a number of distinguished scientists on how they entered the field of chaos and dynamical systems, featuring comments and recollections by James Yorke, Harry Swinney, Floris Takens, Peter Grassberger, Edward Ott, Lou Pecora, Itamar Procaccia, Michael Berry, Giulio Casati, Valentin Afraimovich, Robert MacKay, and last but not least, Celso Grebogi, to whom this volume is dedicated.
Chaos Concepts, Control and Constructive Use
Bolotin, Yurii; Yanovsky, Vladimir
2009-01-01
The study of chaotic behaviour in nonlinear, dynamical systems is now a well established research domain with ramifications into all fields of sciences, spanning a vast range of applications, from celestial mechanics, via climate change, to the functioning of brownian motors in cells. A more recent discovery is that chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter itself for the system under investigation, stochastic resonance being a prime example. The present work is putting emphasis on the latter aspects, and after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing relevant algorithms for both Hamiltonian and dissipative systems amongst others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance and a survey of ratchet models. This short and concise pr...
Ventilatory chaos is impaired in carotid atherosclerosis.
Directory of Open Access Journals (Sweden)
Laurence Mangin
Full Text Available Ventilatory chaos is strongly linked to the activity of central pattern generators, alone or influenced by respiratory or cardiovascular afferents. We hypothesized that carotid atherosclerosis should alter ventilatory chaos through baroreflex and autonomic nervous system dysfunctions. Chaotic dynamics of inspiratory flow was prospectively evaluated in 75 subjects undergoing carotid ultrasonography: 27 with severe carotid stenosis (>70%, 23 with moderate stenosis (<70%, and 25 controls. Chaos was characterized by the noise titration method, the correlation dimension and the largest Lyapunov exponent. Baroreflex sensitivity was estimated in the frequency domain. In the control group, 92% of the time series exhibit nonlinear deterministic chaos with positive noise limit, whereas only 68% had a positive noise limit value in the stenoses groups. Ventilatory chaos was impaired in the groups with carotid stenoses, with significant parallel decrease in the noise limit value, correlation dimension and largest Lyapunov exponent, as compared to controls. In multiple regression models, the percentage of carotid stenosis was the best in predicting the correlation dimension (p<0.001, adjusted R(2: 0.35 and largest Lyapunov exponent (p<0.001, adjusted R(2: 0.6. Baroreflex sensitivity also predicted the correlation dimension values (p = 0.05, and the LLE (p = 0.08. Plaque removal after carotid surgery reversed the loss of ventilatory complexity. To conclude, ventilatory chaos is impaired in carotid atherosclerosis. These findings depend on the severity of the stenosis, its localization, plaque surface and morphology features, and is independently associated with baroreflex sensitivity reduction. These findings should help to understand the determinants of ventilatory complexity and breathing control in pathological conditions.
Distributed chaos and inertial ranges in turbulence
Bershadskii, A
2016-01-01
It is shown that appearance of inertial range of scales, adjacent to distributed chaos range, results in adiabatic invariance of an energy correlation integral for isotropic homogeneous turbulence and for buoyancy driven turbulence (with stable or unstable stratification, including Rayleigh-Taylor mixing zone). Power spectrum of velocity field for distributed chaos dominated by this adiabatic invariant has a stretched exponential form $\\propto \\exp(-k/k_{\\beta})^{3/5}$. Results of recent direct numerical simulations have been used in order to support these conclusions.
Chaos in an imperfectly premixed model combustor
Energy Technology Data Exchange (ETDEWEB)
Kabiraj, Lipika, E-mail: lipika.kabiraj@tu-berlin.de; Saurabh, Aditya; Paschereit, Christian O. [Hermann Föttinger Institut, Technische Universität Berlin (Germany); Karimi, Nader [School of Engineering, University of Glasgow (United Kingdom); Sailor, Anna [University of Wisconsin-Madison, Madison 53706 (United States); Mastorakos, Epaminondas; Dowling, Ann P. [Department of Engineering, University of Cambridge (United Kingdom)
2015-02-15
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.
Quantum chaos on a critical Fermi surface
Patel, Aavishkar A
2016-01-01
We compute parameters characterizing many-body quantum chaos for a critical Fermi surface without quasiparticle excitations. We examine a theory of $N$ species of fermions at non-zero density coupled to a $U(1)$ gauge field in two spatial dimensions, and determine the Lyapunov rate and the butterfly velocity in an extended RPA approximation. The thermal diffusivity is found to be universally related to these chaos parameters, i.e. the relationship is independent of $N$, the gauge coupling constant, the Fermi velocity, the Fermi surface curvature, and high energy details.
Atoms in static fields Chaos or Diffraction?
Dando, P A
1998-01-01
A brief review of the manifestations of classical chaos observed in atomic systems is presented. Particular attention is paid to the analysis of atomic spectra by periodic orbit-type theories. For diamagnetic non-hydrogenic Rydberg atoms, the dynamical explanation for observed spectral features has been disputed. By building on our previous work on the photoabsorption spectrum, we show how, by the addition of diffractive terms, the spectral fluctuations in the energy level spectrum of general Rydberg atoms can be obtained with remarkable precision from the Gutzwiller trace formula. This provides further evidence that non-hydrogenic systems are most naturally described in terms of diffraction rather than classical chaos.
SENSITIVE ERROR ANALYSIS OF CHAOS SYNCHRONIZATION
Institute of Scientific and Technical Information of China (English)
HUANG XIAN-GAO; XU JIAN-XUE; HUANG WEI; L(U) ZE-JUN
2001-01-01
We study the synchronizing sensitive errors of chaotic systems for adding other signals to the synchronizing signal.Based on the model of the Henon map masking, we examine the cause of the sensitive errors of chaos synchronization.The modulation ratio and the mean square error are defined to measure the synchronizing sensitive errors by quality.Numerical simulation results of the synchronizing sensitive errors are given for masking direct current, sinusoidal and speech signals, separately. Finally, we give the mean square error curves of chaos synchronizing sensitivity and threedimensional phase plots of the drive system and the response system for masking the three kinds of signals.
USING OPTIMAL FEEDBACK CONTROL FOR CHAOS TARGETING
Institute of Scientific and Technical Information of China (English)
PENG ZHAO-WANG; ZHONG TING-XIU
2000-01-01
Since the conventional open-loop optimal targeting of chaos is very sensitive to noise, a close-loop optimal targeting method is proposed to improve the targeting performance under noise. The present optimal targeting model takes into consideration both precision and speed of the targeting procedure. The parameters, rather than the output, of the targeting controller, are directly optimized to obtain optimal chaos targeting. Analysis regarding the mechanism is given from physics aspect and numerical experiment on the Hénon map is carried out to compare the targeting performance under noise between the close-loop and the open-loop methods.
Experimental realization of chaos control by thresholding.
Murali, K; Sinha, Sudeshna
2003-07-01
We report the experimental verification of thresholding as a versatile tool for efficient and flexible chaos control. The strategy here simply involves monitoring a single state variable and resetting it when it exceeds a threshold. We demonstrate the success of the technique in rapidly controlling different chaotic electrical circuits, including a hyperchaotic circuit, onto stable fixed points and limit cycles of different periods, by thresholding just one variable. The simplicity of this controller entailing no run-time computation, and the ease and rapidity of switching between different targets it offers, suggests a potent tool for chaos based applications.
Investigation on evolutionary optimization of chaos control
Energy Technology Data Exchange (ETDEWEB)
Zelinka, Ivan [Faculty of Applied Informatics, Tomas Bata University in Zli' n, Nad Stranemi 4511, 762 72 Zli' n (Czech Republic)], E-mail: zelinka@fai.utb.cz; Senkerik, Roman [Faculty of Applied Informatics, Tomas Bata University in Zli' n, Nad Stranemi 4511, 762 72 Zli' n (Czech Republic)], E-mail: senkerik@fai.utb.cz; Navratil, Eduard [Faculty of Applied Informatics, Tomas Bata University in Zli' n, Nad Stranemi 4511, 762 72 Zli' n (Czech Republic)], E-mail: enavratil@fai.utb.cz
2009-04-15
This work deals with an investigation on optimization of the feedback control of chaos based on the use of evolutionary algorithms. The main objective is to show that evolutionary algorithms are capable of optimization of chaos control. As models of deterministic chaotic systems, one-dimensional Logistic equation and two-dimensional Henon map were used. The optimizations were realized in several ways, each one for another set of parameters of evolution algorithms or separate cost functions. The evolutionary algorithm SOMA (self-organizing migrating algorithm) was used in four versions. For each version simulations were repeated several times to show and check for robustness of the applied method.
Quantum dynamical entropies in discrete classical chaos
Energy Technology Data Exchange (ETDEWEB)
Benatti, Fabio [Dipartimento di Fisica Teorica, Universita di Trieste, Strada Costiera 11, 34014 Trieste (Italy); Cappellini, Valerio [Dipartimento di Fisica Teorica, Universita di Trieste, Strada Costiera 11, 34014 Trieste (Italy); Zertuche, Federico [Instituto de Matematicas, UNAM, Unidad Cuernavaca, AP 273-3, Admon. 3, 62251 Cuernavaca, Morelos (Mexico)
2004-01-09
We discuss certain analogies between quantization and discretization of classical systems on manifolds. In particular, we will apply the quantum dynamical entropy of Alicki and Fannes to numerically study the footprints of chaos in discretized versions of hyperbolic maps on the torus.
Dynamic system uncertainty propagation using polynomial chaos
Institute of Scientific and Technical Information of China (English)
Xiong Fenfen; Chen Shishi; Xiong Ying
2014-01-01
The classic polynomial chaos method (PCM), characterized as an intrusive methodology, has been applied to uncertainty propagation (UP) in many dynamic systems. However, the intrusive polynomial chaos method (IPCM) requires tedious modification of the governing equations, which might introduce errors and can be impractical. Alternative to IPCM, the non-intrusive polynomial chaos method (NIPCM) that avoids such modifications has been developed. In spite of the frequent application to dynamic problems, almost all the existing works about NIPCM for dynamic UP fail to elaborate the implementation process in a straightforward way, which is important to readers who are unfamiliar with the mathematics of the polynomial chaos theory. Meanwhile, very few works have compared NIPCM to IPCM in terms of their merits and applicability. Therefore, the mathematic procedure of dynamic UP via both methods considering parametric and initial condition uncertainties are comparatively discussed and studied in the present paper. Comparison of accuracy and efficiency in statistic moment estimation is made by applying the two methods to several dynamic UP problems. The relative merits of both approaches are discussed and summarized. The detailed description and insights gained with the two methods through this work are expected to be helpful to engineering designers in solving dynamic UP problems.
Chaos in Practice: Techniques for Career Counsellors
Pryor, Robert G. L.; Bright, Jim
2005-01-01
The chaos theory of careers emphasises continual change, the centrality and importance of chance events, the potential of minor events to have disproportionately large impacts on subsequent events, and the capacity for dramatic phase shifts in career behaviour. This approach challenges traditional approaches to career counselling, assumptions…
Teaching Chaos to Art College Students
Blum, Ben
2001-03-01
This is a report of the author's teaching the basic concepts of chaos to students at Massachusetts College of Art. In order to bypass the students' aversion to mathematics stemming from earlier difficult experiences with mathematics, the course started with some symbolism which was totally unfamiliar to them: a Boolean system based on Brown's Laws of Form. This was then used to develop the mathematical ideas of duality and self-reference. After that was a general survey of the various areas of mathematics using Guillen's Bridges to Infinity. Chaos was then introduced using Gleick's Chaos, which provides a very engaging narrative, along with an introduction to the basic ideas. Two different strategies were used to introduce the mathematical ideas. First, making use of the students' visual orientation, sensitive dependence on initial conditions, fractional dimension, fractals, the Koch snowflake, self-similiarity, and statistical self-similiarity were covered pictorially. Second, so that the students could get a real feeling for the mathematics of chaos, they individually worked out a recurrence equation with varying seeds, using a hand-held calculator.
Chaos in the Belousov-Zhabotinsky reaction
Field, Richard J.
The dynamics of reacting chemical systems is governed by typically polynomial differential equations that may contain nonlinear terms and/or embedded feedback loops. Thus the dynamics of such systems may exhibit features associated with nonlinear dynamical systems, including (among others): temporal oscillations, excitability, multistability, reaction-diffusion-driven formation of spatial patterns, and deterministic chaos. These behaviors are exhibited in the concentrations of intermediate chemical species. Bifurcations occur between particular dynamic behaviors as system parameters are varied. The governing differential equations of reacting chemical systems have as variables the concentrations of all chemical species involved, as well as controllable parameters, including temperature, the initial concentrations of all chemical species, and fixed reaction-rate constants. A discussion is presented of the kinetics of chemical reactions as well as some thermodynamic considerations important to the appearance of temporal oscillations and other nonlinear dynamic behaviors, e.g., deterministic chaos. The behavior, chemical details, and mechanism of the oscillatory Belousov-Zhabotinsky Reaction (BZR) are described. Furthermore, experimental and mathematical evidence is presented that the BZR does indeed exhibit deterministic chaos when run in a flow reactor. The origin of this chaos seems to be in toroidal dynamics in which flow-driven oscillations in the control species bromomalonic acid couple with the BZR limit cycle...
A Framework for Chaos Theory Career Counselling
Pryor, Robert G. L.
2010-01-01
Theory in career development counselling provides a map that counsellors can use to understand and structure the career counselling process. It also provides a means to communicate this understanding and structuring to their clients as part of the counselling intervention. The chaos theory of careers draws attention to the complexity,…
DEFF Research Database (Denmark)
Rennison, Betina Wolfgang
of management differently. In this chaos of codes the managerial challenge is to take a second order position in order to strategically manage the communication that manages management itself. Key words: Management; personnel management; human-relations; pay-system; communication; system-theory; discursive...
Spatio-temporal chaos : A solvable model
Diks, C; Takens, F; DeGoede, J
1997-01-01
A solvable coupled map lattice model exhibiting spatio-temporal chaos is studied. Exact expressions are obtained for the spectra of Lyapunov exponents as a function of the model parameters. Although the model has spatio-temporal structure, the time series measured at a single lattice site are shown
Chaos and fractals an elementary introduction
Feldman, David P
2012-01-01
For students with a background in elementary algebra, this text provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia sets and the Mandelbrot set, power laws, and cellular automata.
Dynamic system uncertainty propagation using polynomial chaos
Directory of Open Access Journals (Sweden)
Xiong Fenfen
2014-10-01
Full Text Available The classic polynomial chaos method (PCM, characterized as an intrusive methodology, has been applied to uncertainty propagation (UP in many dynamic systems. However, the intrusive polynomial chaos method (IPCM requires tedious modification of the governing equations, which might introduce errors and can be impractical. Alternative to IPCM, the non-intrusive polynomial chaos method (NIPCM that avoids such modifications has been developed. In spite of the frequent application to dynamic problems, almost all the existing works about NIPCM for dynamic UP fail to elaborate the implementation process in a straightforward way, which is important to readers who are unfamiliar with the mathematics of the polynomial chaos theory. Meanwhile, very few works have compared NIPCM to IPCM in terms of their merits and applicability. Therefore, the mathematic procedure of dynamic UP via both methods considering parametric and initial condition uncertainties are comparatively discussed and studied in the present paper. Comparison of accuracy and efficiency in statistic moment estimation is made by applying the two methods to several dynamic UP problems. The relative merits of both approaches are discussed and summarized. The detailed description and insights gained with the two methods through this work are expected to be helpful to engineering designers in solving dynamic UP problems.
Chaos in a Bose-Einstein condensate
Institute of Scientific and Technical Information of China (English)
Wang Zhi-Xia; Ni Zheng-Guo; Cong Fu-Zhong; Liu Xue-Shen; Chen Lei
2010-01-01
It is demonstrated that Smale-horseshoe chaos exists in the time evolution of the one-dimensional Bose-Einstein condensate driven by time-periodic harmonic or inverted-harmonic potential.A formally exact solution of the timedependent Gross-Pitaevskii equation is constructed,which describes the matter shock waves with chaotic or periodic amplitudes and phases.
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.
Control and synchronization of spatiotemporal chaos.
Ahlborn, Alexander; Parlitz, Ulrich
2008-01-01
Chaos control methods for the Ginzburg-Landau equation are presented using homogeneously, inhomogeneously, and locally applied multiple delayed feedback signals. In particular, it is shown that a small number of control cells is sufficient for stabilizing plane waves or for trapping spiral waves, and that successful control is closely connected to synchronization of the dynamics in regions close to the control cells.
Many-body chaos at weak coupling
Stanford, Douglas
2016-10-01
The strength of chaos in large N quantum systems can be quantified using λ L , the rate of growth of certain out-of-time-order four point functions. We calculate λ L to leading order in a weakly coupled matrix Φ4 theory by numerically diagonalizing a ladder kernel. The computation reduces to an essentially classical problem.
Chaos: A Very Short Introduction
Energy Technology Data Exchange (ETDEWEB)
Klages, R [School of Mathematical Sciences, Mile End Road, London, E1 4NS (United Kingdom)
2007-07-20
This book is a new volume of a series designed to introduce the curious reader to anything from ancient Egypt and Indian philosophy to conceptual art and cosmology. Very handy in pocket size, Chaos promises an introduction to fundamental concepts of nonlinear science by using mathematics that is 'no more complicated than X=2. Anyone who ever tried to give a popular science account of research knows that this is a more challenging task than writing an ordinary research article. Lenny Smith brilliantly succeeds to explain in words, in pictures and by using intuitive models the essence of mathematical dynamical systems theory and time series analysis as it applies to the modern world. In a more technical part he introduces the basic terms of nonlinear theory by means of simple mappings. He masterly embeds this analysis into the social, historical and cultural context by using numerous examples, from poems and paintings over chess and rabbits to Olbers' paradox, card games and 'phynance'. Fundamental problems of the modelling of nonlinear systems like the weather, sun spots or golf balls falling through an array of nails are discussed from the point of view of mathematics, physics and statistics by touching upon philosophical issues. At variance with Laplace's demon, Smith's 21st century demon makes 'real world' observations only with limited precision. This poses a severe problem to predictions derived from complex chaotic models, where small variations of initial conditions typically yield totally different outcomes. As Smith argues, this difficulty has direct implications on decision-making in everyday modern life. However, it also asks for an inherently probabilistic theory, which somewhat reminds us of what we are used to in the microworld. There is little to criticise in this nice little book except that some figures are of poor quality thus not really reflecting the beauty of fractals and other wonderful objects in this
CHAOS-BASED ADVANCED ENCRYPTION STANDARD
Abdulwahed, Naif B.
2013-05-01
This thesis introduces a new chaos-based Advanced Encryption Standard (AES). The AES is a well-known encryption algorithm that was standardized by U.S National Institute of Standard and Technology (NIST) in 2001. The thesis investigates and explores the behavior of the AES algorithm by replacing two of its original modules, namely the S-Box and the Key Schedule, with two other chaos- based modules. Three chaos systems are considered in designing the new modules which are Lorenz system with multiplication nonlinearity, Chen system with sign modules nonlinearity, and 1D multiscroll system with stair case nonlinearity. The three systems are evaluated on their sensitivity to initial conditions and as Pseudo Random Number Generators (PRNG) after applying a post-processing technique to their output then performing NIST SP. 800-22 statistical tests. The thesis presents a hardware implementation of dynamic S-Boxes for AES that are populated using the three chaos systems. Moreover, a full MATLAB package to analyze the chaos generated S-Boxes based on graphical analysis, Walsh-Hadamard spectrum analysis, and image encryption analysis is developed. Although these S-Boxes are dynamic, meaning they are regenerated whenever the encryption key is changed, the analysis results show that such S-Boxes exhibit good properties like the Strict Avalanche Criterion (SAC) and the nonlinearity and in the application of image encryption. Furthermore, the thesis presents a new Lorenz-chaos-based key expansion for the AES. Many researchers have pointed out that there are some defects in the original key expansion of AES and thus have motivated such chaos-based key expansion proposal. The new proposed key schedule is analyzed and assessed in terms of confusion and diffusion by performing the frequency and SAC test respectively. The obtained results show that the new proposed design is more secure than the original AES key schedule and other proposed designs in the literature. The proposed
Directory of Open Access Journals (Sweden)
Benjamin John Burger
2013-10-01
Full Text Available A new species of an archaic primate (Pleisadapiformes is described based on a maxilla containing the first and second upper molars from the Fort Union Formation, Atwell Gulch Member in northwestern Colorado. The preserved teeth show the unusual dental characteristics of members of the rare and poorly documented Picrodontidae family, including an elongated centrocrista and wide occlusal surface. The new species is placed within the genus Zanycteris (represented by a single specimen from southern Colorado. This placement is based on similarities in regard to the parastyle, curvilinear centrocrista, and wider anterior stylar shelf on the upper molars. However, the new species differs from the only known species of Zanycteris in exhibiting an upper first molar that is 30% larger in area, while retaining a similarly sized upper second molar. Phylogenetic analysis supports the separation of the Picrodontidae family from the Paromomyidae, while still recognizing picrodontids position within Pleisadapiformes. The unusual dental features of the upper molars likely functioned in life as an enhanced shearing surface between the centrocrista and cristid obliqua crests for a specialized diet of fruit. A similar arrangement is found in the living bat Ariteus (Jamaican fig-eating bat, which feeds on fleshy fruit. The new species showcases the rapid diversification of archaic primates shortly after the extinction of the dinosaurs during the Paleocene, and the unusual dental anatomy of picrodontids to exploit new dietary specializations.
DEFF Research Database (Denmark)
Klösgen, Beate; Bruun, Sara; Hansen, Søren;
with an AFM (2). The intuitive explanation for the depletion based on "hydrophobic mismatch" between the obviously hydrophilic bulk phase of water next to the hydrophobic polymer. It would thus be an intrinsic property of all interfaces between non-matching materials. The detailed physical interaction path...... The presence of a depletion layer of water along extended hydrophobic interfaces, and a possibly related formation of nanobubbles, is an ongoing discussion. The phenomenon was initially reported when we, years ago, chose thick films (~300-400Å) of polystyrene as cushions between a crystalline...
Controlling halo-chaos via wavelet-based feedback
Directory of Open Access Journals (Sweden)
Jin-Qing Fang
2002-01-01
Full Text Available Halo-chaos in high-current accelerator has become one of the key issues because it can cause excessive radioactivity from the accelerators and significantly limits the applications of the new accelerators in industrial and other fields. Some general engineering methods for chaos control have been developed, but they generally are unsuccessful for halo-chaos suppression due to many technical constraints. In this article, controllability condition for beam halo-chaos is analyzed qualitatively. Then Particles-in-Cell (PIC simulations explore the nature of beam halo-chaos formation. A nonlinear control method and wavelet function feedback controller are proposed for controlling beam halo-chaos. After control of beam halo-chaos for initial proton beam with water bag distributions, the beam halo strength factor H is reduced to zero, and other statistical physical quantities of beam halo-chaos are doubly reduced. The results show that the developed methods in this paper are very effective for proton beam halo-chaos suppression. Potential application of the halo-chaos control method is finally pointed out.
Intrinsically Disordered Energy Landscapes
Chebaro, Yassmine; Ballard, Andrew J.; Chakraborty, Debayan; Wales, David J.
2015-05-01
Analysis of an intrinsically disordered protein (IDP) reveals an underlying multifunnel structure for the energy landscape. We suggest that such ‘intrinsically disordered’ landscapes, with a number of very different competing low-energy structures, are likely to characterise IDPs, and provide a useful way to address their properties. In particular, IDPs are present in many cellular protein interaction networks, and several questions arise regarding how they bind to partners. Are conformations resembling the bound structure selected for binding, or does further folding occur on binding the partner in a induced-fit fashion? We focus on the p53 upregulated modulator of apoptosis (PUMA) protein, which adopts an -helical conformation when bound to its partner, and is involved in the activation of apoptosis. Recent experimental evidence shows that folding is not necessary for binding, and supports an induced-fit mechanism. Using a variety of computational approaches we deduce the molecular mechanism behind the instability of the PUMA peptide as a helix in isolation. We find significant barriers between partially folded states and the helix. Our results show that the favoured conformations are molten-globule like, stabilised by charged and hydrophobic contacts, with structures resembling the bound state relatively unpopulated in equilibrium.
Chaos and dynamics of spinning particles in Kerr spacetime
Han, Wen-Biao
2010-01-01
We study chaos dynamics of spinning particles in Kerr spacetime of rotating black holes use the Papapetrou equations by numerical integration. Because of spin, this system exists many chaos solutions, and exhibits some exceptional dynamic character. We investigate the relations between the orbits chaos and the spin magnitude S, pericenter, polar angle and Kerr rotation parameter a by means of a kind of brand new Fast Lyapulov Indicator (FLI) which is defined in general relativity. The classical definition of Lyapulov exponent (LE) perhaps fails in curve spacetime. And we emphasize that the Poincar\\'e sections cannot be used to detect chaos for this case. Via calculations, some new interesting conclusions are found: though chaos is easier to emerge with bigger S, but not always depends on S monotonically; the Kerr parameter a has a contrary action on the chaos occurrence. Furthermore, the spin of particles can destroy the symmetry of the orbits about the equatorial plane. And for some special initial condition...
Optomechanically induced stochastic resonance and chaos transfer between optical fields
Monifi, Faraz; Zhang, Jing; Özdemir, Şahin Kaya; Peng, Bo; Liu, Yu-Xi; Bo, Fang; Nori, Franco; Yang, Lan
2016-06-01
Chaotic dynamics has been reported in many physical systems and has affected almost every field of science. Chaos involves hypersensitivity to the initial conditions of a system and introduces unpredictability into its output. Thus, it is often unwanted. Interestingly, the very same features make chaos a powerful tool to suppress decoherence, achieve secure communication and replace background noise in stochastic resonance—a counterintuitive concept that a system's ability to transfer information can be coherently amplified by adding noise. Here, we report the first demonstration of chaos-induced stochastic resonance in an optomechanical system, as well as the optomechanically mediated chaos transfer between two optical fields such that they follow the same route to chaos. These results will contribute to the understanding of nonlinear phenomena and chaos in optomechanical systems, and may find applications in the chaotic transfer of information and for improving the detection of otherwise undetectable signals in optomechanical systems.
Chaos in electric drive systems analysis control and application
Chau, K T
2011-01-01
In Chaos in Electric Drive Systems: Analysis, Control and Application authors Chau and Wang systematically introduce an emerging technology of electrical engineering that bridges abstract chaos theory and practical electric drives. The authors consolidate all important information in this interdisciplinary technology, including the fundamental concepts, mathematical modeling, theoretical analysis, computer simulation, and hardware implementation. The book provides comprehensive coverage of chaos in electric drive systems with three main parts: analysis, control and application. Corresponding drive systems range from the simplest to the latest types: DC, induction, synchronous reluctance, switched reluctance, and permanent magnet brushless drives.The first book to comprehensively treat chaos in electric drive systemsReviews chaos in various electrical engineering technologies and drive systemsPresents innovative approaches to stabilize and stimulate chaos in typical drivesDiscusses practical application of cha...
Gaussian Intrinsic Entanglement
Mišta, Ladislav; Tatham, Richard
2016-12-01
We introduce a cryptographically motivated quantifier of entanglement in bipartite Gaussian systems called Gaussian intrinsic entanglement (GIE). The GIE is defined as the optimized mutual information of a Gaussian distribution of outcomes of measurements on parts of a system, conditioned on the outcomes of a measurement on a purifying subsystem. We show that GIE vanishes only on separable states and exhibits monotonicity under Gaussian local trace-preserving operations and classical communication. In the two-mode case, we compute GIE for all pure states as well as for several important classes of symmetric and asymmetric mixed states. Surprisingly, in all of these cases, GIE is equal to Gaussian Rényi-2 entanglement. As GIE is operationally associated with the secret-key agreement protocol and can be computed for several important classes of states, it offers a compromise between computable and physically meaningful entanglement quantifiers.
Intrinsic Time Quantum Gravity
Yu, Hoi Lai
2016-01-01
Correct identification of the true gauge symmetry of General Relativity being 3d spatial diffeomorphism invariant(3dDI) (not the conventional infinite tensor product group with principle fibre bundle structure), together with intrinsic time extracted from clean decomposition of the canonical structure yields a self-consistent theory of quantum gravity. A new set of fundamental commutation relations is also presented. The basic variables are the eight components of the unimodular part of the spatial dreibein and eight SU(3) generators which correspond to Klauder's momentric variables that characterize a free theory of quantum gravity. The commutation relations are not canonical, but have well defined group theoretical meanings. All fundamental entities are dimensionless; and the quantum wave functionals are preferentially in the dreibein representation. The successful quantum theory of gravity involves only broad spectrum of knowledge and deep insights but no exotic idea.
Control of Beam Halo-Chaos by Soliton
Institute of Scientific and Technical Information of China (English)
BAI Long; WENG Jia-Qiang; FANG Jin-Qing
2005-01-01
@@ The Kapchinsky-Vladimirsky beam through an alternating-gradient quadrupole magnetic field is studied using the particle-core model. The beam halo-chaos is found, and the soliton controller is proposed based on the mechanism of halo formation and strategy of controlling halo-chaos. We perform a multiparticle simulation to control the halo by soliton controller, and find that the halo-chaos and its regeneration can be eliminated. It is shown that our control method is effective.
Testing for deterministic monetary chaos: Metric and topological diagnostics
Energy Technology Data Exchange (ETDEWEB)
Barkoulas, John T. [Department of Finance and Quantitative Analysis, Georgia Southern University, Statesboro, GA 30460 (United States)], E-mail: jbarkoul@georgiasouthern.edu
2008-11-15
The evidence of deterministic chaos in monetary aggregates tends to be contradictory in the literature. We revisit the issue of monetary chaos by applying tools based on both the metric (correlation dimension and Lyapunov exponents) and topological (recurrence plots) approaches to chaos. For simple-sum and divisia monetary aggregates over an expanded sample period, the empirical evidence from both approaches is negative for monetary chaotic dynamics.
Quantum Chaos in Physical Systems: from Super Conductors to Quarks
Bittner, Elmar; Markum, Harald; Pullirsch, Rainer
2001-01-01
This article is the written version of a talk delivered at the Bexbach Colloquium of Science 2000 and starts with an introduction into quantum chaos and its relationship to classical chaos. The Bohigas-Giannoni-Schmit conjecture is formulated and evaluated within random-matrix theory. Several examples of physical systems exhibiting quantum chaos ranging from nuclear to solid state physics are presented. The presentation concludes with recent research work on quantum chromodynamics and the qua...
Measurement induced chaos with entangled states
Kiss, T; Tóth, L D; Gábris, A; Jex, I; Alber, G
2011-01-01
Quantum control, in a broad sense, may include measurement of quantum systems and, as a feed back operation, selection from an ensemble conditioned on the measurements. The resulting dynamics can be nonlinear and, if applied iteratively, can lead to true chaos in a quantum system. We consider the dynamics of an ensemble of two qubit systems subjected to measurement and conditional selection. We prove that the iterative dynamics leads to true chaos in the entanglement of the qubits. A class of special initial states exhibits high sensitivity to the initial conditions. In the parameter space of the special initial states we identify two types of islands: one converging to a separable state, while the other being asymptotically completely entangled. The islands form a fractal like structure. Adding noise to the initial state introduces a further stable asymptotic cycle.
Tuning quantum measurements to control chaos
Eastman, Jessica K.; Hope, Joseph J.; Carvalho, André R. R.
2017-01-01
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. PMID:28317933
An exploration of dynamical systems and chaos
Argyris, John H; Haase, Maria; Friedrich, Rudolf
2015-01-01
This book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems with particular emphasis on the exploration of chaotic phenomena. The self-contained introductory presentation is addressed both to those who wish to study the physics of chaotic systems and non-linear dynamics intensively as well as those who are curious to learn more about the fascinating world of chaotic phenomena. Basic concepts like Poincaré section, iterated mappings, Hamiltonian chaos and KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity and renormalisation and transitions to chaos are thoroughly explained. To facilitate comprehension, mathematical concepts and tools are introduced in short sub-sections. The text is supported by numerous computer experiments and a multitude of graphical illustrations and colour plates emphasising the geometrical and topological characteristics of the underlying dynamics. This volume is a completely revised and enlar...
Chaos in effective classical and quantum dynamics
Casetti, L; Modugno, M; Casetti, Lapo; Gatto, Raoul; Modugno, Michele
1998-01-01
We investigate the dynamics of classical and quantum N-component phi^4 oscillators in presence of an external field. In the large N limit the effective dynamics is described by two-degree-of-freedom classical Hamiltonian systems. In the classical model we observe chaotic orbits for any value of the external field, while in the quantum case chaos is strongly suppressed. A simple explanation of this behaviour is found in the change in the structure of the orbits induced by quantum corrections. Consistently with Heisenberg's principle, quantum fluctuations are forced away from zero, removing in the effective quantum dynamics a hyperbolic fixed point that is a major source of chaos in the classical model.
Quantum chaos in QCD and hadrons
Markum, H; Pullirsch, R; Sengl, B; Wagenbrunn, R F; Markum, Harald; Plessas, Willibald; Pullirsch, Rainer; Sengl, Bianka; Wagenbrunn, Robert F.
2005-01-01
This article is the written version of a talk delivered at the Workshop on Nonlinear Dynamics and Fundamental Interactions in Tashkent and starts with an introduction into quantum chaos and its relationship to classical chaos. The Bohigas-Giannoni-Schmit conjecture is formulated and evaluated within random-matrix theory. In accordance to the title, the presentation is twofold and begins with research results on quantum chromodynamics and the quark-gluon plasma. We conclude with recent research work on the spectroscopy of baryons. Within the framework of a relativistic constituent quark model we investigate the excitation spectra of the nucleon and the delta with regard to a possible chaotic behavior for the cases when a hyperfine interaction of either Goldstone-boson-exchange or one-gluon-exchange type is added to the confinement interaction. Agreement with predictions from the experimental hadron spectrum is established.
Buoyancy driven turbulence and distributed chaos
Bershadskii, A
2016-01-01
It is shown, using results of recent direct numerical simulations, laboratory experiments and atmospheric measurements, that buoyancy driven turbulence exhibits a broad diversity of the types of distributed chaos with its stretched exponential spectrum $\\exp(-k/k_{\\beta})^{\\beta}$. The distributed chaos with $\\beta = 1/3$ (determined by the helicity correlation integral) is the most common feature of the stably stratified turbulence (due to the strong helical waves presence). These waves mostly dominate spectral properties of the vertical component of velocity field, while the horizontal component is dominated by the diffusive processes both for the weak and strong stable stratification ($\\beta =2/3$). For the last case influence of the low boundary can overcome the wave effects and result in $\\beta =1/2$ for the vertical component of the velocity field (the spontaneous breaking of the space translational symmetry - homogeneity). For the unstably stratified turbulence in the Rayleigh-Taylor mixing zone the di...
Migraine--new perspectives from chaos theory.
Kernick, D
2005-08-01
Converging from a number of disciplines, non-linear systems theory and in particular chaos theory offer new descriptive and prescriptive insights into physiological systems. This paper briefly reviews an approach to physiological systems from these perspectives and outlines how these concepts can be applied to the study of migraine. It suggests a wide range of potential applications including new approaches to classification, treatment and pathophysiological mechanisms. A hypothesis is developed that suggests that dysfunctional consequences can result from a mismatch between the complexity of the environment and the system that is seeking to regulate it and that the migraine phenomenon is caused by an incongruity between the complexity of mid brain sensory integration and cortical control networks. Chaos theory offers a new approach to the study of migraine that complements existing frameworks but may more accurately reflect underlying physiological mechanisms.
Chaos theory perspective for industry clusters development
Yu, Haiying; Jiang, Minghui; Li, Chengzhang
2016-03-01
Industry clusters have outperformed in economic development in most developing countries. The contributions of industrial clusters have been recognized as promotion of regional business and the alleviation of economic and social costs. It is no doubt globalization is rendering clusters in accelerating the competitiveness of economic activities. In accordance, many ideas and concepts involve in illustrating evolution tendency, stimulating the clusters development, meanwhile, avoiding industrial clusters recession. The term chaos theory is introduced to explain inherent relationship of features within industry clusters. A preferred life cycle approach is proposed for industrial cluster recessive theory analysis. Lyapunov exponents and Wolf model are presented for chaotic identification and examination. A case study of Tianjin, China has verified the model effectiveness. The investigations indicate that the approaches outperform in explaining chaos properties in industrial clusters, which demonstrates industrial clusters evolution, solves empirical issues and generates corresponding strategies.
Kac-Moody Algebras and Controlled Chaos
Wesley, D H
2007-01-01
Compactification can control chaotic Mixmaster behavior 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 hyperbolic (but not strictly 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.
Chaos in hydrodynamic BL Herculis models
Smolec, R
2014-01-01
We present non-linear, convective, BL Her-type hydrodynamic models that show complex variability characteristic for deterministic chaos. The bifurcation diagram reveals a rich structure, with many phenomena detected for the first time in hydrodynamic models of pulsating stars. The phenomena include not only period doubling cascades en route to chaos (detected in earlier studies) but also periodic windows within chaotic band, type-I and type-III intermittent behaviour, interior crisis bifurcation and others. Such phenomena are known in many textbook chaotic systems, from the simplest discrete logistic map, to more complex systems like Lorenz equations. We discuss the physical relevance of our models. Although except of period doubling such phenomena were not detected in any BL Her star, chaotic variability was claimed in several higher luminosity siblings of BL Her stars - RV Tau variables, and also in longer-period, luminous irregular pulsators. Our models may help to understand these poorly studied stars. Pa...
Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons
Kröger, H.
2003-01-01
We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.
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.
Complex motions and chaos in nonlinear systems
Machado, José; Zhang, Jiazhong
2016-01-01
This book brings together 10 chapters on a new stream of research examining complex phenomena in nonlinear systems—including engineering, physics, and social science. Complex Motions and Chaos in Nonlinear Systems provides readers a particular vantage of the nature and nonlinear phenomena in nonlinear dynamics that can develop the corresponding mathematical theory and apply nonlinear design to practical engineering as well as the study of other complex phenomena including those investigated within social science.
Computer Auxiliary Analysis for Stochasticity of Chaos
Institute of Scientific and Technical Information of China (English)
ZHAOGeng; FANGJin-qing
2003-01-01
In this work, we propose a mathematics-physical statistic analytical method for stochastic process of chaos, based on stochastic test via combination measurement of Monobit and Runs. Computer auxiliary analysis shows that it is of stochasticity for stochastic number produced from the chaotic circuit. Our software is written by VB and C++, the later can be tested by the former, and at the same time it is verified by stochastic number produced by the computer. So the data treatment results are reliable.
Chaos in a topologically transitive system
Institute of Scientific and Technical Information of China (English)
XIONG; Jincheng
2005-01-01
The chaotic phenomena have been studied in a topologically transitive system and it has been shown that the erratic time dependence of orbits in such a topologically transitive system is more complicated than what described by the well-known technology "Li-Yorke chaos". The concept "sensitive dependency on initial conditions" has been generalized, and the chaotic phenomena has been discussed for transitive systems with the generalized sensitive dependency property.
Frozen spatial chaos induced by boundaries
Eguiluz, V M; Piro, O; Balle, S; Eguiluz, Victor M.; Hernandez-Garcia, Emilio; Piro, Oreste; Balle, Salvador
1999-01-01
We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We exemplify the phenomenon with a nonlinear reaction-diffusion equation in a two-dimensional undulated domain. Concepts from the theory of dynamical systems, and a transverse-single-mode approximation are used to describe the spatially chaotic structures.
Chaos: Understanding and Controlling Laser Instability
Blass, William E.
1997-01-01
In order to characterize the behavior of tunable diode lasers (TDL), the first step in the project involved the redesign of the TDL system here at the University of Tennessee Molecular Systems Laboratory (UTMSL). Having made these changes it was next necessary to optimize the new optical system. This involved the fine adjustments to the optical components, particularly in the monochromator, to minimize the aberrations of coma and astigmatism and to assure that the energy from the beam is focused properly on the detector element. The next step involved the taking of preliminary data. We were then ready for the analysis of the preliminary data. This required the development of computer programs that use mathematical techniques to look for signatures of chaos. Commercial programs were also employed. We discovered some indication of high dimensional chaos, but were hampered by the low sample rate of 200 KSPS (kilosamples/sec) and even more by our sample size of 1024 (1K) data points. These limitations were expected and we added a high speed data acquisition board. We incorporated into the system a computer with a 40 MSPS (million samples/sec) data acquisition board. This board can also capture 64K of data points so that were then able to perform the more accurate tests for chaos. The results were dramatic and compelling, we had demonstrated that the lead salt diode laser had a chaotic frequency output. Having identified the chaotic character in our TDL data, we proceeded to stage two as outlined in our original proposal. This required the use of an Occasional Proportional Feedback (OPF) controller to facilitate the control and stabilization of the TDL system output. The controller was designed and fabricated at GSFC and debugged in our laboratories. After some trial and error efforts, we achieved chaos control of the frequency emissions of the laser. The two publications appended to this introduction detail the entire project and its results.
Optimal chaos control through reinforcement learning.
Gadaleta, Sabino; Dangelmayr, Gerhard
1999-09-01
A general purpose chaos control algorithm based on reinforcement learning is introduced and applied to the stabilization of unstable periodic orbits in various chaotic systems and to the targeting problem. The algorithm does not require any information about the dynamical system nor about the location of periodic orbits. Numerical tests demonstrate good and fast performance under noisy and nonstationary conditions. (c) 1999 American Institute of Physics.
Chaos control of parametric driven Duffing oscillators
Energy Technology Data Exchange (ETDEWEB)
Jin, Leisheng; Mei, Jie; Li, Lijie, E-mail: L.Li@swansea.ac.uk [College of Engineering, Swansea University, Swansea SA2 8PP (United Kingdom)
2014-03-31
Duffing resonators are typical dynamic systems, which can exhibit chaotic oscillations, subject to certain driving conditions. Chaotic oscillations of resonating systems with negative and positive spring constants are identified to investigate in this paper. Parametric driver imposed on these two systems affects nonlinear behaviours, which has been theoretically analyzed with regard to variation of driving parameters (frequency, amplitude). Systematic calculations have been performed for these two systems driven by parametric pumps to unveil the controllability of chaos.
Chaos control of parametric driven Duffing oscillators
Jin, Leisheng; Mei, Jie; Li, Lijie
2014-03-01
Duffing resonators are typical dynamic systems, which can exhibit chaotic oscillations, subject to certain driving conditions. Chaotic oscillations of resonating systems with negative and positive spring constants are identified to investigate in this paper. Parametric driver imposed on these two systems affects nonlinear behaviours, which has been theoretically analyzed with regard to variation of driving parameters (frequency, amplitude). Systematic calculations have been performed for these two systems driven by parametric pumps to unveil the controllability of chaos.
Reducing or enhancing chaos using periodic orbits.
Bachelard, R; Chandre, C; Leoncini, X
2006-06-01
A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local bifurcations). Depending on the values of the residues, reflecting their linear stability properties, a set of invariant tori is destroyed or created in the neighborhood of the chosen periodic orbits. An application on a paradigmatic system, a forced pendulum, illustrates the method.
Chaos in free electron laser oscillators
Energy Technology Data Exchange (ETDEWEB)
Bruni, C. [Univ Paris 11, LAL, UMR 8607, F-91898 Orsay, (France); Bachelard, R.; Couprie, M.E. [Synchrotron SOLEIL, F-91192 Gif Sur Yvette, (France); Garzella, D. [CEA DSM DRECAM SPAM, F-91191 Gif Sur Yvette, (France); Orlandi, G.L. [CR Frascati FIM FISACC, ENEA, I-00044 Frascati, (Italy)
2009-07-01
The chaotic nature of a storage-ring free electron laser (FEL) is investigated. The derivation of a low embedding dimension for the dynamics allows the low-dimensionality of this complex system to be observed, whereas its unpredictability is demonstrated, in some ranges of parameters, by a positive Lyapounov exponent. The route to chaos is then explored by tuning a single control parameter, and a period-doubling cascade is evidenced, as well as intermittence. (authors)
Murakami, A; Ohtsubo, J
2001-06-01
Chaos synchronization using a continuous chaos control method was studied in two identical chaotic laser systems consisting of semiconductor lasers and optical feedback from an external mirror. Numerical calculations for rate equations indicate that the stability of chaos synchronization depends significantly on the external mirror position. We performed a linear stability analysis for the rate equations. Our results show that the stability of the synchronization is much influenced by the mode interaction between the relaxation oscillation frequency of the semiconductor laser and the external cavity frequency. Due to this interaction, an intensive mode competition between the two frequencies destroys the synchronization, but stable synchronization can be achieved when the mode competition is very weak.
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
Bifurcations and Chaos in Duffing Equation
Institute of Scientific and Technical Information of China (English)
2007-01-01
The Duffing equation with even-odd asymmetrical nonlinear-restoring force and one external forcing is investigated. The conditions of existence of primary resonance, second-order, third-order subharmonics, m-order subharmonics and chaos are given by using the second-averaging method, the Melnikov method and bifurcation theory. Numerical simulations including bifurcation diagram, bifurcation surfaces and phase portraits show the consistence with the theoretical analysis. The numerical results also exhibit new dynamical behaviors including onset of chaos, chaos suddenly disappearing to periodic orbit, cascades of inverse period-doubling bifurcations, period-doubling bifurcation, symmetry period-doubling bifurcations of period-3 orbit, symmetry-breaking of periodic orbits, interleaving occurrence of chaotic behaviors and period-one orbit, a great abundance of periodic windows in transient chaotic regions with interior crises and boundary crisis and varied chaotic attractors. Our results show that many dynamical behaviors are strictly departure from the behaviors of the Duffing equation with odd-nonlinear restoring force.
Chaos in Chiral Condensates in Gauge Theories
Hashimoto, Koji; Murata, Keiju; Yoshida, Kentaroh
2016-12-01
Assigning a chaos index for dynamics of generic quantum field theories is a challenging problem because the notion of a Lyapunov exponent, which is useful for singling out chaotic behavior, works only in classical systems. We address the issue by using the AdS /CFT correspondence, as the large Nc limit provides a classicalization (other than the standard ℏ→0 ) while keeping nontrivial quantum condensation. We demonstrate the chaos in the dynamics of quantum gauge theories: The time evolution of homogeneous quark condensates ⟨q ¯q ⟩ and ⟨q ¯γ5q ⟩ in an N =2 supersymmetric QCD with the S U (Nc) gauge group at large Nc and at a large 't Hooft coupling λ ≡NcgYM2 exhibits a positive Lyapunov exponent. The chaos dominates the phase space for energy density E ≳(6 ×1 02)×mq4(Nc/λ2), where mq is the quark mass. We evaluate the largest Lyapunov exponent as a function of (Nc,λ ,E ) and find that the N =2 supersymmetric QCD is more chaotic for smaller Nc.
Intrinsic Angular Momentum of Light.
Santarelli, Vincent
1979-01-01
Derives a familiar torque-angular momentum theorem for the electromagnetic field, and includes the intrinsic torques exerted by the fields on the polarized medium. This inclusion leads to the expressions for the intrinsic angular momentum carried by the radiation traveling through a charge-free medium. (Author/MA)
Using a quantum computer to investigate quantum chaos
Schack, Ruediger
1997-01-01
We show that the quantum baker's map, a prototypical map invented for theoretical studies of quantum chaos, has a very simple realization in terms of quantum gates. Chaos in the quantum baker's map could be investigated experimentally on a quantum computer based on only 3 qubits.
Chaos: A Topic for Interdisciplinary Education in Physics
Bae, Saebyok
2009-01-01
Since society and science need interdisciplinary works, the interesting topic of chaos is chosen for interdisciplinary education in physics. The educational programme contains various university-level activities such as computer simulations, chaos experiment and team projects besides ordinary teaching. According to the participants, the programme…
Major open problems in chaos theory and nonlinear dynamics
Li, Y Charles
2013-01-01
Nowadays, chaos theory and nonlinear dynamics lack research focuses. Here we mention a few major open problems: 1. an effective description of chaos and turbulence, 2. rough dependence on initial data, 3. arrow of time, 4. the paradox of enrichment, 5. the paradox of pesticides, 6. the paradox of plankton.
Controlling Beam Halo-Chaos via Time-Delayed Feedback
Institute of Scientific and Technical Information of China (English)
FANG Jin-Qing; WENG Jia-Qiang; ZHU Lun-Wu; LUO Xiao-Shu
2004-01-01
The study of controlling high-current proton beam halo-chaos has become a key concerned issue for many important applications. In this paper, time-delayed feedback control method is proposed for beam halo-chaos. Particle in cell simulation results show that the method is very effective and has some advantages for high-current beam experiments and engineering.
The "Chaos" Pattern in Piaget's Theory of Cognitive Development.
Lindsay, Jean S.
Piaget's theory of the cognitive development of the child is related to the recently developed non-linear "chaos" model. The term "chaos" refers to the tendency of dynamical, non-linear systems toward irregular, sometimes unpredictable, deterministic behavior. Piaget identified this same pattern in his model of cognitive development in children.…
Universal properties of dynamically complex systems - The organization of chaos
Procaccia, Itamar
1988-06-01
The complex dynamic behavior of natural systems far from equilibrium is discussed. Progress that has been made in understanding universal aspects of the paths to such behavior, of the trajectories at the borderline of chaos, and of the nature of the complexity in the chaotic regime, is reviewed. The emerging grammar of chaos is examined.
Experimental Control of Instabilities and Chaos in Fast Dynamical Systems
1997-06-01
is short (- 10 cm) [153]-[155]; these studies have more recently been considered from the chaos control viewpoint [42]. The apparatus required to...13] Christini, David J., and James A. Collins. Controlling Nonchaotic Neuronal Noise Using Chaos Control Techniques. Phys. Rev. Lett. 75:2782-2785
Time generated by intrinsic observers
Svozil, Karl
2009-01-01
We shortly review the construction of knowledge by intrinsic observers. Intrinsic observers are embedded in a system and are inseparable parts thereof. The intrinsic viewpoint has to be contrasted with an extrinsic, "God's eye" viewpoint, from which the system can be observed externally without in any way changing it. This epistemological distinction has concrete, formalizable consequences. One consequence is the emergence of "complementarity" for intrinsic observers, even if the underlying system is totally deterministic (computable). Another consequence is the appearence of time and inertial frames for intrinsic observers. The necessary operational techniques are developed in the context of Cellular Automata. We finish with a somewhat speculative question. Given space-time frames generated by clocks which use sound waves for synchronization; why could supersonic travel not cause time paradoxes?
Replication of chaos in neural networks, economics and physics
Akhmet, Marat
2016-01-01
This book presents detailed descriptions of chaos for continuous-time systems. It is the first-ever book to consider chaos as an input for differential and hybrid equations. Chaotic sets and chaotic functions are used as inputs for systems with attractors: equilibrium points, cycles and tori. The findings strongly suggest that chaos theory can proceed from the theory of differential equations to a higher level than previously thought. The approach selected is conducive to the in-depth analysis of different types of chaos. The appearance of deterministic chaos in neural networks, economics and mechanical systems is discussed theoretically and supported by simulations. As such, the book offers a valuable resource for mathematicians, physicists, engineers and economists studying nonlinear chaotic dynamics.
$\\mathcal{PT}$-Symmetry-Breaking Chaos in Optomechanics
Lü, Xin-You; Ma, Jin-Yong; Wu, Ying
2015-01-01
We demonstrate a $\\mathcal{PT}$-symmetry-breaking chaos in optomechanical system (OMS), which features an ultralow driving threshold. In principle, this chaos will emerge once a driving laser is applied to the cavity mode and lasts for a period of time. The driving strength is inversely proportional to the starting time of chaos. This originally comes from the dynamical enhancement of nonlinearity by field localization in $\\mathcal{PT}$-symmetry-breaking phase ($\\mathcal{PT}$BP). Moreover, this chaos is switchable by tuning the system parameters so that a $\\mathcal{PT}$-symmetry phase transition occurs. This work may fundamentally broaden the regimes of cavity optomechanics and nonlinear optics. It offers the prospect of exploring ultralow-power-laser triggered chaos and its potential applications in secret communication.
Erbium - doped fiber laser systems: Routes to chaos
Directory of Open Access Journals (Sweden)
Rubežić Vesna
2014-01-01
Full Text Available Erbium-doped fiber laser systems exhibit a large variety of complex dynamical behaviors, bifurcations and attractors. In this paper, the chaotic behavior which can be achieved under certain conditions in a laser system with erbium-doped fiber, is discussed. The chaos in this system occurs through several standard scenarios. In this paper, the simulation sequence of quasiperiodic, intermittent and period-doubling scenario transitions to chaos is shown. Quasiperiodic and intermittent transitions to chaos are shown on the example system with a single ring. The electro-optical modulator was applied to the system for modulating the loss in the cavity. We used the sinusoidal and rectangular signals for modulation. Generation of chaos is achieved by changing the parameters of signal for modulation. Period-doubling transition to chaos is illustrated in a system with two rings. Simulation results are shown in the time domain and phase space.
Dynamical chaos in chip-scale optomechanical oscillators
Wu, Jiagui; Huang, Yongjun; Zhou, Hao; Yang, Jinghui; Liu, Jia-Ming; Yu, Mingbin; Lo, Guoqiang; Kwong, Dim-Lee; Xia, Guangqiong; Wong, Chee Wei
2016-01-01
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 first generation of dynamical chaos in silicon optomechanical oscillators, enabled by the strong and coupled nonlinearities of Drude electron-hole plasma. Deterministic chaotic oscillation is achieved, and statistical and entropic characterization quantifies the complexity of chaos. The correlation dimension D2 is determined at ~ 1.67 for the chaotic attractor, along with a maximal Lyapunov exponent rate about 2.94*the fundamental optomechanical oscillation. The corresponding nonlinear dynamical maps demonstrate the plethora of subharmonics, bifurcations, and stable regimes, along with distinct transitional routes into chaotic states. The chaos generation in our mesoscopic...
Population Floors and the Persistence of Chaos in Ecological Models.
Ruxton; Rohani
1998-06-01
Chaotic dynamics have been observed in a wide range of population models. Here we describe the effects of perturbing several of these models so as to introduce a non-zero minimum population size. This perturbation generally reduces the likelihood of observing chaos, in both discrete and continuous time models. The extent of this effect depends on whether chaos is generated through period-doubling, quasiperiodicity, or intermittence. Chaos reached via the quasiperiodic route is more robust against the perturbation than period-doubling chaos, whilst the inclusion of a population floor in a model exhibiting intermittent chaos may increase the frequency of population bursts although these become non-chaotic. Copyright 1998 Academic Press.
ORDER IN THE CHAOS IN SPORTS ORGANIZATIONS
Directory of Open Access Journals (Sweden)
Mehran Azarian
2014-07-01
Full Text Available Purpose: Nowadays, scientists consider the world as a combination of some systems that work in a self -organizing way and the result of such a way is unpredictable and accidential states. Compulsory Natural rules are affective in such circumstances. Also it is known that systems work in a circular form in which order ends in disorder and vice versa. The idea of world as something simple has already replaced by a complicated and contradictory world. The study aim is to survey chaordic organizations characters of sport organizations. Materials and methods : For this purpose we used a standard questionnaire with appropriate reliability and validity. The statistical population of the study are whole staff of sport and youth head-quarter of west Azarbaijan province that are 89 (sample number is equal to the population's. We used Kolmogrov- Smirnov test to study data normal distribution, and in respect of normal distribution of data to test hypothesis we used sample t test and also descriptive statistical methods like mean and standard deviation, through SPSS 18. Questionnaires were filled out by whole staff of sport and youth head-quarters of west Azarbaijan province. Results: Results of this study, which have got through a single-sample t-test, show that sport organizations have six characteristics of welcoming to innovation, coherence, uncertainty, non-linearity, unpredictability, and ugly structure. It’s just the grade of the characteristic of recruiting competent staffs that is low in sport organizations; in fact they don’t enjoy it. But, within assessing the main hypothesis of the research that was around the feature of chaos-order, it was resulted that sport organizations have characteristics of a chaos-order organization and they can be considered as a chaos-order organization. Conclusions: According to the results of this study and t-table we can deduce that sport organizations are chaordic organization.
Intramolecular quantum chaos in doped helium nanodroplets
Polyakova, E.; Stolyarov, D.; Zhang, X.; Kresin, V. V.; Wittig, C.
2003-07-01
A mass spectrometric depletion spectrum (17 700-18 300 cm -1) is reported for NO 2 in superfluid (0.37 K) helium nanodroplets. Gas phase NO 2 is believed to be vibronically chaotic at these energies. Transitions are broadened and blue-shifted relative to their gas phase counterparts. The spectrum is fitted reasonably well by setting all of the widths and shifts equal to 7 cm -1. Modest dispersions (i.e., 90% lie within 2 cm -1 of the central values) are consistent with quantum chaos in NO 2. Relaxation is dominated by interactions of NO 2 with its non-superfluid helium nearest neighbors.
Conduction at the onset of chaos
Baldovin, Fulvio
2017-02-01
After a general discussion of the thermodynamics of conductive processes, we introduce specific observables enabling the connection of the diffusive transport properties with the microscopic dynamics. We solve the case of Brownian particles, both analytically and numerically, and address then whether aspects of the classic Onsager's picture generalize to the non-local non-reversible dynamics described by logistic map iterates. While in the chaotic case numerical evidence of a monotonic relaxation is found, at the onset of chaos complex relaxation patterns emerge.
Bose-Hubbard Hamiltonian: Quantum chaos approach
Kolovsky, Andrey R.
2016-03-01
We discuss applications of the theory of quantum chaos to one of the paradigm models of many-body quantum physics — the Bose-Hubbard (BH) model, which describes, in particular, interacting ultracold Bose atoms in an optical lattice. After preliminary, pure quantum analysis of the system we introduce the classical counterpart of the BH model and the governing semiclassical equations of motion. We analyze these equations for the problem of Bloch oscillations (BOs) of cold atoms where a number of experimental results are available. The paper is written for nonexperts and can be viewed as an introduction to the field.
River of kings [Mae Nam Chao Phraya
Energy Technology Data Exchange (ETDEWEB)
Mogg, R.
1997-10-01
Low rainfall and a growing demand for water have had profound effects on water supplies in Thailand`s Mae Nam Chao Phraya river basin. In particular, low water levels are causing problems at the Bhumibol and Sirikit dams, as rice farms are threatened. The work of a Government sponsored think-tank set up to coordinate water management in the region is describe. Strategies may include use of groundwater at peak demand, recycling waste water and improve technical efficiency to reduce distribution losses. Any such policy changes will inevitably have widespread political, economic and social consequences. (UK)
Feigenbaum graphs at the onset of chaos
Energy Technology Data Exchange (ETDEWEB)
Luque, Bartolo; Lacasa, Lucas [Dept. Matemática Aplicada y Estadística, ETSI Aeronáuticos, Universidad Politécnica de Madrid (Spain); Robledo, Alberto, E-mail: robledo@fisica.unam.mx [Instituto de Física y Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México (Mexico)
2012-11-01
We analyze the properties of networks obtained from the trajectories of unimodal maps at the transition to chaos via the horizontal visibility (HV) algorithm. We find that the network degrees fluctuate at all scales with amplitude that increases as the size of the network grows, and can be described by a spectrum of graph-theoretical generalized Lyapunov exponents. We further define an entropy growth rate that describes the amount of information created along paths in network space, and find that such entropy growth rate coincides with the spectrum of generalized graph-theoretical exponents, constituting a set of Pesin-like identities for the network.
Effect of Chaos on Relativistic Quantum Tunneling
2012-06-01
andAkis R., Phys. Rev. Lett., 103 (2009) 054101;Huang L., Lai Y.-C. and Grebogi C., Chaos, 21 (2011) 013102. [3] Novoselov K. S., Geim A. K., Morozov S. V...Feng R., Dai Z., Marchenkov A. N., Conrad E. H., First P. N. and de Heer W. A., J. Phys. Chem. B, 108 (2004) 19912; Novoselov K. S., Geim A. K., Morozov...P., Nature, 438 (2005) 201; Castro Neto A. H., Guinea F., Peres N. M. R., Novoselov K. S. and Geim A. K., Rev. Mod. Phys., 81 (2009) 109; Das Sarma S
Chaos Synchronization in Two Coupled Duffing Oscillators
Institute of Scientific and Technical Information of China (English)
方见树; 荣曼生; 方焯; 刘小娟
2001-01-01
We have obtained two general unstable periodic solutions near the homoclinic orbits of two coupled Duffing oscillators with weak periodic perturbations by using the direct perturbation technique. Theoretical analysis reveals that the stable periodic orbits are embedded in the Melnikov chaotic attractors. The corresponding numerical results show that the phase portraits in the (x, u) and (y, v) planes are identical and are synchronized when the parameters of the two coupled oscillators are identical, but they are different and asynchronized when there is any difference between these parameters. It has been shown that the system parameters play a very important role in chaos control and synchronization.
Quantum chaos and the black hole horizon
CERN. Geneva
2016-01-01
Thanks to AdS/CFT, the analogy between black holes and thermal systems has become a practical tool, shedding light on thermalization, transport, and entanglement dynamics. Continuing in this vein, recent work has shown how chaos in the boundary CFT can be analyzed in terms of high energy scattering right on the horizon of the dual black hole. The analysis revolves around certain out-of-time-order correlation functions, which are simple diagnostics of the butterfly effect. We will review this work, along with a general bound on these functions that implies black holes are the most chaotic systems in quantum mechanics. (NB Room Change to Main Auditorium)
Self-organized chaos through polyhomeostatic optimization.
Markovic, D; Gros, Claudius
2010-08-06
The goal of polyhomeostatic control is to achieve a certain target distribution of behaviors, in contrast to homeostatic regulation, which aims at stabilizing a steady-state dynamical state. We consider polyhomeostasis for individual and networks of firing-rate neurons, adapting to achieve target distributions of firing rates maximizing information entropy. We show that any finite polyhomeostatic adaption rate destroys all attractors in Hopfield-like network setups, leading to intermittently bursting behavior and self-organized chaos. The importance of polyhomeostasis to adapting behavior in general is discussed.
Importance of packing in spiral defect chaos
Indian Academy of Sciences (India)
Kapilanjan Krishna
2008-04-01
We develop two measures to characterize the geometry of patterns exhibited by the state of spiral defect chaos, a weakly turbulent regime of Rayleigh-Bénard convection. These describe the packing of contiguous stripes within the pattern by quantifying their length and nearest-neighbor distributions. The distributions evolve towards unique distribution with increasing Rayleigh number that suggests power-law scaling for the dynamics in the limit of infinite system size. The techniques are generally applicable to patterns that are reducible to a binary representation.
Polarization chaos in an optically pumped laser.
Serrat, C; Kul'minskii, A; Vilaseca, R; Corbalán, R
1995-06-15
We study the steady-state and dynamic behavior of an optically pumped J = 0 ? J = 1 ? J = 0 laser operating with an isotropic ring cavity and an axial magnetic field. The gain anisotropy induced by a linearly polarized pump-laser f ield leads, in the steady state, to locking of the two circularly polarized components of the laser field, which acquires a linear polarization parallel to that of the pump field. In the presence of laser intensity instabilities, however, locking does not occur, and polarization instabilities appear. For the f irst time to our knowledge, polarization chaos has been found in a laser system.
Cryptography with chaos at the physical level
Energy Technology Data Exchange (ETDEWEB)
Machado, Romuel F. E-mail: romuelm@iceb.ufop.br; Baptista, Murilo S.; Grebogi, C
2004-09-01
In this work, we devise a chaos-based secret key cryptography scheme for digital communication where the encryption is realized at the physical level, that is, the encrypting transformations are applied to the wave signal instead to the symbolic sequence. The encryption process consists of transformations applied to a two-dimensional signal composed of the message carrying signal and an encrypting signal that has to be a chaotic one. The secret key, in this case, is related to the number of times the transformations are applied. Furthermore, we show that due to its chaotic nature, the encrypting signal is able to hide the statistics of the original signal.
Geometry in the large and hyperbolic chaos
Energy Technology Data Exchange (ETDEWEB)
Hasslacher, B.; Mainieri, R.
1998-11-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The authors calculated observables in strongly chaotic systems. This is difficult to do because of a lack of a workable orbit classification for such systems. This is due to global geometrical information from the original dynamical system being entangled in an unknown way throughout the orbit sequence. They used geometrical methods from modern mathematics and recent connections between global geometry and modern quantum field theory to study the natural geometrical objects belonging to hard chaos-hyperbolic manifolds.
Time reversibility, computer simulation, and chaos
Hoover, William Graham
1999-01-01
A small army of physicists, chemists, mathematicians, and engineers has joined forces to attack a classic problem, the "reversibility paradox", with modern tools. This book describes their work from the perspective of computer simulation, emphasizing the author's approach to the problem of understanding the compatibility, and even inevitability, of the irreversible second law of thermodynamics with an underlying time-reversible mechanics. Computer simulation has made it possible to probe reversibility from a variety of directions and "chaos theory" or "nonlinear dynamics" has supplied a useful
Delayed self-synchronization in homoclinic chaos
Arecchi, F. T.; Meucci, R.; Allaria, E.; di Garbo, A.; Tsimring, L. S.
2002-04-01
The chaotic spike train of a homoclinic dynamical system is self-synchronized by applying a time-delayed correction proportional to the laser output intensity. Due to the sensitive nature of the homoclinic chaos to external perturbations, stabilization of very long-periodic orbits is possible. On these orbits, the dynamics appears chaotic over a finite time, but then it repeats with a recurrence time that is slightly longer than the delay time. The effect, called delayed self-synchronization, displays analogies with neurodynamic events that occur in the buildup of long-term memories.
Wave Dynamical Chaos in Superconducting Microwave Cavities
Rehfeld, H; Dembowski, C; Gräf, H D; Hofferbert, R; Richter, A; Lengeler, Herbert
1997-01-01
During the last few years we have studied the chaotic behavior of special Euclidian geometries, so-called billiards, from the quantum or in more general sense "wave dynamical" point of view. Due to the equivalence between the stationary Schroedinger equation and the classical Helmholtz equation in the two-dimensional case (plain billiards), it is possible to simulate "quantum chaos" with the help of macroscopic, superconducting microwave cavities. Using this technique we investigated spectra of three billiards from the family of Pascal's Snails (Robnik-Billiards) with a different chaoticity in each case in order to test predictions of standard stochastical models for classical chaotic systems.
A new optimization algorithm based on chaos
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this article, some methods are proposed for enhancing the converging velocity of the COA (chaos optimization algorithm) based on using carrier wave two times, which can greatly increase the speed and efficiency of the first carrier wave's search for the optimal point in implementing the sophisticated searching during the second carrier wave is faster and more accurate.In addition, the concept of using the carrier wave three times is proposed and put into practice to tackle the multi-variables optimization problems, where the searching for the optimal point of the last several variables is frequently worse than the first several ones.
Asano, Yuhma; Kawai, Daisuke; Yoshida, Kentaroh
2015-06-01
We study classical chaotic motions in the Berenstein-Maldacena-Nastase (BMN) matrix model. For this purpose, it is convenient to focus upon a reduced system composed of two-coupled anharmonic oscillators by supposing an ansatz. We examine three ansätze: 1) two pulsating fuzzy spheres, 2) a single Coulomb-type potential, and 3) integrable fuzzy spheres. For the first two cases, we show the existence of chaos by computing Poincaré sections and a Lyapunov spectrum. The third case leads to an integrable system. As a result, the BMN matrix model is not integrable in the sense of Liouville, though there may be some integrable subsectors.
Asano, Yuhma; Yoshida, Kentaroh
2015-01-01
We study classical chaotic motions in the Berenstein-Maldacena-Nastase (BMN) matrix model. For this purpose, it is convenient to focus upon a reduced system composed of two-coupled anharmonic oscillators by supposing an ansatz. We examine three ans\\"atze: 1) two pulsating fuzzy spheres, 2) a single Coulomb-type potential, and 3) integrable fuzzy spheres. For the first two cases, we show the existence of chaos by computing Poincar\\'e sections and a Lyapunov spectrum. The third case leads to an integrable system. As a result, the BMN matrix model is not integrable in the sense of Liouville, though there may be some integrable subsectors.
Using chaos to improve measurement precision
Institute of Scientific and Technical Information of China (English)
何斌; 杨灿军; 周银生; 陈鹰
2002-01-01
If the measuring signals wore input to the chaotic dynamic system as initial parameters, the system outputs might be in steady state, periodic state or chaos state. If the chaotic dynamic system outputs controlled in the periodic states, the periodic numbers would be changed most with the signals. Our novel method is to add chaotic dynamic vibration to the measurement or sensor system. The sensor sensitivity and precision of a measurement system would be improved with this method. Chaotic dynamics measurement algorithms are given and their sensitivity to parameters are analyzed in this paper. The effects of noises on the system are discussed,
Using chaos to improve measurement precision
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
If the measuring signals were input to the chaotic dynamic system as initial parameters, the system outputs might be in steady state, periodic state or chaos state. If the chaotic dynamic system outputs controlled in the periodic states, the periodic numbers would be changed most with the signals. Our novel method is to add chaotic dynamic vibration to the measurement or sensor system.The sensor sensitivity and precision of a measurement system would be improved with this method. Chaotic dynamics measurement algorithms are given and their sensitivity to parameters are analyzed in this paper. The effects of noises on the system are discussed.
Intrinsic time geometrodynamics: explicit examples
Lin, Huei-Chen
2016-01-01
Intrinsic time quantum geometrodynamics resolved `the problem of time' and bridged the deep divide between quantum mechanics and canonical quantum gravity with a Schrodinger equation which describes evolution in intrinsic time variable. In this formalism, Einstein's general relativity is a particular realization of a wider class of theories. Explicit classical black hole and cosmological solutions and the motion of test particles are derived and analyzed in this work in the context of constant three-curvature solutions in intrinsic time geometrodynamics; and we exemplify how this formalism yields results which agree with the predictions of Einstein's theory.
Recent progress on intrinsic charm
Hobbs, T. J.
2017-03-01
Over the past ˜10 years, the topic of the nucleon's nonperturbative or intrinsic charm (IC) content has enjoyed something of a renaissance, largely motivated by theoretical developments involving quark modelers and PDF-fitters. In this talk I will briefly describe the importance of intrinsic charm to various issues in high-energy phenomenology, and survey recent progress in constraining its overall normalization and contribution to the momentum sum rule of the nucleon. I end with the conclusion that progress on the side of calculation has now placed the onus on experiment to unambiguously resolve the proton's intrinsic charm component.
Lavrov, Roman; Peil, Michael; Jacquot, Maxime; Larger, Laurent; Udaltsov, Vladimir; Dudley, John
2009-08-01
We demonstrate experimentally how nonlinear optical phase dynamics can be generated with an electro-optic delay oscillator. The presented architecture consists of a linear phase modulator, followed by a delay line, and a differential phase-shift keying demodulator (DPSK-d). The latter represents the nonlinear element of the oscillator effecting a nonlinear transformation. This nonlinearity is considered as nonlocal in time since it is ruled by an intrinsic differential delay, which is significantly greater than the typical phase variations. To study the effect of this specific nonlinearity, we characterize the dynamics in terms of the dependence of the relevant feedback gain parameter. Our results reveal the occurrence of regular GHz oscillations (approximately half of the DPSK-d free spectral range), as well as a pronounced broadband phase-chaotic dynamics. Beyond this, the observed dynamical phenomena offer potential for applications in the field of microwave photonics and, in particular, for the realization of novel chaos communication systems. High quality and broadband phase-chaos synchronization is also reported with an emitter-receiver pair of the setup.
Intrinsic motivation and learning dynamics
Zgonnikov, Arkady
2013-01-01
We investigate the effects of intrinsic motivation on the dynamics of learning processes. We construct a simple model of a single agent adapting to unknown environment. Performing a repeated choice between a number of initially unexplored alternatives, the agent gains rewards for each selected alternative and in doing so gradually comprehends the environment. In our model the agent choice is governed by two stimuli. The traditional extrinsic motive inclines the agent to maximize the cumulative payoff throughout the process, while the second, intrinsic one, biases the agent towards the novel options that she inherently likes. We show that the intrinsic motivation can induce an instability and periodic dynamics of the learning process which is always stationary in the case of selfish, rational agent. Interestingly, the opposite effect can arise as well: when the impact of intrinsic motivation on the agent choice is strong, the equiprobable choice equilibrium strategy becomes stable. Based on the presented resul...
Equilibrium behavior of coarse-grained chaos
Egolf, David A.; Ballard, Christopher C.; Esty, C. Clark
2015-03-01
A wide variety of systems exhibiting spatiotemporal chaos have been shown to be extensive, in that their fractal dimensions grow linearly with volume. Ruelle argued that this extensivity is evidence that these systems can be viewed as a gas of weakly-interacting regions. We have tested this idea by performing large-scale computational studies of spatiotemporal chaos in the 1D complex Ginzburg-Landau equation, and we have found that aspects of the coarse-grained system are well-described not only as a gas, but as an equilibrium gas -- in particular, a Tonks gas (and variants) in the grand canonical ensemble. Furthermore, for small system sizes, the average number of particles in the corresponding Tonks gas exhibits oscillatory, decaying deviations from extensivity in agreement with deviations in the fractal dimension found by Fishman and Egolf. This result not only supports Ruelle's picture but also suggests that the coarse-grained behavior of this far-from-equilibrium system might be understood using equilibrium statistical mechanics.
Chaos and structure of level densities
Energy Technology Data Exchange (ETDEWEB)
Moller, Peter [Los Alamos National Laboratory; Aberg, Sven [LUND SWEDEN; Uhrenholt, Henrik [LUND SWEDEN; Ickhikawa, Takatoshi [RIKEN
2008-01-01
The energy region of the first few MeV above the ground state shows interesting features of the nucleus. Beyond an ordered energy region just above the ground-state the dynamics changes, and chaotic features are observed in the neutron resonance region. The statistical properties of energies and wave-functions are common to all chaotic nuclei. However, if instead a global property, like the local level-density function is studied, strong structure effects emerge. In this contribution we discuss these two different facets of warm nuclei. In section 2 the onset of chaos with increasing excitation energy is discussed, with both experimental observations and proposed theoretical mechanisms as starting points. The structure of level densities in the same excitation energy region based on the two different starting points, is treated in section 3, where we give a short presentation of a newly developed combinatorial level-density modell. Some results from the model are presented and discussed. Two coexisting facets of warm nuclei, quantum chaos and structure of the level density, are considered. A newly developed combinatorial level-density model is presented, and the role of collective enhancements discussed. An example of extreme parity enhancement is shown.
Rapid dynamical chaos in an exoplanetary system
Deck, Katherine M; Agol, Eric; Carter, Joshua A; Lissauer, Jack J; Ragozzine, Darin; Winn, Joshua N
2012-01-01
We report on the long-term dynamical evolution of the two-planet Kepler-36 system, which we studied through numerical integrations of initial conditions that are consistent with observations of the system. The orbits are chaotic with a Lyapunov time of only ~10 years. The chaos is a consequence of a particular set of orbital resonances, with the inner planet orbiting 34 times for every 29 orbits of the outer planet. The rapidity of the chaos is due to the interaction of the 29:34 resonance with the nearby first order 6:7 resonance, in contrast to the usual case in which secular terms in the Hamiltonian play a dominant role. Only one contiguous region of phase space, accounting for ~4.5% of the sample of initial conditions studied, corresponds to planetary orbits that do not show large scale orbital instabilities on the timescale of our integrations (~200 million years). The long-lived subset of the allowed initial conditions are those that satisfy the Hill stability criterion by the largest margin. Any succes...
Order and chaos in soft condensed matter
Indian Academy of Sciences (India)
A K Sood; Rajesh Ganapathy
2006-07-01
Soft matter, like colloidal suspensions and surfactant gels, exhibit strong response to modest external perturbations. This paper reviews our recent experiments on the nonlinear flow behaviour of surfactant worm-like micellar gels. A rich dynamic behaviour exhibiting regular, quasi-periodic, intermittency and chaos is observed. In particular, we have shown experimentally that the route to chaos is via Type-II intermittency in shear thinning worm-like micellar solution of cetyltrimethylammonium tosylate where the strength of flow-concentration coupling is tuned by the addition of sodium chloride. A Poincaré first return map of the time series and the probability distribution of laminar length between burst events show that our data are consistent with Type-II intermittency. The existence of a `Butterfly' intensity pattern in small angle light scattering (SALS) measurements performed simultaneously with the rheological measurements confirms the coupling of flow to concentration fluctuations in the system under study. The scattered depolarised intensity in SALS, sensitive to orientational order fluctuations, shows the same time-dependence (like intermittency) as that of shear stress.
Quantum chaos and holographic tensor models
Krishnan, Chethan; Sanyal, Sambuddha; Subramanian, P. N. Bala
2017-03-01
A class of tensor models were recently outlined as potentially calculable examples of holography: their perturbative large- N behavior is similar to the Sachdev-Ye-Kitaev (SYK) model, but they are fully quantum mechanical (in the sense that there is no quenched disorder averaging). These facts make them intriguing tentative models for quantum black holes. In this note, we explicitly diagonalize the simplest non-trivial Gurau-Witten tensor model and study its spectral and late-time properties. We find parallels to (a single sample of) SYK where some of these features were recently attributed to random matrix behavior and quantum chaos. In particular, the spectral form factor exhibits a dip-ramp-plateau structure after a running time average, in qualitative agreement with SYK. But we also observe that even though the spectrum has a unique ground state, it has a huge (quasi-?)degeneracy of intermediate energy states, not seen in SYK. If one ignores the delta function due to the degeneracies however, there is level repulsion in the unfolded spacing distribution hinting chaos. Furthermore, there are gaps in the spectrum. The system also has a spectral mirror symmetry which we trace back to the presence of a unitary operator with which the Hamiltonian anticommutes. We use it to argue that to the extent that the model exhibits random matrix behavior, it is controlled not by the Dyson ensembles, but by the BDI (chiral orthogonal) class in the Altland-Zirnbauer classification.
Harmonic structures and intrinsic torsion
DEFF Research Database (Denmark)
Conti, Diego; Madsen, Thomas Bruun
2015-01-01
We discuss the construction of Sp(2)Sp(1)-structures whose fundamental form is closed. In particular, we find 10 new examples of 8-dimensional nilmanifolds that admit an invariant closed 4-form with stabiliser Sp(2) Sp(1). Our constructions entail the notion of SO(4)-structures on 7-manifolds. We...... present a thorough investigation of the intrinsic torsion of such structures, leading to the construction of explicit Lie group examples with invariant intrinsic torsion....
Harmonic structures and intrinsic torsion
DEFF Research Database (Denmark)
Conti, Diego; Madsen, Thomas Bruun
We discuss the construction of 8-manifolds with harmonic Sp(2)Sp(1)-structures. In particular, we find 10 new examples of nilmanifolds that admit a closed 4-form Omega whose stabiliser is Sp(2)Sp(1). Our constructions entail the notion of SO(4)-structures on 7-manifolds. We present a thorough inv...... investigation of the intrinsic torsion of such structures; in addition to the construction of harmonic structures, this analysis leads to explicit Lie group examples with invariant intrinsic torsion....
HOPF BIFURCATION AND CHAOS OF FINANCIAL SYSTEM ON CONDITION OF SPECIFIC COMBINATION OF PARAMETERS
Institute of Scientific and Technical Information of China (English)
Junhai MA; Yaqiang CUI; Lixia LIU
2008-01-01
This paper studies the global bifurcation and Hopf bifurcation of one kind of complicated financial system with different parameter combinations. Conditions on which bifurcation happens, and the critical system structure when the system transforms from one kind of topological structure to another are studied as well. The criterion for identifying Hopf bifurcation under different parameter combinations is also given. The chaotic character of this system under quasi-periodic force is finally studied. The bifurcation structure graphs are given when two parameters of the combination are fixed while the other parameter varies. The presence and stability of 2 and 3 dimensional torus bifurcation are studied. All of the Lyapunov exponents of the system with different bifurcation parameters and routes leading the system to chaos with different parameter combinations are studied. It is of important theoretical and practical meaning to probe the intrinsic mechanism of such continuous complicated financial system and to find the macro control policies for such kind of system.
Dynamical systems approach to one-dimensional spatiotemporal chaos: A cyclist's view
Lan, Yueheng
We propose a dynamical systems approach to the study of weak turbulence (spatiotemporal chaos) based on the periodic orbit theory, emphasizing the role of recurrent patterns and coherent structures. After a brief review of the periodic orbit theory and its application to low-dimensional dynamics, we discuss its possible extension to study dynamics of spatially extended systems. The discussion is three-fold. First, we introduce a novel variational scheme for finding periodic orbits in high-dimensional systems. Second, we prove rigorously the existence of periodic structures (modulated amplitude waves) near the first instability of the complex Ginzburg-Landau equation, and check their role in pattern formation. Third, we present the extensive numerical exploration of the Kuramoto-Sivashinsky system in the chaotic regime: structure of the equilibrium solutions, our search for the shortest periodic orbits, description of the chaotic invariant set in terms of intrinsic coordinates and return maps on the Poincare section.
Spatiotemporal Chaos in Large Systems The Scaling of Complexity with Size
Greenside, H S
1996-01-01
The dynamics of a nonequilibrium system can become complex because the system has many components (e.g., a human brain), because the system is strongly driven from equilibrium (e.g., large Reynolds-number flows), or because the system becomes large compared to certain intrinsic length scales. Recent experimental and theoretical work is reviewed that addresses this last route to complexity. In the idealized case of a sufficiently large, nontransient, homogeneous, and chaotic system, the fractal dimension D becomes proportional to the system's volume V which defines the regime of extensive chaos. The extensivity of the fractal dimension suggests a new way to characterize correlations in high-dimensional systems in terms of an intensive dimension correlation length $\\xi_\\delta$. Recent calculations at Duke University show that $\\xi_\\delta$ is a length scale smaller than and independent of some commonly used measures of disorder such as the two-point and mutual-information correlation lengths. Identifying the bas...
Topological chaos of the spatial prisoner's dilemma game on regular networks.
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.
Study on Chaos Created by Hopf Bifurcation of One Kind of Financial System and Its Application
Institute of Scientific and Technical Information of China (English)
JunhaiMa; BiaoRen; YanGao
2004-01-01
From a mathematical model of one kind complicated financial system, corresponding local topological structures of such kind system on condition of certain parametercombination, unstable equilibrium point of the system, conditions on which Hopf bifurcation is created and stability of the limit circle corresponding to the Hopf bifurcation as well as condition on which the limit circle is stable have been studied. From relationship between each parameter and the Hopf bifurcation all the way to route which leads to chaos etc have been studied. Following the above, conditions on which complicated behaviors created locally in such kind system has been analyzed. By applying fractal dimension, Lyapunov index, the intrinsic complexity of the system on such condition has been studied, and result of the numerical simulation proves the theory of this paper correct.
Chaos in temporarily destabilized regular systems with the slow passage effect
Energy Technology Data Exchange (ETDEWEB)
Perc, Matjaz [Department of Physics, Faculty of Education, University of Maribor, Koroska cesta 160, SI-2000 Maribor (Slovenia)] e-mail: matjaz.perc@uni-mb.si; Marhl, Marko [Department of Physics, Faculty of Education, University of Maribor, Koroska cesta 160, SI-2000 Maribor (Slovenia)
2006-01-01
We provide evidences for chaotic behaviour in temporarily destabilized regular systems. In particular, we focus on time-continuous systems with the slow passage effect. The extreme sensitivity of the slow passage phase enables the existence of long chaotic transients induced by random pulsatile perturbations, thereby evoking chaotic behaviour in an initially regular system. We confirm the chaotic behaviour of the temporarily destabilized system by calculating the largest Lyapunov exponent. Moreover, we show that the newly obtained unstable periodic orbits can be easily controlled with conventional chaos control techniques, thereby guaranteeing a rich diversity of accessible dynamical states that is usually expected only in intrinsically chaotic systems. Additionally, we discuss the biological importance of presented results.
Decrease of cardiac chaos in congestive heart failure
Poon, Chi-Sang; Merrill, Christopher K.
1997-10-01
The electrical properties of the mammalian heart undergo many complex transitions in normal and diseased states. It has been proposed that the normal heartbeat may display complex nonlinear dynamics, including deterministic chaos,, and that such cardiac chaos may be a useful physiological marker for the diagnosis and management, of certain heart trouble. However, it is not clear whether the heartbeat series of healthy and diseased hearts are chaotic or stochastic, or whether cardiac chaos represents normal or abnormal behaviour. Here we have used a highly sensitive technique, which is robust to random noise, to detect chaos. We analysed the electrocardiograms from a group of healthy subjects and those with severe congestive heart failure (CHF), a clinical condition associated with a high risk of sudden death. The short-term variations of beat-to-beat interval exhibited strongly and consistently chaotic behaviour in all healthy subjects, but were frequently interrupted by periods of seemingly non-chaotic fluctuations in patients with CHF. Chaotic dynamics in the CHF data, even when discernible, exhibited a high degree of random variability over time, suggesting a weaker form of chaos. These findings suggest that cardiac chaos is prevalent in healthy heart, and a decrease in such chaos may be indicative of CHF.
Spirals, chaos, and new mechanisms of wave propagation.
Chen, P S; Garfinkel, A; Weiss, J N; Karagueuzian, H S
1997-02-01
The chaos theory is based on the idea that phenomena that appear disordered and random may actually be produced by relatively simple deterministic mechanisms. The disordered (aperiodic) activation that characterizes a chaotic motion is reached through one of a few well-defined paths that are characteristic of nonlinear dynamical systems. Our group has been studying VF using computerized mapping techniques. We found that in electrically induced VF, reentrant wavefronts (spiral waves) are present both in the initial tachysystolic stage (resembling VT) and the later tremulous incoordination stage (true VF). The electrophysiological characteristics associated with the transition from VT to VF is compatible with the quasiperiodic route to chaos as described in the Ruelle-Takens theorem. We propose that specific restitution of action potential duration (APD) and conduction velocity properties can cause a spiral wave (the primary oscillator) to develop additional oscillatory modes that lead to spiral meander and breakup. When spiral waves begin to meander and are modulated by other oscillatory processes, the periodic activity is replaced by unstable quasiperiodic oscillation, which then undergoes transition to chaos, signaling the onset of VF. We conclude that VF is a form of deterministic chaos. The development of VF is compatible with quasiperiodic transition to chaos. These results indicate that both the prediction and the control of fibrillation are possible based on the chaos theory and with the advent of chaos control algorithms.
Quantum Chaos in Physical Systems from Super Conductors to Quarks
Bittner, E; Pullirsch, R; Bittner, Elmar; Markum, Harald; Pullirsch, Rainer
2001-01-01
This article is the written version of a talk delivered at the Bexbach Colloquium of Science 2000 and starts with an introduction into quantum chaos and its relationship to classical chaos. The Bohigas-Giannoni-Schmit conjecture is formulated and evaluated within random-matrix theory. Several examples of physical systems exhibiting quantum chaos ranging from nuclear to solid state physics are presented. The presentation concludes with recent research work on quantum chromodynamics and the quark-gluon plasma. In the case of a chemical potential the eigenvalue spectrum becomes complex and one has to deal with non-Hermitian random-matrix theory.
Contributions of plasma physics to chaos and nonlinear dynamics
Escande, D. F.
2016-11-01
This topical review focusses on the contributions of plasma physics to chaos and nonlinear dynamics bringing new methods which are or can be used in other scientific domains. It starts with the development of the theory of Hamiltonian chaos, and then deals with order or quasi order, for instance adiabatic and soliton theories. It ends with a shorter account of dissipative and high dimensional Hamiltonian dynamics, and of quantum chaos. Most of these contributions are a spin-off of the research on thermonuclear fusion by magnetic confinement, which started in the fifties. Their presentation is both exhaustive and compact. [15 April 2016
Evidence of low-dimensional chaos in magnetized plasma turbulence
Zivkovic, Tatjana
2008-01-01
We analyze probe data obtained from a toroidal magnetized plasma configuration suitable for studies of low-frequency gradient-driven instabilities. These instabilities give rise to field-aligned convection rolls analogous to Rayleigh-Benard cells in neutral fluids, and may theoretically develop similar routes to chaos. When using mean-field dimension analysis, we observe low dimensionality, but this could originate from either low-dimensional chaos, periodicity or quasi-periodicity. Therefore, we apply recurrence plot analysis as well as estimation of the largest Lyapunov exponent. These analyses provide evidence of low-dimensional chaos, in agreement with theoretical predictions.
Diffusive Lorenz dynamics： Coherent structures and spatiotemporal chaos
Institute of Scientific and Technical Information of China (English)
YuehongQIAN; HudongCHEN; Da-HsuanFENG
2000-01-01
In this paper, we are interested in collective behaviors of many interacting Lorenz strange attractors. With an intermediate diffusion coupling between the attractors,a new remarkable synchronization of well organized structures merges as a result of two competing mechanisms: temporal chaos and spatial diffusive stabilization. A window of the coupling parameter for coherent structures is found numerically. Different from all existing scenarios of routes to chaos (period doubling, intermittency and strange attractors), an algorithmetic increase of wavenumbers before an abrupt change to chaos (compared to the periodic doubling geometrical) is unexpectedly discovered. Meta-stable states are also observed in simulations.
CHAOS THEORY: A CONTRIBUTION TO THE FORMATION OF STRATEGIES
Directory of Open Access Journals (Sweden)
Marcio Luiz Marietto
2011-12-01
Full Text Available It is our intention, through this work, to contribute to the understanding of the influence of chaos theory on the formation of organizational strategies in the dynamic and complex environment in which organizations are embedded. In this sense, we present a theoretical review, leveraged by a dialectical epistemology, in which we propose to show some attributes of chaos theory and theoretical assumptions to be considered in the context of different areas of organizational strategy, with the goal of trying to elucidate and approximate the analytical characteristics of both theories and make evident how chaos theory can contribute to and/or influence the formation of business strategies.
New chaos-based encryption scheme for digital sequence
Institute of Scientific and Technical Information of China (English)
Zhang Zhengwei; Fan Yangyu; Zeng Li
2007-01-01
To enhance the anti-breaking performance of privacy information, this article proposes a new encryption method utilizing the leaping peculiarity of the periodic orbits of chaos systems. This method maps the secret sequence to several chaos periodic orbits, and a short sequence obtained by evolving the system parameters of the periodic orbits in another nonlinear system will be the key to reconstruct these periodic orbits. In the decryption end, the shadowing method of chaos trajectory based on the modified Newton-Raphson algorithm is adopted to restore these system parameters. Through deciding which orbit each pair coordinate falls on, the original digital sequence can be decrypted.
From chaos to order methodologies, perspectives and applications
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
Controlling beam halo-chaos via backstepping design
Institute of Scientific and Technical Information of China (English)
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.
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.
Theory of the nucleus as applied to quantum chaos
Energy Technology Data Exchange (ETDEWEB)
Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu [St. Petersburg State University, Petersburg Nuclear Physics Institute, National Research Center Kurchatov Institute (Russian Federation)
2014-12-15
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. It is proposed to specify a regular versus a chaotic behavior on the basis of symmetries of the system being considered and global integrals of motion that are associated with these symmetries in accordance with the Liouville-Arnold theorem rather than on the basis of the concept of Lyapunov’s instability of trajectories. Numerical criteria of quantum chaos that follow from the proposed concept are analyzed.
Quasiperiodicity route to chaos in cardiac conduction model
Quiroz-Juárez, M. A.; Vázquez-Medina, R.; Ryzhii, E.; Ryzhii, M.; Aragón, J. L.
2017-01-01
It has been suggested that cardiac arrhythmias are instances of chaos. In particular that the ventricular fibrillation is a form of spatio-temporal chaos that arises from normal rhythm through a quasi-periodicity or Ruelle-Takens-Newhouse route to chaos. In this work, we modify the heterogeneous oscillator model of cardiac conduction system proposed in Ref. [Ryzhii E, Ryzhii M. A heterogeneous coupled oscillator model for simulation of ECG signals. Comput Meth Prog Bio 2014;117(1):40-49. doi:10.1016/j.cmpb.2014.04.009.], by including an ectopic pacemaker that stimulates the ventricular muscle to model arrhythmias. With this modification, the transition from normal rhythm to ventricular fibrillation is controlled by a single parameter. We show that this transition follows the so-called torus of quasi-periodic route to chaos, as verified by using numerical tools such as power spectrum and largest Lyapunov exponent.
Chaos-assisted, broadband trapping of light in optical resonators
Liu, C; Molinari, D; Khan, Y; Ooi, B S; Krauss, T F; Fratalocchi, A
2012-01-01
Chaos is a phenomenon that occurs in many aspects of contemporary science. In classical dynamics, chaos is defined as a hypersensitivity to initial conditions. The presence of chaos is often unwanted, as it introduces unpredictability, which makes it difficult to predict or explain experimental results. Conversely, we demonstrate here how chaos can be used to enhance the ability of an optical resonator to store energy. We combine analytic theory with ab-initio simulations and experiments in photonic crystal resonators to show that a chaotic resonator can store six times more energy than its classical counterpart of the same volume. We explain the observed increase with the equipartition of energy among all degrees of freedom of the chaotic resonator, i.e. the cavity modes, which is evident from the convergence of their lifetime towards a single value. A compelling illustration of the theory is provided by demonstrating enhanced absorption in deformed polystyrene microspheres.
Bifurcation of Periodic Orbits and Chaos in Duffing Equation
Institute of Scientific and Technical Information of China (English)
Mei-xiang Cai; Jian-ping Yang
2006-01-01
Duffing equation with fifth nonlinear-restoring force, one external forcing and a phase shift is investigated. The conditions of existences for primary resonance, second-order, third-order subharmonics, morder subharmonics and chaos are given by using second-averaging method, Melnikov methods and bifurcation theory. Numerical simulations including bifurcation diagrams, bifurcation surfaces, phase portraits, not only show the consistence with the theoretical analysis, but also exhibit the new dynamical behaviors. We show the onset of chaos, chaos suddenly disappearing to period orbit, one-band and double-band chaos, period-doubling bifurcations from period 1, 2, and 3 orbits, period-windows (period-2, 3 and 5) in chaotic regions.
Chaos as a Source of Complexity and Diversity in Evolution
Kaneko, K
1993-01-01
The relevance of chaos to evolution is discussed in the context of the origin and maintenance of diversity and complexity. Evolution to the edge of chaos is demonstrated in an imitation game. As an origin of diversity, dynamic clustering of identical chaotic elements, globally coupled each to other, is briefly reviewed. The clustering is extended to nonlinear dynamics on hypercubic lattices, which enables us to construct a self-organizing genetic algorithm. A mechanism of maintenance of diversity, ``homeochaos", is given in an ecological system with interaction among many species. Homeochaos provides a dynamic stability sustained by high-dimensional weak chaos. A novel mechanism of cell differentiation is presented, based on dynamic clustering. Here, a new concept -- ``open chaos" -- is proposed for the instability in a dynamical system with growing degrees of freedom. It is suggested that studies based on interacting chaotic elements can replace both top-down and bottom-up approaches.
Fractional Chaos Based Communication Systems-An Introduction
Institute of Scientific and Technical Information of China (English)
Juebang Yu
2008-01-01
As one of secure communication means, chaotic communication systems has been well-developed during the past three decades. Technical papers, both for theoretical and practical investigations, have reached a huge amount in number. On the other hand, fractional chaos, as a parallel ongoing research topic, also attracts many researchers to investigate. As far as the IT field is concerned, the research on control systems by using fractional chaos known as FOC (fractional order control) has been a hot issue for quite a long time. As a comparison, interesting enough, up to now we have not found any research result related to Fractional Chaos Communi cation (FCC) system, Le., a system based on fractional chaos. The motivation of the present article is to reveal the feasibility of realizing communication systems based upon FCC and their superiority over the conventional integer chaotic communication systems. Principles of FCC and its advantages over integer chaotic communication systems are also discussed.
Biological conditions for oscillations and chaos generated by multispecies competition
Huisman, J; Weissing, FJ
2001-01-01
We investigate biological mechanisms that generate oscillations and chaos in multispecies competition models. For this purpose, we use a competition model concerned with competition for abiotic essential resources. Because phytoplankton and plants consume quite a number of abiotic essential resource
The transition to chaos conservative classical systems and quantum manifestations
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...
Complex Nonlinearity Chaos, Phase Transitions, Topology Change and Path Integrals
Ivancevic, Vladimir G
2008-01-01
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to th...
Extension of spatiotemporal chaos in glow discharge-semiconductor systems
Energy Technology Data Exchange (ETDEWEB)
Akhmet, Marat, E-mail: marat@metu.edu.tr; Fen, Mehmet Onur [Department of Mathematics, Middle East Technical University, 06800 Ankara (Turkey); Rafatov, Ismail [Department of Physics, Middle East Technical University, 06800 Ankara (Turkey)
2014-12-15
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).].
Secular Chaos and the Production of Hot Jupiters
Wu, Yanqin
2010-01-01
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 towards 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 (Lithwick & Wu, 2010). After an extended period of eccentricity diffusion, the inner planet's pericentre can approach the star to within a few stellar radii. Strong tidal interactions and ensuing tidal dissipation extracts orbital energy from the planet and pulls it inward, creating a hot Jupiter. In contrast to other proposed channels for the production of hot Jupiters, such a scenario (which we term...
Controlling chaos using an exponential control
Gadre, S D; Gadre, Sangeeta D; Varma, V S
1995-01-01
We demonstrate that chaos can be controlled using a multiplicative exponential feedback control. All three types of unstable orbits - unstable fixed points, limit cycles and chaotic trajectories can be stabilized using this control. The control is effective both for maps and flows. The control is significant, particularly for systems with several degrees of freedom, as knowledge of only one variable on the desired unstable orbit is sufficient to settle the system on to that orbit. We find, that in all the cases studied, the transient time is a decreasing function of the stiffness of control. But increasing the stiffness beyond an optimum value can increase the transient time. The control can also be used to create suitable new stable attractors in a map, which did not exist in the original system.
Digital Communications Using Chaos and Nonlinear Dynamics
Larson, Lawrence E; Liu, Jia-Ming
2006-01-01
This book introduces readers to a new and exciting cross-disciplinary field of digital communications with chaos. This field was born around 15 years ago, when it was first demonstrated that nonlinear systems which produce complex non-periodic noise-like chaotic signals, can be synchronized and modulated to carry useful information. Thus, chaotic signals can be used instead of pseudo-random digital sequences for spread-spectrum and private communication applications. This deceptively simple idea spun hundreds of research papers, and many novel communication schemes based on chaotic signals have been proposed. However, only very recently researchers have begun to make a transition from academic studies toward practical implementation issues, and many "promising" schemes had to be discarded or re-formulated. This book describes the state of the art (both theoretical and experimental) of this novel field. The book is written by leading experts in the fields of Nonlinear Dynamics and Electrical Engineering who pa...
Theory of Secular Chaos and Mercury's Orbit
Lithwick, Yoram
2010-01-01
We study the chaotic orbital evolution of planetary systems, focusing on secular (i.e., orbit-averaged) interactions, because these often dominate on long timescales. We first focus on the evolution of a test particle that is forced by multiple massive planets. To linear order in eccentricity and inclination, its orbit precesses with constant frequencies. But nonlinearities can shift the frequencies into and out of secular resonance with the planets' eigenfrequencies, or with linear combinations of those frequencies. The overlap of these nonlinear secular resonances drive secular chaos in planetary systems. We quantify the resulting dynamics for the first time by calculating the locations and widths of nonlinear secular resonances. When results from both analytical calculations and numerical integrations are displayed together in a newly developed "map of the mean momenta" (MMM), the agreement is excellent. This map is particularly revealing for non-coplanar planetary systems and demonstrates graphically that...
Chaos in body-vortex interactions
DEFF Research Database (Denmark)
Pedersen, Johan Rønby; Aref, Hassan
2010-01-01
The model of body–vortex interactions, where the fluid flow is planar, ideal and unbounded, and the vortex is a point vortex, is studied. The body may have a constant circulation around it. The governing equations for the general case of a freely moving body of arbitrary shape and mass density...... 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...... and an arbitrary number of point vortices are presented. The case of a body and a single vortex is then investigated numerically in detail. In this paper, the body is a homogeneous, elliptical cylinder. For large body–vortex separations, the system behaves much like a vortex pair regardless of body shape. The case...
Spatial chaos-based image encryption design
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
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, permutation and sub- stitution methods are incorporated to present a stronger image encryption algorithm. Spatial chaotic maps are used to realize the position permutation, and to confuse the relationship between the ci- pher-image and the plain-image. The experimental results demonstrate that the suggested encryption scheme of image has the advantages of large key space and high security; moreover, the distribution of grey values of the encrypted image has a random-like behavior.
Spatial chaos-based image encryption design
Institute of Scientific and Technical Information of China (English)
LIU ShuTang; SUN FuYan
2009-01-01
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, permutation and sub-stitution methods are incorporated to present a stronger image encryption algorithm. Spatial chaotic maps are used to realize the position permutation, and to confuse the relationship between the ci-pher-image and the plain-image. The experimental results demonstrate that the suggested encryption scheme of image has the advantages of large key space and high security; moreover, the distribution of grey values of the encrypted image has a random-like behavior.
Time reversibility, computer simulation, algorithms, chaos
Hoover, William Graham
2012-01-01
A small army of physicists, chemists, mathematicians, and engineers has joined forces to attack a classic problem, the "reversibility paradox", with modern tools. This book describes their work from the perspective of computer simulation, emphasizing the author's approach to the problem of understanding the compatibility, and even inevitability, of the irreversible second law of thermodynamics with an underlying time-reversible mechanics. Computer simulation has made it possible to probe reversibility from a variety of directions and "chaos theory" or "nonlinear dynamics" has supplied a useful vocabulary and a set of concepts, which allow a fuller explanation of irreversibility than that available to Boltzmann or to Green, Kubo and Onsager. Clear illustration of concepts is emphasized throughout, and reinforced with a glossary of technical terms from the specialized fields which have been combined here to focus on a common theme. The book begins with a discussion, contrasting the idealized reversibility of ba...
Chaos synchronization based on intermittent state observer
Institute of Scientific and Technical Information of China (English)
Li Guo-Hui; Zhou Shi-Ping; Xu De-Ming
2004-01-01
This paper describes the method of synchronizing slave to the master trajectory using an intermittent state observer by constructing a synchronizer which drives the response system globally tracing the driving system asymptotically. It has been shown from the theory of synchronization error-analysis that a satisfactory result of chaos synchronization is expected under an appropriate intermittent period and state observer. Compared with continuous control method,the proposed intermittent method can target the desired orbit more efficiently. The application of the method is demonstrated on the hyperchaotic Rossler systems. Numerical simulations show that the length of the synchronization interval rs is of crucial importance for our scheme, and the method is robust with respect to parameter mismatch.
Mechanics From Newton's Laws to Deterministic Chaos
Scheck, Florian
2010-01-01
This book covers all topics in mechanics from elementary Newtonian mechanics, the principles of canonical mechanics and rigid body mechanics to relativistic mechanics and nonlinear dynamics. It was among the first textbooks to include dynamical systems and deterministic chaos in due detail. As compared to the previous editions the present fifth edition is updated and revised with more explanations, additional examples and sections on Noether's theorem. Symmetries and invariance principles, the basic geometric aspects of mechanics as well as elements of continuum mechanics also play an important role. The book will enable the reader to develop general principles from which equations of motion follow, to understand the importance of canonical mechanics and of symmetries as a basis for quantum mechanics, and to get practice in using general theoretical concepts and tools that are essential for all branches of physics. The book contains more than 120 problems with complete solutions, as well as some practical exa...
Stochastic chaos in a turbulent swirling flow
Faranda, Davide; Saint-Michel, Brice; Wiertel, Cecile; Padilla, Vincent; Dubrulle, Berengere; Daviaud, Francois
2016-01-01
We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can first reconstruct the associated turbulent attractor and then follow its route towards chaos. We further show that the experimental attractor can be modeled by stochastic Duffing equations, that match the quantitative properties of the experimental flow, namely the number of quasi-stationary states and transition rates among them, the effective dimensions, and the continuity of the first Lyapunov exponents. Such properties can neither be recovered using deterministic models nor using stochastic differential equations based on effective potentials obtained by inverting the probability distributions of the experimental global observables. Our findings open the way to low dimensional modeling of systems featuring a large number of degrees of freedom and multiple quasi-station...
Chaos suppression in gas-solid fluidization.
Pence, Deborah V.; Beasley, Donald E.
1998-06-01
Fluidization in granular materials occurs primarily as a result of a dynamic balance between gravitational forces and forces resulting from the flow of a fluid through a bed of discrete particles. For systems where the fluidizing medium and the particles have significantly different densities, density wave instabilities create local pockets of very high void fraction termed bubbles. The fluidization regime is termed the bubbling regime. Such a system is appropriately termed a self-excited nonlinear system. The present study examines chaos suppression resulting from an opposing oscillatory flow in gas-solid fluidization. Time series data representing local, instantaneous pressure were acquired at the surface of a horizontal cylinder submerged in a bubbling fluidized bed. The particles had a weight mean diameter of 345 &mgr;m and a narrow size distribution. The state of fluidization corresponded to the bubbling regime and total air flow rates employed in the present study ranged from 10% to 40% greater than that required for minimum fluidization. The behavior of time-varying local pressure in fluidized beds in the absence of a secondary flow is consistent with deterministic chaos. Kolmogorov entropy estimates from local, instantaneous pressure suggest that the degree of chaotic behavior can be substantially suppressed by the presence of an opposing, oscillatory secondary flow. Pressure signals clearly show a "phase-locking" phenomenon coincident with the imposed frequency. In the present study, the greatest degree of suppression occurred for operating conditions with low primary and secondary flow rates, and a secondary flow oscillation frequency of 15 Hz. (c) 1998 American Institute of Physics.
Chaotic operation and chaos control of travelling wave ultrasonic motor.
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.
Controlling of Beam Halo-chaos by Adaptation Method
Institute of Scientific and Technical Information of China (English)
FANGJin-qing; GAOYuan; LUOXiao-shu
2003-01-01
In this paper, the parametric adaptation method for controlling the beam halo-chaos in the periodic focusing channels of high-current proton linacs is proposed. The study of proton beam halo-chaos based on controlled beam envelope equation and the Particles-in-Cell simulations for proton beam dynamics show that the proton beam chaotic envelope as well as the beam rsm radius can be controlled to the matched radius using this method.
Chaos and Nonlinear Dynamics in a Quantum Artificial Economy
Gonçalves, Carlos Pedro
2012-01-01
Chaos and nonlinear economic dynamics are addressed for a quantum coupled map lattice model of an artificial economy, with quantized supply and demand equilibrium conditions. The measure theoretic properties and the patterns that emerge in both the economic business volume dynamics' diagrams as well as in the quantum mean field averages are addressed and conclusions are drawn in regards to the application of quantum chaos theory to address signatures of chaotic dynamics in relevant discrete economic state variables.
Secure Communication System Based on Chaos in Optical Fibre
Institute of Scientific and Technical Information of China (English)
Pak; L; Chu; Fan; Zhang; William; Mak; Robust; Lai
2003-01-01
1 IntroductionRecently, there have been intense research activities on the study of synchronized chaos generated by fibre lasers and its application to secure communication systems. So far, all studies concentrate on two aspects: (1) the effect of the transmission channel between the transmitter and the receiver has been neglected, and (2) the chaos and the signal are carried by one wavelength. Both theoretical and experimental investigations make
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.
Chaos in a double driven dissipative nonlinear oscillator.
Adamyan, H H; Manvelyan, S B; Kryuchkyan, G Y
2001-10-01
We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the framework of the statistical ensemble of quantum trajectories in a quantum state diffusion approach. The quantum dynamical manifestations of chaotic behavior, including the emergence of chaos, properties of strange attractors, and quantum entanglement, are studied by numerical simulation of the ensemble averaged Wigner function and von Neumann entropy.
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.
Bifurcations and chaos control in discrete small-world networks
Institute of Scientific and Technical Information of China (English)
Li Ning; Sun Hai-Yi; Zhang Qing-Ling
2012-01-01
An impulsive delayed feedback control strategy to control period-doubling bifurcations and chaos is proposed.The control method is then applied to a discrete small-world network model.Qualitative analyses and simulations show that under a generic condition,the bifurcations and the chaos can be delayed or eliminated completely.In addition,the periodic orbits embedded in the chaotic attractor can be stabilized.
Chaos control applied to coherent states in transitional flows
Energy Technology Data Exchange (ETDEWEB)
Pausch, Marina; Eckhardt, Bruno, E-mail: bruno.eckhardt@physik.uni-marburg.de [Fachbereich Physik, Philipps-Universitaet Marburg, Renthof 6, 35032 Marburg (Germany)
2011-12-22
Chaos control refers to a group of techniques by which an otherwise unstable dynamical state of a system can be maintained by small control forces. We here discuss their application to stabilizing the fixed points in a low dimensional model for shear flows. The simulations demonstrate a prototypical application of chaos control, show that control is almost always possible, and give insights into optimizing the control matrix from a design point of view.
The Complex Network Synchronization via Chaos Control Nodes
Directory of Open Access Journals (Sweden)
Yin Li
2013-01-01
Full Text Available We investigate chaos control nodes of the complex network synchronization. The structure of the coupling functions between the connected nodes is obtained based on the chaos control method and Lyapunov stability theory. Moreover a complex network with nodes of the new unified Loren-Chen-Lü system, Coullet system, Chee-Lee system, and the New system is taken as an example; numerical simulations are used to verify the effectiveness of the method.
Chaos control of chaotic dynamical systems using backstepping design
Energy Technology Data Exchange (ETDEWEB)
Yassen, M.T. [Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)] e-mail: mtyassen@yahoo.com
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.
Intrinsic energy partition in fission
Directory of Open Access Journals (Sweden)
Mirea M.
2013-03-01
Full Text Available The intrinsic energy partition between two complementary fission fragments is investigated microscopically. The intrinsic excitation energy of fission fragments is dynamically evaluated in terms of the time-dependent pairing equations. These equations are corroborated with two conditions. One of them fixes the number of particles and the other separates the pairing active spaces associated to the two fragments in the vicinity of the scission configuration. The excitation energy in a wide distribution of fission fragments is calculated for the 234U parent nucleus.
OnN Kac's Chaos and Related Problems
Hauray, Maxime
2012-01-01
This paper is devoted to establish quantitative and qualitative estimates related to the notion of chaos as firstly formulated by M. Kac [37] in his study of mean-field limit for systems of N undistinguishable particles as N \\rightarrow \\infty. First, we quantitatively liken three usual measures of Kac's chaos, some involving the all N variables, other involving a finite fixed number of variables. The cornerstone of the proof is a new representation of the Monge-Kantorovich-Wasserstein (MKW) distance for symmetric N-particle probabilities in terms of the distance between the law of the associated empirical measures on the one hand, and a new estimate on some MKW distance on probability spaces endowed with a suitable Hilbert norm taking advantage of the associated good algebraic structure. Next, we define the notion of entropy chaos and Fisher information chaos in a similar way as defined by Carlen et al [17]. We show that Fisher information chaos is stronger than entropy chaos, which in turn is stronger than ...
Chaos and dynamics of spinning particles in Kerr spacetime
Han, Wenbiao
2008-09-01
We study chaos dynamics of spinning particles in Kerr spacetime of rotating black holes use the Papapetrou equations by numerical integration. Because of spin, this system exists many chaos solutions, and exhibits some exceptional dynamic character. We investigate the relations between the orbits chaos and the spin magnitude S, pericenter, polar angle and Kerr rotation parameter a by means of a kind of brand new Fast Lyapulov Indicator (FLI) which is defined in general relativity. The classical definition of Lyapulov exponent (LE) perhaps fails in curve spacetime. And we emphasize that the Poincaré sections cannot be used to detect chaos for this case. Via calculations, some new interesting conclusions are found: though chaos is easier to emerge with bigger S, but not always depends on S monotonically; the Kerr parameter a has a contrary action on the chaos occurrence. Furthermore, the spin of particles can destroy the symmetry of the orbits about the equatorial plane. And for some special initial conditions, the orbits have equilibrium points.
Chaos Suppression in a Sine Square Map through Nonlinear Coupling
Institute of Scientific and Technical Information of China (English)
Eduardo L. Brugnago; Paulo C. Rech
2011-01-01
We study a pair of nonlinearly coupled identical chaotic sine square maps.More specifically,we investigate the chaos suppression associated with the variation of two parameters.Two-dimensional parameter-space regions where the chaotic dynamics of the individual chaotic sine square map is driven towards regular dynamics are delimited.Additionally,the dynamics of the coupled system is numerically characterized as the parameters are changed.In recent years,many efforts have been devoted to chaos suppression in a nonlinear dynamics field.Iglesias et al.[1] reported a chaos suppression method through numerical truncation and rounding errors,with applications in discrete-time systems.Hénon map[2] and the Burgers map[3] were used to illustrate the method.A method of feedback impulsive chaos suppression was introduced by Osipov et al.[4]It is an algorithm of suppressing chaos in continuoustime dissipative systems with an external impulsive force,whose necessary condition is a reduction of the continuous flow to a discrete-time one-dimensional map.%We study a pair of nonlinearly coupled identical chaotic sine square maps. More specifically, we investigate the chaos suppression associated with the variation of two parameters. Two-dimensional parameter-space regions where the chaotic dynamics of the individual chaotic sine square map is driven towards regular dynamics are delimited. Additionally, the dynamics of the coupled system is numerically characterized as the parameters are changed.
The bifurcation threshold value of the chaos detection system for a weak signal
Institute of Scientific and Technical Information of China (English)
李月; 杨宝俊; 杜立志; 袁野
2003-01-01
Recently, it has become an important problem to confirm the bifurcation threshold value of a chaos detectionsystem for a weak signal in the fields of chaos detection. It is directly related to whether the results of chaos detectionare correct or not. In this paper, the discrimination system for the dynamic behaviour of a chaos detection system fora weak signal is established by using the theory of linear differential equation with periodic coefficients and computingthe Lyapunov exponents of the chaos detection system; and then, the movement state of the chaos detection system isdefined. The simulation experiments show that this method can exactly confirm the bifurcation threshold value of thechaos detection system.
Intrinsic Motivation in Physical Education
Davies, Benjamin; Nambiar, Nathan; Hemphill, Caroline; Devietti, Elizabeth; Massengale, Alexandra; McCredie, Patrick
2015-01-01
This article describes ways in which educators can use Harter's perceived competence motivation theory, the achievement goal theory, and self-determination theory to develop students' intrinsic motivation to maintain physical fitness, as demonstrated by the Sound Body Sound Mind curriculum and proven effective by the 2013 University of…
Directory of Open Access Journals (Sweden)
Novelletto Andrea
2011-03-01
Full Text Available Abstract Background The process of Greek colonization of the central and western Mediterranean during the Archaic and Classical Eras has been understudied from the perspective of population genetics. To investigate the Y chromosomal demography of Greek colonization in the western Mediterranean, Y-chromosome data consisting of 29 YSNPs and 37 YSTRs were compared from 51 subjects from Provence, 58 subjects from Smyrna and 31 subjects whose paternal ancestry derives from Asia Minor Phokaia, the ancestral embarkation port to the 6th century BCE Greek colonies of Massalia (Marseilles and Alalie (Aleria, Corsica. Results 19% of the Phokaian and 12% of the Smyrnian representatives were derived for haplogroup E-V13, characteristic of the Greek and Balkan mainland, while 4% of the Provencal, 4.6% of East Corsican and 1.6% of West Corsican samples were derived for E-V13. An admixture analysis estimated that 17% of the Y-chromosomes of Provence may be attributed to Greek colonization. Using the following putative Neolithic Anatolian lineages: J2a-DYS445 = 6, G2a-M406 and J2a1b1-M92, the data predict a 0% Neolithic contribution to Provence from Anatolia. Estimates of colonial Greek vs. indigenous Celto-Ligurian demography predict a maximum of a 10% Greek contribution, suggesting a Greek male elite-dominant input into the Iron Age Provence population. Conclusions Given the origin of viniculture in Provence is ascribed to Massalia, these results suggest that E-V13 may trace the demographic and socio-cultural impact of Greek colonization in Mediterranean Europe, a contribution that appears to be considerably larger than that of a Neolithic pioneer colonization.
The chaos avant-garde memories of the early days of chaos theory
Abraham, Ralph H
2001-01-01
This book is an authoritative and unique reference for the history of chaos theory, told by the pioneers themselves. It also provides an excellent historical introduction to the concepts. There are eleven contributions, and six of them are published here for the first time - two by Steve Smale, three by Yoshisuke Ueda, and one each by Ralph Abraham, Edward Lorenz, Christian Mira, Floris Takens, T Y Li and James A Yorke, and Otto E Rossler. Contents: On How I Got Started in Dynamical Systems 1959-1962 (S Smale); Finding a Horseshoe on the Beaches of Rio (S Smale); Strange Attractors and the Ori
Sources of Chaos in Planetary Systems Formed Through Numerical Methods
Clement, Matthew S.
2017-01-01
The formation of the solar system’s terrestrial planets has been numerically modeled in countless works, and many other studies have been devoted to char- acterizing our modern planets’ chaotic dynamical state. However, it is still not known whether our planets fragile chaotic state is an expected outcome of terrestrial planet accretion. We use a large suite of numerical simulations to present a detailed analysis and characterization of the dynamical chaos in 145 different systems produced via terrestrial planet formation in Kaib & Cowan (2015). These systems were created in the presence of a fully formed Jupiter and Saturn, using a variety of different initial conditions. We provide the first analysis of the dynamical states of fully evolved (4.5 Gyr) planetary systems formed using numerical simulations. We find that dynamical chaos is preva- lent in roughly half of the systems, with the largest source of the chaos being perturbations from Jupiter. Chaos is most prevalent in systems that form 4 or 5 terrestrial planets. Additionally, an eccentric Jupiter and Saturn is shown to enhance the prevalence of chaos in systems. Furthermore, systems with a center of mass highly concentrated between 0.8-1.2 AU generally prove to be less chaotic than systems with more exotic mass distributions. Through the process of evolving systems to the current epoch, we show that late instabilities are quite common in our systems. Of greatest interest, many of the sources of chaos observed in our own solar system (such as the secularly driven chaos between Mercury and Jupiter) are shown to be common outcomes of terrestrial planetary formation. Thus, the solar system’s marginally stable, chaotic state may naturally arise from the process of terrestrial planet formation.
Chaos in the Showalter-Noyes-Bar-Eli model of the Belousov-Zhabotinskii reaction
Lindberg, David; Turner, Jack S.; Barkley, Dwight
1990-03-01
The observation of robust, large-scale chaos in the Showalter-Noyes-Bar-Eli model of the Belousov-Zhabotinskii reaction is reported. The chaos observed is comparable to that found in CSTR experiments at low flow rates.
Controlling Chaos Probability of a Bose-Einstein Condensate in a Weak Optical Superlattice
Institute of Scientific and Technical Information of China (English)
XU Jun; LUO Xiao-Bing
2009-01-01
@@ The spatial chaos probability of a Bose-Einstein condensate perturbed by a weak optical superlattice is studied. It is demonstrated that the spatial chaotic solution appears with a certain probability in a given parameter region under a random boundary condition. The effects of the lattice depths and wave vectors on the chaos probability are illustrated, and different regions associated with different chaos probabilities are found. This suggests a feasible scheme for suppressing and strengthening chaos by adjusting the optical superlattice experimentally.
Attractors, bifurcations, & chaos nonlinear phenomena in economics
Puu, Tönu
2003-01-01
The present book relies on various editions of my earlier book "Nonlinear Economic Dynamics", first published in 1989 in the Springer series "Lecture Notes in Economics and Mathematical Systems", and republished in three more, successively revised and expanded editions, as a Springer monograph, in 1991, 1993, and 1997, and in a Russian translation as "Nelineynaia Economicheskaia Dinamica". The first three editions were focused on applications. The last was differ ent, as it also included some chapters with mathematical background mate rial -ordinary differential equations and iterated maps -so as to make the book self-contained and suitable as a textbook for economics students of dynamical systems. To the same pedagogical purpose, the number of illus trations were expanded. The book published in 2000, with the title "A ttractors, Bifurcations, and Chaos -Nonlinear Phenomena in Economics", was so much changed, that the author felt it reasonable to give it a new title. There were two new math ematics ch...
Lectures in nonlinear mechanics and chaos theory
Stetz, Albert W
2016-01-01
This elegant book presents a rigorous introduction to the theory of nonlinear mechanics and chaos. It turns out that many simple mechanical systems suffer from a peculiar malady. They are deterministic in the sense that their motion can be described with partial differential equations, but these equations have no proper solutions and the behavior they describe can be wildly unpredictable. This is implicit in Newtonian physics, and although it was analyzed in the pioneering work of Poincaré in the 19th century, its full significance has only been realized since the advent of modern computing. This book follows this development in the context of classical mechanics as it is usually taught in most graduate programs in physics. It starts with the seminal work of Laplace, Hamilton, and Liouville in the early 19th century and shows how their formulation of mechanics inevitably leads to systems that cannot be 'solved' in the usual sense of the word. It then discusses perturbation theory which, rather than providing...
Muthuswamy, Bharathwaj
2015-01-01
The purpose of this introductory book is to couple the teaching of chaotic circuit and systems theory with the use of field programmable gate arrays (FPGAs). As such, it differs from other texts on chaos: first, it puts emphasis on combining theoretical methods, simulation tools and physical realization to help the reader gain an intuitive understanding of the properties of chaotic systems. Second, the "medium" used for physical realization is the FPGA. These devices are massively parallel architectures that can be configured to realize a variety of logic functions. Hence, FPGAs can be configured to emulate systems of differential equations. Nevertheless maximizing the capabilities of an FPGA requires the user to understand the underlying hardware and also FPGA design software. This is achieved by the third distinctive feature of this book: a lab component in each chapter. Here, readers are asked to experiment with computer simulations and FPGA designs, to further their understanding of con...
Tachyons, Lamb shifts and superluminal chaos
Tomaschitz, R.
2000-10-01
An elementary account on the origins of cosmic chaos in an open and multiply connected universe is given; there is a finite region in the open 3-space in which the world-lines of galaxies are chaotic, and the mixing taking place in this chaotic nucleus of the universe provides a mechanism to create equidistribution. The galaxy background defines a distinguished frame of reference and a unique cosmic time order; in this context superluminal signal transfer is studied. Tachyons are described by a real Proca field with negative mass square, coupled to a current of subluminal matter. Estimates on tachyon mixing in the geometric optics limit are derived. The potential of a static point source in this field theory is a damped periodic function. We treat this tachyon potential as a perturbation of the Coulomb potential, and study its effects on energy levels in hydrogenic systems. By comparing the induced level shifts to high-precision Lamb shift measurements and QED calculations, we suggest a tachyon mass of 2.1 keV/c2 and estimate the tachyonic coupling strength to subluminal matter. The impact of the tachyon field on ground state hyperfine transitions in hydrogen and muonium is investigated. Bounds on atomic transition rates effected by tachyon radiation as well as estimates on the spectral energy density of a possible cosmic tachyon background radiation are derived.
Practical and algorithmical manifestations of quantum chaos
Li, B; Li, Baowen; Robnik, Marko
1995-01-01
Quantum chaos manifests itself also in algorithmical complexity of methods, including the numerical ones, in solving the Schr\\"odinger equation. In this contribution we address the problem of calculating the eigenenergies and the eigenstates by various numerical methods applied to 2-dim generic billiard systems. In particular we analyze the dependence of the accuracy (errors) on the density of discretization of the given numerical method. We do this for several different billiard shapes, especially for the Robnik billiard. We study the numerical error of the boundary integral method and the plane wave decomposition method as a function of the discretization parameter b which by definition is the number of discretization nodes on the boundary per one de Broglie wavelength (arclength) interval. For boundary integral method, we discover that at each \\lambda the error scales as a power law = A b^{-\\alpha}, where \\alpha is a strong function of \\lambda: In the KAM-like regime 0\\le \\lambda\\le 1/4 it is large and cl...
Asynchronous Rate Chaos in Spiking Neuronal Circuits
Harish, Omri; Hansel, David
2015-01-01
The brain exhibits temporally complex patterns of activity with features similar to those of chaotic systems. Theoretical studies over the last twenty years have described various computational advantages for such regimes in neuronal systems. Nevertheless, it still remains unclear whether chaos requires specific cellular properties or network architectures, or whether it is a generic property of neuronal circuits. We investigate the dynamics of networks of excitatory-inhibitory (EI) spiking neurons with random sparse connectivity operating in the regime of balance of excitation and inhibition. Combining Dynamical Mean-Field Theory with numerical simulations, we show that chaotic, asynchronous firing rate fluctuations emerge generically for sufficiently strong synapses. Two different mechanisms can lead to these chaotic fluctuations. One mechanism relies on slow I-I inhibition which gives rise to slow subthreshold voltage and rate fluctuations. The decorrelation time of these fluctuations is proportional to the time constant of the inhibition. The second mechanism relies on the recurrent E-I-E feedback loop. It requires slow excitation but the inhibition can be fast. In the corresponding dynamical regime all neurons exhibit rate fluctuations on the time scale of the excitation. Another feature of this regime is that the population-averaged firing rate is substantially smaller in the excitatory population than in the inhibitory population. This is not necessarily the case in the I-I mechanism. Finally, we discuss the neurophysiological and computational significance of our results. PMID:26230679
Chaos-based cryptosystem on DSP
Energy Technology Data Exchange (ETDEWEB)
Guglielmi, Veronique [Laboratoire ELIAUS, University of Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan cedex 9 (France)], E-mail: veronique.guglielmi@univ-perp.fr; Pinel, Pierre; Fournier-Prunaret, Daniele; Taha, Abdel-Kaddous [Laboratoire LATTIS, INSA Toulouse, 135 Avenue de Rangueil, 31077 Toulouse cedex 4 (France)
2009-11-30
We present a numeric chaos-based cryptosystem, implemented on a Digital Signal Processor (DSP), which resists all the attacks we have thought of. The encryption scheme is a synchronous stream cipher. Its security arises from the properties of the trajectories in a chaotic attractor, reinforced by the use of a nonlinear non-invertible two-dimensional map, the introduction of jumps between successive points of the orbits and the retaining of only one bit of the representation of real values. We describe the results obtained through a cryptanalytic study, we detail how to adjust the different parameters of the cryptosystem in order to ensure security, and we apply the NIST (National Institute of Standards and Technology) standard tests for pseudo-randomness to our construction. The originality of this work lies in the end in the way we were able to improve the security of our system, so that it is from now on possible to envisage the use, in more general cryptographic purposes, of other recurrences than those classically employed.
Kinematic dynamo, supersymmetry breaking, and chaos
Ovchinnikov, Igor V.; Enßlin, Torsten A.
2016-04-01
The kinematic dynamo (KD) describes the growth of magnetic fields generated by the flow of a conducting medium in the limit of vanishing backaction of the fields onto the flow. The KD is therefore an important model system for understanding astrophysical magnetism. Here, the mathematical correspondence between the KD and a specific stochastic differential equation (SDE) viewed from the perspective of the supersymmetric theory of stochastics (STS) is discussed. The STS is a novel, approximation-free framework to investigate SDEs. The correspondence reported here permits insights from the STS to be applied to the theory of KD and vice versa. It was previously known that the fast KD in the idealistic limit of no magnetic diffusion requires chaotic flows. The KD-STS correspondence shows that this is also true for the diffusive KD. From the STS perspective, the KD possesses a topological supersymmetry, and the dynamo effect can be viewed as its spontaneous breakdown. This supersymmetry breaking can be regarded as the stochastic generalization of the concept of dynamical chaos. As this supersymmetry breaking happens in both the diffusive and the nondiffusive cases, the necessity of the underlying SDE being chaotic is given in either case. The observed exponentially growing and oscillating KD modes prove physically that dynamical spectra of the STS evolution operator that break the topological supersymmetry exist with both real and complex ground state eigenvalues. Finally, we comment on the nonexistence of dynamos for scalar quantities.
ICT Capstone projects: The edge of chaos
Directory of Open Access Journals (Sweden)
Sue Chard
Full Text Available Capstone project processes and assessment methodologies continue to be problematic. Experience has led us to review our assessment rubrics and methods with every iteration in an attempt to refine and improve the practice and outcomes. This review has surveyed a broad range of capstone projects describing approaches to practice, assessment and sizing. In their widest sense capstone projects are described as being ambiguous and complex, tantamount, as the title of this paper implies, to artfully practising as if one is \\'on the edge of chaos.\\' There have been promising taxonomies mooted or developed to give insight into evidence of the skills, practice, knowledge and understanding associated with capstone projects. There appears to be, however, a dilemma in terms of creating a succinct vision that might inform the sizing and assessment of projects and enable us to capture its ephemeral nature. Complexity theory appears to go some way towards unpacking relevant factors which could inform the development of tools for assessment and sizing of projects. There are professional heuristics employed in the sizing of projects and standards for the assessment of capstone projects. From this review it can be seen that a fluid but accurate methodology should be developed which addresses the dilemma in such a way as to provide robust conceptual, pedagogical and sociological sizing and assessment practices.
Galileo disposal strategy: stability, chaos and predictability
Rosengren, Aaron J.; Daquin, Jérôme; Tsiganis, Kleomenis; Alessi, Elisa Maria; Deleflie, Florent; Rossi, Alessandro; Valsecchi, Giovanni B.
2017-02-01
Recent studies have shown that the medium-Earth orbit (MEO) region of the global navigation satellite systems is permeated by a devious network of lunisolar secular resonances, which can interact to produce chaotic and diffusive motions. The precarious state of the four navigation constellations, perched on the threshold of instability, makes it understandable why all past efforts to define stable graveyard orbits, especially in the case of Galileo, were bound to fail; the region is far too complex to allow for an adoption of the simple geosynchronous disposal strategy. We retrace one such recent attempt, funded by ESA's General Studies Programme in the frame of the GreenOPS initiative, that uses a systematic parametric approach and the straightforward maximum-eccentricity method to identify long-term-stable regions, suitable for graveyards, as well as large-scale excursions in eccentricity, which can be used for post-mission deorbiting of constellation satellites. We then apply our new results on the stunningly rich dynamical structure of the MEO region towards the analysis of these disposal strategies for Galileo, and discuss the practical implications of resonances and chaos in this regime. We outline how the identification of the hyperbolic and elliptic fixed points of the resonances near Galileo can lead to explicit criteria for defining optimal disposal strategies.
Topological chaos in inviscid and viscous mixers
Finn, M. D.; Cox, S. M.; Byrne, H. M.
2003-10-01
Topological chaos may be used to generate highly effective laminar mixing in a simple batch stirring device. Boyland, Aref & Stremler (2000) have computed a material stretch rate that holds in a chaotic flow, provided it has appropriate topological properties, irrespective of the details of the flow. Their theoretical approach, while widely applicable, cannot predict the size of the region in which this stretch rate is achieved. Here, we present numerical simulations to support the observation of Boyland et al. that the region of high stretch is comparable with that through which the stirring elements move during operation of the device. We describe a fast technique for computing the velocity field for either inviscid, irrotational or highly viscous flow, which enables accurate numerical simulation of dye advection. We calculate material stretch rates, and find close agreement with those of Boyland et al., irrespective of whether the fluid is modelled as inviscid or viscous, even though there are significant differences between the flow fields generated in the two cases.
Nonadiabatic quantum chaos in atom optics
Prants, S V
2012-01-01
Coherent dynamics of atomic matter waves in a standing-wave laser field is studied. In the dressed-state picture, wave packets of ballistic two-level atoms propagate simultaneously in two optical potentials. The probability to make a transition from one potential to another one is maximal when centroids of wave packets cross the field nodes and is given by a simple formula with the single exponent, the Landau--Zener parameter $\\kappa$. If $\\kappa \\gg 1$, the motion is essentially adiabatic. If $\\kappa \\ll 1$, it is (almost) resonant and periodic. If $\\kappa \\simeq 1$, atom makes nonadiabatic transitions with a splitting of its wave packet at each node and strong complexification of the wave function as compared to the two other cases. This effect is referred as nonadiabatic quantum chaos. Proliferation of wave packets at $\\kappa \\simeq 1$ is shown to be connected closely with chaotic center-of-mass motion in the semiclassical theory of point-like atoms with positive values of the maximal Lyapunov exponent. Th...
Implementation of LT codes based on chaos
Institute of Scientific and Technical Information of China (English)
Zhou Qian; Li Liang; Chen Zeng-Qiang; Zhao Jia-Xiang
2008-01-01
Fountain codes provide an efficient way to transfer information over erasure channels like the Internet.LT codes are the first codes fully realizing the digital fountain concept.They are asymptotically optimal rateless erasure codes with highly efficient encoding and decoding algorithms.In theory,for each encoding symbol of LT codes,its degree is randomly chosen according to a predetermined degree distribution,and its neighbours used to generate that encoding symbol are chosen uniformly at random.Practical implementation of LT codes usually realizes the randomness through pseudo-randomness number generator like linear congruential method.This paper applies the pseudo-randomness of chaotic sequence in the implementation of LT codes.Two Kent chaotic maps are used to determine the degree and neighbour(s)of each encoding symbol.It is shown that the implemented LT codes based on chaos perform better than the LT codes implemented by the traditional pseudo-randomness number generator.
Chaos and Christianity: A Response to Butz and a Biblical Alternative.
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)
Pole placement method of controlling chaos in DC-DC buck converters
Institute of Scientific and Technical Information of China (English)
Zou Yan-Li; Luo Xiao-Shu; Chen Guan-Rong
2006-01-01
Based on the mechanism for the generation of chaos in a buck converter, a pole placement method is proposed and applied to controlling the chaos in a circuit. The control circuit is designed and tested. Numerical calculation and circuit implementation demonstrate the validity of this chaos control method.
Intrinsic Patterns of Human Activity
Hu, Kun; Ivanov, Plamen Ch.; Chen, Zhi; Hilton, Michael; Stanley, H. Eugene; Shea, Steven
2003-03-01
Activity is one of the defining features of life. Control of human activity is complex, being influenced by many factors both extrinsic and intrinsic to the body. The most obvious extrinsic factors that affect activity are the daily schedule of planned events, such as work and recreation, as well as reactions to unforeseen or random events. These extrinsic factors may account for the apparently random fluctuations in human motion observed over short time scales. The most obvious intrinsic factors are the body clocks including the circadian pacemaker that influences our sleep/wake cycle and ultradian oscillators with shorter time scales [2, 3]. These intrinsic rhythms may account for the underlying regularity in average activity level over longer periods of up to 24 h. Here we ask if the known extrinsic and intrinsic factors fully account for all complex features observed in recordings of human activity. To this end, we measure activity over two weeks from forearm motion in subjects undergoing their regular daily routine. Utilizing concepts from statistical physics, we demonstrate that during wakefulness human activity possesses previously unrecognized complex dynamic patterns. These patterns of activity are characterized by robust fractal and nonlinear dynamics including a universal probability distribution and long-range power-law correlations that are stable over a wide range of time scales (from minutes to hours). Surprisingly, we find that these dynamic patterns are unaffected by changes in the average activity level that occur within individual subjects throughout the day and on different days of the week, and between subjects. Moreover, we find that these patterns persist when the same subjects undergo time-isolation laboratory experiments designed to account for the phase of the circadian pacemaker, and control the known extrinsic factors by restricting behaviors and manipulating scheduled events including the sleep/wake cycle. We attribute these newly
Chaos-induced resonant effects and its control
Energy Technology Data Exchange (ETDEWEB)
Zambrano, Samuel [Departamento de Fisica, Universidad Rey Juan Carlos, Tulipan s/n, 28933 Mostoles, Madrid (Spain); Casado, Jose M. [Area de Fisica Teorica, Universidad de Sevilla, Apartado de Correos 1065, 41080 Sevilla (Spain); Sanjuan, Miguel A.F. [Departamento de Fisica, Universidad Rey Juan Carlos, Tulipan s/n, 28933 Mostoles, Madrid (Spain)]. E-mail: miguel.sanjuan@urjc.es
2007-07-02
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.
PENGEMBANGAN MEDIA PEMBELAJARAN UNTUK MENGHINDARI MIND IN CHAOS TERHADAP MATEMATIKA
Directory of Open Access Journals (Sweden)
Maman Fathurrohman
2016-02-01
Full Text Available The Development of Instructional Media to Avoid Mind in Chaos in Mathematics. The study was designed as a Research and Development, which was aimed at developing Mathematics instructional media for elementary school students in order to avoid Mind in Chaos towards mathematics. The research procedures involved the analysis of the products to be developed, the development of initial product, expert validation, and a tryout. The subjects of the study were the 3rd graders of SDN Wadasari, Serang. The instruments used in the study included documentation guide, pedoman documenter, observation guide, and questionnaire. Qualitative and quantitative data analysis technique were employed in the data analysis process. The study was successful in developing a prototype of Mathematics instructional media, which can be used in the Mathematics teaching and learning process that will provide the students with the opportunity to experience fun learning which is also helpful in avoiding mind in chaos.
Color image authentication based on spatiotemporal chaos and SVD
Energy Technology Data Exchange (ETDEWEB)
Peng Zhenni [College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China)], E-mail: jennyp8201@yahoo.com.cn; Liu Wenbo [College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China)], E-mail: wenboliu@nuaa.edu.cn
2008-05-15
In this paper, a new semi-fragile watermarking scheme for color image authentication is proposed based on spatiotemporal chaos and SVD (singular value decomposition). Wavelet transform is applied to watermarking. In contrast to conventional approaches where the watermark is embedded directly on the wavelet coefficients, we embed the watermark onto the SVs (singular values) of the blocks within wavelet subband. In order to enhance the security, spatiotemporal chaos is employed to select the embedding positions for each watermark bit as well as for watermark encryption. The experiment results show that the proposed scheme is able to identify malicious attacks to the image, while is robust to JPEG compression. And due to the sensitivity to the initial conditions of the spatiotemporal chaos, the security of the scheme is greatly improved.
Control of beam halo-chaos by sample function
Institute of Scientific and Technical Information of China (English)
Bai Long; Zhang Rong; Weng Jia-Qiang; Luo Xiao-Shu; Fang Jin-Qing
2006-01-01
The K-V beam through an axisymmetric uniform-focusing channel is studied using the particle-core model. The beam halo-chaos is found, and a sample function controller is proposed based on mechanism of halo formation and strategy of controlling halo-chaos. We perform multiparticle simulation to control the halo by using the sample function controller. The numerical results show that our control method is effective. We also find that the radial ion density changes when the ion beam is in the channel: not only can the halo-chaos and its regeneration be eliminated by using the sample function control method, but also the density uniformity can be found at the beam's centre as long as an appropriate control method is chosen.
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.
Level statistics in arithmetical and pseudo-arithmetical chaos
Energy Technology Data Exchange (ETDEWEB)
Braun, Petr; Haake, Fritz, E-mail: Petr.Braun@uni-due.d [Fachbereich Physik, Universitaet Duisburg-Essen, 47048 Duisburg (Germany)
2010-07-02
We investigate a long-standing riddle in quantum chaos, posed by certain fully chaotic billiards with constant negative curvature whose periodic orbits are highly degenerate in length. Depending on the boundary conditions for the quantum wavefunctions, the energy spectra either have uncorrelated levels usually associated with classical integrability or conform to the 'universal' Wigner-Dyson type although the classical dynamics in both cases is the same. The resolution turns out surprisingly simple. The Maslov indices of orbits within multiplets of degenerate length either yield equal phases for the respective Feynman amplitudes (and thus Poissonian level statistics) or give rise to amplitudes with uncorrelated phases (leading to Wigner-Dyson level correlations). The recent semiclassical explanation of spectral universality in quantum chaos is thus extended to the latter case of 'pseudo-arithmetical' chaos. (fast track communication)
When chaos meets hyperchaos: 4D Rössler model
Energy Technology Data Exchange (ETDEWEB)
Barrio, Roberto, E-mail: rbarrio@unizar.es [Departamento de Matemática Aplicada and IUMA, University of Zaragoza, E-50009 Zaragoza (Spain); Computational Dynamics group, University of Zaragoza, E-50009 Zaragoza (Spain); Angeles Martínez, M., E-mail: gelimc@unizar.es [Computational Dynamics group, University of Zaragoza, E-50009 Zaragoza (Spain); Serrano, Sergio, E-mail: sserrano@unizar.es [Departamento de Matemática Aplicada and IUMA, University of Zaragoza, E-50009 Zaragoza (Spain); Computational Dynamics group, University of Zaragoza, E-50009 Zaragoza (Spain); Wilczak, Daniel, E-mail: wilczak@ii.uj.edu.pl [Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków (Poland)
2015-10-09
Chaotic behavior is a common feature of nonlinear dynamics, as well as hyperchaos in high-dimensional systems. In numerical simulations of these systems it is quite difficult to distinguish one from another behavior in some situations, as the results are frequently quite “noisy”. We show that in such systems a global hyperchaotic invariant set is present giving rise to long hyperchaotic transient behaviors. This fact provides a mechanism for these noisy results. The coexistence of chaos and hyperchaos is proved via Computer-Assisted Proofs techniques. - Highlights: • The coexistence of chaos and hyperchaos in the 4D Rössler system is proved via Computer-Assisted Proofs techniques. • A global hyperchaotic invariant set is present giving rise to long hyperchaotic transient behaviors. • The long transient behaviors make difficult in numerical simulations to distinguish chaos from hyperchaos in some situations.
Applications of chaos and nonlinear dynamics in engineering - Vol 1
Rondoni, Lamberto; Banerjee, Santo
2011-01-01
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 quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. This volume concentrates on reviewing the most relevant contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. The book covers the theory as applied to robotics, electronic and communication engineering (for example chaos synchronization and cryptography) as well as to civil and mechanical engineering, where its use in damage monitoring and control is explored). Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘r...
Applications of chaos and nonlinear dynamics in science and engineering
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...
Controlling chaos in a satellite power supply subsystem
Macau, E. E. N.; Ramos Turci, L. F.; Yoneyama, T.
2008-12-01
In this work, we show that chaos control techniques can be used to increase the region that can be efficiently used to supply the power requests for an artificial satellite. The core of a satellite power subsystem relies on its DC/DC converter. This is a very nonlinear system that presents a multitude of phenomena ranging from bifurcations, quasi-periodicity, chaos, coexistence of attractors, among others. The traditional power subsystem design techniques try to avoid these nonlinear phenomena so that it is possible to use linear system theory in small regions about the equilibrium points. Here, we show that chaos control can be used to efficiently extend the applicability region of the satellite power subsystem when it operates in regions of high nonlinearity.
Dynamical topology and statistical properties of spatiotemporal chaos.
Zhuang, Quntao; Gao, Xun; Ouyang, Qi; Wang, Hongli
2012-12-01
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a large extent, the location and movement of these topologically special points determine the qualitative structure of the disordered states. We analyze numerically statistical properties of the topologically special points in one-dimensional spatiotemporal chaos. The probability distribution functions for the number of point, the lifespan, and the distance covered during their lifetime are obtained from numerical simulations. Mathematically, we establish a probabilistic model to describe the dynamics of these topologically special points. In spite of the different definitions in different spatiotemporal chaos, the dynamics of these special points can be described in a uniform approach.
A NOVEL APPROACH TO GENERATE FRACTAL IMAGES USING CHAOS THEORY
Directory of Open Access Journals (Sweden)
K. Thamizhchelvy
2014-08-01
Full Text Available We propose the fractal generation method to generate the different types of fractals using chaos theory. The fractals are generated by Iterated Function System (IFS technique. The chaos theory is an unpredictable behavior arises in the dynamical system. Chaos in turns explains the nonlinearity and randomness. Chaotic behavior depends upon the initial condition called as “seed” or “key”. Pseudo Random Number Generator (PRNG fixes the initial condition from the difference equations. The system uses the PRNG value and it generates the fractals, also it is hard to break. We apply the rules to generate the fractals. The different types of fractals are generated for the same data, because of the great sensitivity to the initial condition. It can be used as a digital signature in online applications such as e-Banking and online shopping.
Sensitivity and chaos control for the forced nonlinear oscillations
Energy Technology Data Exchange (ETDEWEB)
Bashkirtseva, Irina [Department of Mathematics, Ural State University, 620083 Ekaterinburg (Russian Federation); Ryashko, Lev [Department of Mathematics, Ural State University, 620083 Ekaterinburg (Russian Federation)] e-mail: lev.ryashko@usu.ru
2005-12-01
This paper is devoted to study the problem of controlling chaos for forced nonlinear dynamic systems. We suggest a new control technique based on sensitivity analysis. With the help of approximation of nonequilibrium quasipotential, stochastic sensitivity function (SSF) is constructed. This function is used as basic tool of a quantitative description for a system response on the random external disturbances. The possibilities of SSF to predict chaotic dynamics for the periodic and stochastic forced Brusselator are shown. The problem of chaos control based on SSF is considered. A design of attractors with the desired features by feedback regulator is discussed. Analysis of controllability and effective technique for regulator synthesis is presented. An example of suppressing chaos for Brusselator is considered.
Chaos and its control in an impulsive differential system
Energy Technology Data Exchange (ETDEWEB)
Jiang Guirong [School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083 (China); Department of Computational Science and Mathematics, Guilin University of Electronic Technology, Guilin 541004 (China); Lu Qishao [School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083 (China)]. E-mail: qishaolu@hotmail.com; Qian Linning [School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083 (China)
2007-11-15
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.
Polymer additives in fluid turbulence and distributed chaos
Bershadskii, A
2016-01-01
The fluids and polymers have different fundamental symmetries. Namely, the Lagrangian relabeling symmetry of fluids is absent for polymers (while the translational and rotational symmetries are still present). This fact results in spontaneous breaking of the relabeling symmetry in fluid turbulence even at a tiny polymer addition. Since helicity conservation in inviscid fluid motions is a consequence of the relabeling symmetry (due to the Noether's theorem) violation of this conservation by the polymer additives results in the strong effects in the distributed chaos. The distributed chaos in turbulence with the spontaneously broken relabeling symmetry is characterized by stretched exponential spectra $\\propto \\exp(-k/k_{\\beta})^{\\beta}$ with $\\beta =2/5$. The spectral range of this distributed chaos is extended in direction of the small wavenumbers and $k_{\\beta}$ becomes much larger in comparison with the pure fluid (Newtonian) case. This results in substantial suppression of small-scale turbulence and large-...
Simultaneous time-frequency control of bifurcation and chaos
Liu, Meng-Kun; Suh, C. Steve
2012-06-01
Control scheme facilitated either in the time- or frequency-domain alone is insufficient in controlling route-to-chaos, where the corresponding response deteriorates in the time and frequency domains simultaneously. A novel chaos control scheme is formulated by addressing the fundamental characteristics inherent of chaotic response. The proposed control scheme has its philosophical basis established in simultaneous time-frequency control, on-line system identification, and adaptive control. Physical features that embody the concept include multiresolution analysis, adaptive Finite Impulse Response (FIR) filter, and Filtered-x Least Mean Square (FXLMS) algorithm. A non-stationary Duffing oscillator is investigated to demonstrate the effectiveness of the control methodology. Results presented herein indicate that for the control of dynamic instability including chaos to be deemed viable, mitigation has to be adaptive and engaged in the time and frequency domains at the same time.
Job assignments, intrinsic motivation and explicit incentives
Nafziger, Julia
2008-01-01
This paper considers the interplay of job assignments with the intrinsic and extrinsic motivation of an agent. Job assignments influence the self confidence of the agent, and thereby his intrinsic motivation. Monetary reward allow the principal to complement intrinsic motivation with extrinsic incentives. The main result is that the principal chooses an inefficient job assignment rule to enhance the agent's intrinsic motivation even though she can motivate him with monetary rewards. This show...
Multistability, chaos, and random signal generation in semiconductor superlattices
Ying, Lei; Huang, Danhong; Lai, Ying-Cheng
2016-06-01
Historically, semiconductor superlattices, artificial periodic structures of different semiconductor materials, were invented with the purpose of engineering or manipulating the electronic properties of semiconductor devices. A key application lies in generating radiation sources, amplifiers, and detectors in the "unusual" spectral range of subterahertz and terahertz (0.1-10 THz), which cannot be readily realized using conventional radiation sources, the so-called THz gap. Efforts in the past three decades have demonstrated various nonlinear dynamical behaviors including chaos, suggesting the potential to exploit chaos in semiconductor superlattices as random signal sources (e.g., random number generators) in the THz frequency range. We consider a realistic model of hot electrons in semiconductor superlattice, taking into account the induced space charge field. Through a systematic exploration of the phase space we find that, when the system is subject to an external electrical driving of a single frequency, chaos is typically associated with the occurrence of multistability. That is, for a given parameter setting, while there are initial conditions that lead to chaotic trajectories, simultaneously there are other initial conditions that lead to regular motions. Transition to multistability, i.e., the emergence of multistability with chaos as a system parameter passes through a critical point, is found and argued to be abrupt. Multistability thus presents an obstacle to utilizing the superlattice system as a reliable and robust random signal source. However, we demonstrate that, when an additional driving field of incommensurate frequency is applied, multistability can be eliminated, with chaos representing the only possible asymptotic behavior of the system. In such a case, a random initial condition will lead to a trajectory landing in a chaotic attractor with probability 1, making quasiperiodically driven semiconductor superlattices potentially as a reliable
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.
Stochastic Intrinsic Kriging for Simulation Metamodelling
Mehdad, E.; Kleijnen, Jack P.C.
2014-01-01
We derive intrinsic Kriging, using Matherons intrinsic random functions which eliminate the trend in classic Kriging. We formulate this intrinsic Kriging as a metamodel in deterministic and random simulation models. For random simulation we derive an experimental design that also specifies the numbe
Quantum chaos in the nuclear collective model. II. Peres lattices.
Stránský, Pavel; Hruska, Petr; Cejnar, Pavel
2009-06-01
This is a continuation of our paper [Phys. Rev. E 79, 046202 (2009)] devoted to signatures of quantum chaos in the geometric collective model of atomic nuclei. We apply the method by Peres to study ordered and disordered patterns in quantum spectra drawn as lattices in the plane of energy vs average of a chosen observable. Good qualitative agreement with standard measures of chaos is manifested. The method provides an efficient tool for studying structural changes in eigenstates across quantum spectra of general systems.
In the Wake of Chaos Unpredictable Order in Dynamical Systems
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
Chaos in human behavior: the case of work motivation.
Navarro, José; Arrieta, Carlos
2010-05-01
This study considers the complex dynamics of work motivation. Forty-eight employees completed a work-motivation diary several times per day over a period of four weeks. The obtained time series were analysed using different methodologies derived from chaos theory (i.e. recurrence plots, Lyapunov exponents, correlation dimension and surrogate data). Results showed chaotic dynamics in 75% of cases. The findings confirm the universality of chaotic behavior within human behavior, challenge some of the underlying assumptions on which work motivation theories are based, and suggest that chaos theory may offer useful and relevant information on how this process is managed within organizations.
Nonlinearity and Chaos in the Magnetopause Shear System
Institute of Scientific and Technical Information of China (English)
傅绥燕; 濮祖荫; 刘振兴
1994-01-01
Chaotic phenomena in the magnetopause boundary region are studied in the MHD framework by using the Fourier truncation method. The MHD system is considered as a one-dimensional current sheet with a co-existing velocity shear and continuous energy transfer. The nonlinearity of the system, the evolution processes and properties of its different attractors are analysed. The possible routs and parameter conditions for chaos onset are also investigated. Numerical solutions show that when the Reynolds number (R) and the magnetic Reynolds number (Km) are very large, chaos appears in the system and its onset may provide a physical mechanism leading to turbulent reconnection at the magnetopause.
Distributed chaos tuned to large scale coherent motions in turbulence
Bershadskii, A
2016-01-01
It is shown, using direct numerical simulations and laboratory experiments data, that distributed chaos is often tuned to large scale coherent motions in anisotropic inhomogeneous turbulence. The examples considered are: fully developed turbulent boundary layer (range of coherence: $14 < y^{+} < 80$), turbulent thermal convection (in a horizontal cylinder), and Cuette-Taylor flow. Two ways of the tuning have been described: one via fundamental frequency (wavenumber) and another via subharmonic (period doubling). For the second way the large scale coherent motions are a natural component of distributed chaos. In all considered cases spontaneous breaking of space translational symmetry is accompanied by reflexional symmetry breaking.
Application of chaos and fractals to computer vision
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
Analysing spatially extended high-dimensional chaos by recurrence plots
Marwana, Norbert; Foerster, Saskia
2014-01-01
Recurrence plot based measures of complexity are capable tools for characterizing complex dynamics. In this letter we show the potential of selected recurrence plot measures for the investigation of even high-dimensional chaos. We apply this method on spatially extended chaos, such as derived from the Lorenz96 model and show that the recurrence plot based measures can qualitatively characterize typical dynamical properties such as chaotic or periodic dynamics. Moreover, we demonstrate its power by analyzing satellite image time series of vegetation cover with contrasting dynamics as a high-dimensional example from the real world.
Phase chaos in the anisotropic complex Ginzburg-Landau Equation
Faller, R
1998-01-01
Of the various interesting solutions found in the two-dimensional complex Ginzburg-Landau equation for anisotropic systems, the phase-chaotic states show particularly novel features. They exist in a broader parameter range than in the isotropic case, and often even broader than in one dimension. They typically represent the global attractor of the system. There exist two variants of phase chaos: a quasi-one dimensional and a two-dimensional solution. The transition to defect chaos is of intermittent type.
Study of chaos based on a hierarchical model
Energy Technology Data Exchange (ETDEWEB)
Yagi, Masatoshi; Itoh, Sanae-I. [Kyushu Univ., Fukuoka (Japan). Research Inst. for Applied Mechanics
2001-12-01
Study of chaos based on a hierarchical model is briefly reviewed. Here we categorize hierarchical model equations, i.e., (1) a model with a few degrees of freedom, e.g., the Lorenz model, (2) a model with intermediate degrees of freedom like a shell model, and (3) a model with many degrees of freedom such as a Navier-Stokes equation. We discuss the nature of chaos and turbulence described by these models via Lyapunov exponents. The interpretation of results observed in fundamental plasma experiments is also shown based on a shell model. (author)
Dynamic Ice-Water Interactions Form Europa's Chaos Terrains
Blankenship, D. D.; Schmidt, B. E.; Patterson, G. W.; Schenk, P.
2011-12-01
Unique to the surface of Europa, chaos terrain is diagnostic of the properties and dynamics of its icy shell. We present a new model that suggests large melt lenses form within the shell and that water-ice interactions above and within these lenses drive the production of chaos. This model is consistent with key observations of chaos, predicts observables for future missions, and indicates that the surface is likely still active today[1]. We apply lessons from ice-water interaction in the terrestrial cryosphere to hypothesize a dynamic lense-collapse model to for Europa's chaos terrain. Chaos terrain morphology, like that of Conamara chaos and Thera Macula, suggests a four-phase formation [1]: 1) Surface deflection occurs as ice melts over ascending thermal plumes, as regularly occurs on Earth as subglacial volcanoes activate. The same process can occur at Europa if thermal plumes cause pressure melt as they cross ice-impurity eutectics. 2) Resulting hydraulic gradients and driving forces produce a sealed, pressurized melt lense, akin to the hydraulic sealing of subglacial caldera lakes. On Europa, the water cannot escape the lense due to the horizontally continuous ice shell. 3) Extension of the brittle ice lid above the lense opens cracks, allowing for the ice to be hydrofractured by pressurized water. Fracture, brine injection and percolation within the ice and possible iceberg toppling produces ice-melange-like granular matrix material. 4) Refreezing of the melt lense and brine-filled pores and cracks within the matrix results in raised chaos. Brine soaking and injection concentrates the ice in brines and adds water volume to the shell. As this englacial water freezes, the now water-filled ice will expand, not unlike the process of forming pingos and other "expansion ice" phenomena on Earth. The refreezing can raise the surface and create the oft-observed matrix "domes" In this presentation, we describe how catastrophic ice-water interactions on Earth have
Predicting vibration signals of automobile engine using chaos theory
Institute of Scientific and Technical Information of China (English)
LIU Chun; ZHANG Laibin; WANG Zhaohui
2004-01-01
Condition monitoring and life prediction of the vehicle engine is an important and urgent problem during the vehicle development process. The vibration signals that are closely associated with the engine running condition and its development trend are complex and nonlinear. The chaos theory is used to treat the nonlinear dynamical system recently. A novel chaos method in conjunction with SVD (singular value decomposition)denoising skill are used to predict the vibration time series. Two types of time series and their prediction errors are provided to illustrate the practical utility of the method.
Predicting vibration signals of automobile engine using chaos theory
Liu, Chun; Zhang, Laibin; Wang, Zhaohui
2004-01-01
Condition monitoring and life prediction of the vehicle engine is an important and urgent problem during the vehicle development process. The vibration signals that are closely associated with the engine running condition and its development trend are complex and nonlinear. The chaos theory is used to treat the nonlinear dynamical system recently. A novel chaos method in conjunction with SVD (singular value decomposition) denoising skill are used to predict the vibration time series. Two types of time series and their prediction errors are provided to illustrate the practical utility of the method.
Chaotic iterations versus Spread-spectrum: chaos and stego security
Guyeux, Christophe; Friot, Nicolas; Bahi, Jacques
2010-01-01
International audience; A new framework for information hiding security, called chaos-security, has been proposed in a previous study. It is based on the evaluation of unpredictability of the scheme, whereas existing notions of security, as stego-security, are more linked to information leaks. It has been proven that spread-spectrum techniques, a well-known stego-secure scheme, are chaos-secure too. In this paper, the links between the two notions of security is deepened and the usability of ...
Topological chaos and periodic braiding of almost-cyclic sets.
Stremler, Mark A; Ross, Shane D; Grover, Piyush; Kumar, Pankaj
2011-03-18
In certain (2+1)-dimensional dynamical systems, the braiding of periodic orbits provides a framework for analyzing chaos in the system through application of the Thurston-Nielsen classification theorem. Periodic orbits generated by the dynamics can behave as physical obstructions that "stir" the surrounding domain and serve as the basis for this topological analysis. We provide evidence that, even in the absence of periodic orbits, almost-cyclic regions identified using a transfer operator approach can reveal an underlying structure that enables topological analysis of chaos in the domain.
Transition to Chaos in the Floating Half Zone Convection
Institute of Scientific and Technical Information of China (English)
AA Yan; CAO Zhong-Hua; HU Wen-Rui
2007-01-01
The transition process from steady convection to chaos is experimentally studied in thermocapillary convections of floating half zone. The onset of temperature oscillations in the liquid bridge of floating half zone and further transitions of the temporal convective behaviour are detected by measuring the temperature in the liquid bridge.The fast Fourier transform reveals the frequency and amplitude characteristics of the flow transition. The experimental results indicate the existence of a sequence of period-doubling bifurcations that culminate in chaos.The measured Feigenbaum numbers are δ2 = 4.69 and δ4 = 4.6, which are comparable with the theoretical asymptotic value δ = 4.669.
Energy enhancement and chaos control in microelectromechanical systems.
Park, Kwangho; Chen, Qingfei; Lai, Ying-Cheng
2008-02-01
For a resonator in an electrostatic microelectromechanical system (MEMS), nonlinear coupling between applied electrostatic force and the mechanical motion of the resonator can lead to chaotic oscillations. Better performance of the device can be achieved when the oscillations are periodic with large amplitude. We investigate the nonlinear dynamics of a system of deformable doubly clamped beam, which is the core in many MEMS resonators, and propose a control strategy to convert chaos into periodic motions with enhanced output energy. Our study suggests that chaos control can lead to energy enhancement and consequently high performance of MEM devices.
Chaos control in a discrete time system through asymmetric coupling
Energy Technology Data Exchange (ETDEWEB)
Rech, Paulo C. [Departamento de Fisica, Universidade do Estado de Santa Catarina, 89223-100 Joinville (Brazil)], E-mail: dfi2pcr@joinville.udesc.br
2008-06-09
We study a pair of asymmetrically coupled identical chaotic quadratic maps. We investigate, via numerical simulations, chaos suppression associated with the variation of both parameters, the coupling parameter and the parameter which measures the asymmetry. This is a new technique recently introduced for chaos suppression in continuous systems and, as far we know, not yet tested for discrete systems. Parameter-space regions where the chaotic dynamics is driven towards regular dynamics are shown. Lyapunov exponents and phase-space plots are also used to characterize the phenomenon observed as the parameters are changed.
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.
Chaos control by using Motor Maps.
Arena, Paolo; Fortuna, Luigi; Frasca, Mattia
2002-09-01
In this paper a new method for chaos control is proposed, consisting of an unsupervised neural network, namely a Motor Map. In particular a feedback entrainment scheme is adopted: a chaotic system with a given parameter set generates the reference trajectory for another chaotic system with different parameters to be controlled: the Motor Map is required to provide the appropriate time-varying gain value for the feedback signal. The state of the controlled system is considered as input to the Motor Map. Particular efforts have been paid to the feasibility of the implementation. Indeed, the simulations performed have been oriented to design a Motor Map suitable for an hardware realization, thus some restrictive hypotheses, such as for example a low number of neurons, have been assumed. A huge number of simulations has been carried out by considering as system to be controlled a Double Scroll Chua Attractor as well as other chaotic attractors. Several reference trajectories have also been considered: a limit cycle generated by a Chua's circuit with different parameters values, a double scroll Chua attractor, a chaotic attractor of the family of the Chua's circuit attractors. In all the simulations instead of controlling the whole state space, only two state variables have been fed back. Good results in terms of settling time (namely, the period in which the map learns the control task) and steady state errors have been obtained with a few neurons. The Motor Map based adaptive controller offers high performances, specially in the case when the reference trajectory is switched into another one. In this case, a specialization of the neurons constituting the Motor Map is observed: while a group of neurons learns the appropriate control law for a reference trajectory, another group specializes itself to control the system when the other trajectory is used as a reference. A discrete components electronic realization of the Motor Map is presented and experimental results
Controlling chaos in a pendulum equation with ultra-subharmonic resonances
Energy Technology Data Exchange (ETDEWEB)
Yang Jianping [College of Science, China Agricultural University, Beijing 100083 (China)], E-mail: jpyangcau@gmail.com; Jing Zhujun [College of Mathematics and Computer Science, Hunan Normal University, Hunan, Changsha 410081 (China); Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080 (China)
2009-10-30
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. {omega}/{omega}=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{sup +}) orbits by adjusting amplitude and phase-difference of parametric excitation, and the distribution of maximum Lyapunov exponents in parameter-plane ({psi},{beta}) gives the regions in which chaos can be controlled.
Emulating “Chaos + Chaos = Order” in Chen’s Circuit of Fractional Order by Parameter Switching
Tang, Wallace K. S.; Danca, Marius-F.
2016-06-01
In this paper, the effect of the parameter switching (PS) algorithm in a fractional order chaotic circuit is investigated both in simulation and experiment. The Chen system of fractional order is focused and realized in an electronic circuit. By designing a switching circuit, the PS algorithm is implemented and it is the first time, the paradoxical “Chaos + Chaos = Order” is presented in an electronic circuit. Both the simulation and experimental results confirm that the obtained attractor under switching approximates the attractor of the time-averaged model. Some important design issues for the circuitry realization of the PS scheme are pointed out. Finally, our work confirms the practical usage of PS algorithm in potential applications such as attractor synthesis and chaos control.
Experimental observation of a chaos-to-chaos transition in laser droplet generation
Krese, Blaz; Govekar, Edvard
2010-01-01
We examine the dynamics of laser droplet generation in dependence on the detachment pulse power. In the absence of the detachment pulse, undulating pendant droplets are formed at the end of a properly fed metal wire due to the impact of the primary laser pulse that induces melting. Eventually, these droplets detach, i.e. overcome the surface tension, because of their increasing mass. We show that this spontaneous dripping is deterministically chaotic by means of a positive largest Lyapunov exponent and a negative divergence. In the presence of the detachment pulse, however, the generation of droplets is fastened depending on the pulse power. At high powers, the spontaneity of dripping is completely overshadowed by the impact of the detachment pulse. Still, amplitude chaos can be detected, which similarly as the spontaneous dripping, is characterized by a positive largest Lyapunov exponent and a negative divergence, thus indicating that the observed dynamics is deterministically chaotic with an attractor as so...
The bifurcation threshold value of the chaos detection system for a weak signal
Institute of Scientific and Technical Information of China (English)
李月; 杨宝俊; 杜立志; 袁野
2003-01-01
Recently, it has become an important problem to confirm the bifurcation threshold value of a chaos detection system for a weak signal in the fields of chaos detection. It is directly related to whether the results of chaos detection are correct or not. In this paper, the discrimination system for the dynamic behaviour of a chaos detection system for a weak signal is established by using the theory of linear differential equation with periodic coefficients and computing the Lyapunov exponents of the chaos detection system; and then, the movement state of the chaos detection system is defined. The simulation experiments show that this method can exactly confirm the bifurcation threshold value of the chaos detection system.
Institute of Scientific and Technical Information of China (English)
FANG Jin-Qing; YU Xing-Huo
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.
Presymplectic structures and intrinsic Lagrangians
Grigoriev, Maxim
2016-01-01
It is well-known that a Lagrangian induces a compatible presymplectic form on the equation manifold (stationary surface, understood as a submanifold of the respective jet-space). Given an equation manifold and a compatible presymplectic form therein, we define the first-order Lagrangian system which is formulated in terms of the intrinsic geometry of the equation manifold. It has a structure of a presymplectic AKSZ sigma model for which the equation manifold, equipped with the presymplectic form and the horizontal differential, serves as the target space. For a wide class of systems (but not all) we show that if the presymplectic structure originates from a given Lagrangian, the proposed first-order Lagrangian is equivalent to the initial one and hence the Lagrangian per se can be entirely encoded in terms of the intrinsic geometry of its stationary surface. If the compatible presymplectic structure is generic, the proposed Lagrangian is only a partial one in the sense that its stationary surface contains the...
Intrinsic Alignments in the Illustris Simulation
Hilbert, Stefan; Schneider, Peter; Springel, Volker; Vogelsberger, Mark; Hernquist, Lars
2016-01-01
We study intrinsic alignments (IA) of galaxy image shapes within the Illustris cosmic structure formation simulations. We investigate how IA correlations depend on observable galaxy properties such as stellar mass, apparent magnitude, redshift, and photometric type, and on the employed shape measurement method. The correlations considered include the matter density-intrinsic ellipticity (mI), galaxy density-intrinsic ellipticity (dI), gravitational shear-intrinsic ellipticity (GI), and intrinsic ellipticity-intrinsic ellipticity (II) correlations. We find stronger correlations for more massive and more luminous galaxies, as well as for earlier photometric types, in agreement with observations. Moreover, shape measurement methods that down-weight the outer parts of galaxy images produce much weaker IA signals on intermediate and large scales than methods employing flat radial weights. Thus, the expected contribution of intrinsic alignments to the observed ellipticity correlation in tomographic cosmic shear sur...
Homoclinic chaos in the discrete self-trapping trimer
DEFF Research Database (Denmark)
Hennig, D.; Gabriel, H.; Jørgensen, Michael Finn;
1995-01-01
We study the discrete self-trapping (DST) equation with three degrees of freedom. By taking the DST dimer as the underlying unperturbed system we treat the coupling to the additional oscillator as a small perturbation. Using the generalized Melnikov method we prove the existence of homoclinic chaos...... in the DST-trimer dynamics....
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 p...
Review of Stephen Arons's "Short Route to Chaos."
Glenn, Charles L.
1998-01-01
"Short Route to Chaos" criticizes the Goals 2000 program, related educational reforms, and the agenda of the Religious Right from the viewpoint of the secular Left. Arons supports school choice, school and teacher independence from government regulation of instructional content, publicly funded schools, and equity in funding. (SLD)
Two-mode chaos and its synchronization properties
DEFF Research Database (Denmark)
Postnov, D.E.; Shishkin, A.V.; Sosnovtseva, Olga;
2005-01-01
Using a simple model with bimodal dynamics, we investigate the intra- and inter-system entrainment of the two different time scales involved in the chaotic oscillations. The transition between mode-locked and mode-unlocked chaos is analyzed for a single system. For coupled oscillators, we...
Chaos Synchronization on Parameters Adaptive Control for Chen Chaotic System
Institute of Scientific and Technical Information of China (English)
ZHOU Ping
2003-01-01
Chaos synchronization of Chen chaotic system for parameters unknown is discussed in this paper using a scalar output. Using the concept of conditional Lyapunov exponents, the negativity of all Lyapunov exponents shows the synchronization of transmitter systems with receiver systems even though system parametes are not known to receiver systems.
SLAC: A Tool for Addressing Chaos in the Ecology Classroom
Hamilton, A. J.
2005-01-01
Until the early 1970s, ecologists generally assumed that erratic fluctuations observed in natural populations were a product of stochastic noise. It is now known that extremely complex dynamics can arise from basic deterministic processes. This field of study is generally called chaos theory. Here, a computer program, SLAC (Stability, Limits, And…
Organisational Leadership and Chaos Theory: Let's Be Careful
Galbraith, Peter
2004-01-01
This article addresses issues associated with applications of ideas from "chaos theory" to educational administration and leadership as found in the literature. Implications are considered in relation to claims concerning the behaviour of non-linear dynamic systems, and to the nature of the interpretations and recommendations that are made. To aid…
Between order and chaos: The quest for meaningful information
P. Adriaans
2009-01-01
The notion of meaningful information seems to be associated with the sweet spot between order and chaos. This form of meaningfulness of information, which is primarily what science is interested in, is not captured by both Shannon information and Kolmogorov complexity. In this paper I develop a theo
Learning Dialogically: The Art of Chaos-Informed Transformation
van Eijnatten, Frans M.; van Galen, Maarten C.; Fitzgerald, Laurie A.
2003-01-01
A decision to don the chaos lens, adopt dialogue as its primary mode of communication, and to recognize the power of the organizational mind has fundamentally and irreversibly changed the way a Dutch capital-equipment manufacturer operates in its rapidly complexifying global marketplace. Beginning in September 1999, the focus of an ever widening…
What Does Chaos Theory Have to Offer Educational Administration?
Blair, Billie Goode
1993-01-01
Chaos theory, based on quantum physics research, boasts six central concepts: the butterfly effect, onset of turbulence, dissipative structures, random shocks, strange attractors, and recursive symmetries and feedback mechanisms. This article examines five principals' daily experiences, focusing on participants' efforts to generate meaning from a…
Emergence of chaos in a spatially confined reactive system
Voorsluijs, Valérie; De Decker, Yannick
2016-11-01
In spatially restricted media, interactions between particles and local fluctuations of density can lead to important deviations of the dynamics from the unconfined, deterministic picture. In this context, we investigated how molecular crowding can affect the emergence of chaos in small reactive systems. We developed to this end an amended version of the Willamowski-Rössler model, where we account for the impenetrability of the reactive species. We analyzed the deterministic kinetics of this model and studied it with spatially-extended stochastic simulations in which the mobility of particles is included explicitly. We show that homogeneous fluctuations can lead to a destruction of chaos through a fluctuation-induced collision between chaotic trajectories and absorbing states. However, an interplay between the size of the system and the mobility of particles can counterbalance this effect so that chaos can indeed be found when particles diffuse slowly. This unexpected effect can be traced back to the emergence of spatial correlations which strongly affect the dynamics. The mobility of particles effectively acts as a new bifurcation parameter, enabling the system to switch from stationary states to absorbing states, oscillations or chaos.
Synchronization of spatiotemporal chaos using nonlinear feedback functions
Directory of Open Access Journals (Sweden)
M. K. Ali
1997-01-01
Full Text Available Synchronization of spatiotemporal chaos is studied using the method of variable feedback with coupled map lattices as model systems. A variety of feedback functions are introduced and the diversity in their choices for synchronizing any given system is exemplified. Synchronization in the presence of noise and with sporadic feedback is also presented.
Confidential Communication Through Chaos Encryption in Wireless Sensor Network
Institute of Scientific and Technical Information of China (English)
CHEN Shuai; ZHONG Xian-xin
2007-01-01
A new byte block cipher algorithm with discrete chaos and Feistel structure has been studied for confidential communication in wireless sensor network to improve security. After permutation, the byte block was encrypted through a Feistel structure in multiple turns and afterwards replaced again. The child keys are the composite sequence of discrete chaos and linear congruence sequences. Both the plain text and cipher text are of 8 bits. The number of keys is alterable. A nonlinear encryption function in the Feistel structure with chaos was constructed. The cipher algorithm was realized in the Micaz node,and the confidential communication experiment in wireless sensor network was completed successfully. Additional ROM memory required for the cipher algorithm is 4144 bytes and an additional RAM memory 61 bytes. The cipher algorithm is nonlinear chaos and the Feistel structure holds the best of the RC6, DES and SKIPJACK cipher algorithms.The result shows that the algorithm needs a little memory and is safe at a high level.
The New Math for Leaders: Useful Ideas from Chaos Theory
2007-11-02
Jossey- Bass Publishers, 1994. Krasner, Saul , ed. The Ubiquity of Chaos. Washington, DC: AAAS, 1990. Laird, Paul A. and National War College. Complexity...Managing Change/ Innovation/ and Organizational Renewal. (San Francisco: Jossey- Bass Publishers, 1994)/ 4-6. He goes on to develop the need for dynamic
Institute of Scientific and Technical Information of China (English)
王冰
2011-01-01
There are a lot of archaic words of the Northern Dynasties retained in the present-day Henan dialect.This paper presents a dual analysis on the usage of 32 words by comparing the literature of the Northern Dynasties and the Henan dialectal materials,and then reviews the inclusion and paraphrase of these words in reference books.It concludes by pointing out that research on the archaic words of the Northern Dynasties is of huge value to the exploration into the roots of Henan dialectal words and the compilation of relevant reference books in this regard.%河南方言中保留了不少北朝文献词语,文章通过北朝文献和河南方言材料对32个词语的使用情况进行了互证,并考察了一些工具书的收录和释义,从而指出北朝词汇研究在方言词语探源和工具书编写等方面的重要价值。
Institute of Scientific and Technical Information of China (English)
邓冲
2016-01-01
This paper analyzes the rhyming of Long Ying ' s archaic poems. It is found that entering rhymes has been disappeared, there is various degree of cross-rhyme in [-m、-n、-N] Yangsheng rhymes, a few initial characters of You-Hou(尤侯) Group rhyme category or Zhi-Wei(之微) Group rhyme category have changed into Yu-Mu(虞模) Group rhyme category, it can be concluded that the rhyme feature of Long Ying's archaic poems reflects the phonetic characteristics of Wuling Dialect in Ming dynasty from this phe-nomenon.%明代湖广武陵诗人龙膺的古体诗用韵，入声韵消失，阳声韵尾[-n]、[-m]、[-η]混并，尤侯韵与虞模韵混押、之微韵与虞模韵混押。这一方面是由古体诗韵放宽所致，另一方面应当是受诗人乡音武陵方言影响。龙膺古体诗用韵在一定程度上反映了当时武陵方言的一些语音特点。
BOOK REVIEW: Chaos: A Very Short Introduction
Klages, R.
2007-07-01
This book is a new volume of a series designed to introduce the curious reader to anything from ancient Egypt and Indian philosophy to conceptual art and cosmology. Very handy in pocket size, Chaos promises an introduction to fundamental concepts of nonlinear science by using mathematics that is `no more complicated than X=2. Anyone who ever tried to give a popular science account of research knows that this is a more challenging task than writing an ordinary research article. Lenny Smith brilliantly succeeds to explain in words, in pictures and by using intuitive models the essence of mathematical dynamical systems theory and time series analysis as it applies to the modern world. In a more technical part he introduces the basic terms of nonlinear theory by means of simple mappings. He masterly embeds this analysis into the social, historical and cultural context by using numerous examples, from poems and paintings over chess and rabbits to Olbers' paradox, card games and `phynance'. Fundamental problems of the modelling of nonlinear systems like the weather, sun spots or golf balls falling through an array of nails are discussed from the point of view of mathematics, physics and statistics by touching upon philosophical issues. At variance with Laplace's demon, Smith's 21st century demon makes `real world' observations only with limited precision. This poses a severe problem to predictions derived from complex chaotic models, where small variations of initial conditions typically yield totally different outcomes. As Smith argues, this difficulty has direct implications on decision-making in everyday modern life. However, it also asks for an inherently probabilistic theory, which somewhat reminds us of what we are used to in the microworld. There is little to criticise in this nice little book except that some figures are of poor quality thus not really reflecting the beauty of fractals and other wonderful objects in this field. I feel that occasionally the book
vs. a polynomial chaos-based MCMC
Siripatana, Adil
2014-08-01
Bayesian Inference of Manning\\'s n coefficient in a Storm Surge Model Framework: comparison between Kalman lter and polynomial based method Adil Siripatana Conventional coastal ocean models solve the shallow water equations, which describe the conservation of mass and momentum when the horizontal length scale is much greater than the vertical length scale. In this case vertical pressure gradients in the momentum equations are nearly hydrostatic. The outputs of coastal ocean models are thus sensitive to the bottom stress terms de ned through the formulation of Manning\\'s n coefficients. This thesis considers the Bayesian inference problem of the Manning\\'s n coefficient in the context of storm surge based on the coastal ocean ADCIRC model. In the first part of the thesis, we apply an ensemble-based Kalman filter, the singular evolutive interpolated Kalman (SEIK) filter to estimate both a constant Manning\\'s n coefficient and a 2-D parameterized Manning\\'s coefficient on one ideal and one of more realistic domain using observation system simulation experiments (OSSEs). We study the sensitivity of the system to the ensemble size. we also access the benefits from using an in ation factor on the filter performance. To study the limitation of the Guassian restricted assumption on the SEIK lter, 5 we also implemented in the second part of this thesis a Markov Chain Monte Carlo (MCMC) method based on a Generalized Polynomial chaos (gPc) approach for the estimation of the 1-D and 2-D Mannning\\'s n coe cient. The gPc is used to build a surrogate model that imitate the ADCIRC model in order to make the computational cost of implementing the MCMC with the ADCIRC model reasonable. We evaluate the performance of the MCMC-gPc approach and study its robustness to di erent OSSEs scenario. we also compare its estimates with those resulting from SEIK in term of parameter estimates and full distributions. we present a full analysis of the solution of these two methods, of the
Intrinsic Instability of Coronal Streamers
Chen, Y; Song, H Q; Shi, Q Q; Feng, S W; Xia, L D; 10.1088/0004-637X/691/2/1936
2009-01-01
Plasma blobs are observed to be weak density enhancements as radially stretched structures emerging from the cusps of quiescent coronal streamers. In this paper, it is suggested that the formation of blobs is a consequence of an intrinsic instability of coronal streamers occurring at a very localized region around the cusp. The evolutionary process of the instability, as revealed in our calculations, can be described as follows: (1) through the localized cusp region where the field is too weak to sustain the confinement, plasmas expand and stretch the closed field lines radially outward as a result of the freezing-in effect of plasma-magnetic field coupling; the expansion brings a strong velocity gradient into the slow wind regime providing the free energy necessary for the onset of a subsequent magnetohydrodynamic instability; (2) the instability manifests itself mainly as mixed streaming sausage-kink modes, the former results in pinches of elongated magnetic loops to provoke reconnections at one or many loc...
Intrinsic optimization using stochastic nanomagnets
Sutton, Brian; Camsari, Kerem Yunus; Behin-Aein, Behtash; Datta, Supriyo
2017-01-01
This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic constituents are stochastic nanomagnets which switch randomly between the ±1 Ising states and can be monitored continuously with standard electronics. Their mutual interactions can be short or long range, and their strengths can be reconfigured as needed to solve specific problems and to anneal the system at room temperature. The natural laws of statistical mechanics guide the network of stochastic nanomagnets at GHz speeds through the collective states with an emphasis on the low energy states that represent optimal solutions. As proof-of-concept, we present simulation results for standard NP-complete examples including a 16-city traveling salesman problem using experimentally benchmarked models for spin-transfer torque driven stochastic nanomagnets. PMID:28295053
Incentives and intrinsic motivation in healthcare
Directory of Open Access Journals (Sweden)
Mikel Berdud
2016-11-01
Conclusions: The conclusions could act as a guide to support the optimal design of incentive policies and schemes within health organisations when healthcare professionals are intrinsically motivated.
Algebraic description of intrinsic modes in nuclei
Energy Technology Data Exchange (ETDEWEB)
Leviatan, A. (Los Alamos National Lab., NM (USA))
1990-01-01
We present a procedure for extracting normal modes in algebraic number-conserving systems of interacting bosons relevant for collective states in even-even nuclei. The Hamiltonian is resolved into intrinsic (bandhead related) and collective (in-band related) parts. Shape parameters are introduced through non-spherical boson bases. Intrinsic modes decoupled from the spurious modes are obtained from the intrinsic part of the Hamiltonian in the limit of large number of bosons. Intrinsic states are constructed and serve to evaluate electromagnetic transition rates. The method is illustrated for systems with one type of boson as well as with proton-neutron bosons. (author).
Design of intrinsically safe power supply
Institute of Scientific and Technical Information of China (English)
LI Rui-jin; JIN Lin
2012-01-01
Aiming to make a high power direct current supply safely used in coal mine production,this paper made a deep research on characteristics of intrinsically safe power supply,using the mathematical model established according to coal mine intrinsic safety standards.It provides theory support for the application of high power intrinsically safe power supply.The released energy of output short circuit of switch power supply,and the close related factors that influence the biggest output short-circuit spark discharge energy are the theoretical basis of the power supply.It is shown how to make a high power intrinsically safe power supply using the calculated values in the mathematical model,and take values from intrinsically safe requirements parameters scope,then this theoretical calculation value can be developed as the ultimate basis for research of the power supply.It gets the identification method of intrinsically safe from mathematics model of intrinsically safe power supply characteristics study,which solves the problem of theory and application of designing different power intrinsically safe power supply,and designs a kind of high power intrinsically safe power supply through this method.
Outflow channel sources, reactivation, and chaos formation, Xanthe Terra, Mars
Rodriguez, J.A.P.; Sasaki, S.; Kuzmin, R.O.; Dohm, J.M.; Tanaka, K.L.; Miyamoto, H.; Kurita, K.; Komatsu, G.; Fairen, A.G.; Ferris, J.C.
2005-01-01
The undulating, warped, and densely fractured surfaces of highland regions east of Valles Marineris (located north of the eastern Aureum Chaos, east of the Hydraotes Chaos, and south of the Hydaspis Chaos) resulted from extensional surface warping related to ground subsidence, caused when pressurized water confined in subterranean caverns was released to the surface. Water emanations formed crater lakes and resulted in channeling episodes involved in the excavation of Ares, Tiu, and Simud Valles of the eastern part of the circum-Chryse outflow channel system. Progressive surface subsidence and associated reduction of the subsurface cavernous volume, and/or episodes of magmatic-driven activity, led to increases of the hydrostatic pressure, resulting in reactivation of both catastrophic and non-catastrophic outflow activity. Ancient cratered highland and basin materials that underwent large-scale subsidence grade into densely fractured terrains. Collapse of rock materials in these regions resulted in the formation of chaotic terrains, which occur in and near the headwaters of the eastern circum-Chryse outflow channels. The deepest chaotic terrain in the Hydaspis Chaos region resulted from the collapse of pre-existing outflow channel floors. The release of volatiles and related collapse may have included water emanations not necessarily linked to catastrophic outflow. Basal warming related to dike intrusions, thermokarst activity involving wet sediments and/or dissected ice-enriched country rock, permafrost exposed to the atmosphere by extensional tectonism and channel incision, and/or the injection of water into porous floor material, may have enhanced outflow channel floor instability and subsequent collapse. In addition to the possible genetic linkage to outflow channel development dating back to at least the Late Noachian, clear disruption of impact craters with pristine ejecta blankets and rims, as well as preservation of fine tectonic fabrics, suggest that
Intrinsically photosensitive retinal ganglion cells
Institute of Scientific and Technical Information of China (English)
Gary; E.PICKARD; Patricia; J.SOLLARS
2010-01-01
A new mammalian photoreceptor was recently discovered to reside in the ganglion cell layer of the inner retina.These intrinsically photosensitive retinal ganglion cells(ipRGCs) express a photopigment,melanopsin,that confers upon them the ability to respond to light in the absence of all rod and cone photoreceptor input.Although relatively few in number,ipRGCs extend their dendrites across large expanses of the retina making them ideally suited to function as irradiance detectors to assess changes in ambient light levels.Phototransduction in ipRGCs appears to be mediated by transient receptor potential channels more closely resembling the phototransduction cascade of invertebrate rather than vertebrate photoreceptors.ipRGCs convey irradiance information centrally via the optic nerve to influence several functions.ipRGCs are the primary retinal input to the hypothalamic suprachiasmatic nucleus(SCN),a circadian oscillator and biological clock,and this input entrains the SCN to the day/night cycle.ipRGCs contribute irradiance signals that regulate pupil size and they also provide signals that interface with the autonomic nervous system to regulate rhythmic gene activity in major organs of the body.ipRGCs also provide excitatory drive to dopaminergic amacrine cells in the retina,providing a novel basis for the restructuring of retinal circuits by light.Here we review the ground-breaking discoveries,current progress and directions for future investigation.
Chaos and maps in relativistic rynamical systems
Directory of Open Access Journals (Sweden)
L. P. Horwitz
2000-01-01
Full Text Available The basic work of Zaslavskii et al showed that the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on the phase space; the resulting evolution contains a stochastic flow to unbounded energy. Subsequent studies have formulated the problem in terms of a relativistic charged particle in interaction with the electromagnetic field. We review the structure of the covariant Lorentz force used to study this problem. We show that the Lorentz force equation can be derived as well from the manifestly covariant mechanics of Stueckelberg in the presence of a standard Maxwell field, establishing a connection between these equations and mass shell constraints. We argue that these relativistic generalizations of the problem are intrinsically inaccurate due to an inconsistency in the structure of the relativistic Lorentz force, and show that a reformulation of the relativistic problem, permitting variations (classically in both the particle mass and the effective “mass” of the interacting electromagnetic field, provides a consistent system of classical equations for describing such processes.
Recursive proportional feedback and its use to control chaos in an electrochemical system
Rollins, R W; Sherard, P; Dewald, H D
1995-01-01
The recursive proportional feedback (RPF) algorithm for controlling chaos is described and applied to control chemical chaos observed during the electrodissolution of a rotating copper disk in a sodium acetate/acetic acid buffer. Experimental evidence is presented to indicate why the RPF method was used and the theoretical robustness of the algorithm is discussed. (This paper appears in the "Proceedings of the 2nd Conference on EXPERIMENTAL CHAOS," World Scientific Press, River Ridge, NJ, 1995)
Intrinsic bioremediation of landfills interim report
Energy Technology Data Exchange (ETDEWEB)
Brigmon, R.L. [Westinghouse Savannah River Company, Aiken, SC (United States); Fliermans, C.B.
1997-07-14
Intrinsic bioremediation is a risk management option that relies on natural biological and physical processes to contain the spread of contamination from a source. Evidence is presented in this report that intrinsic bioremediation is occurring at the Sanitary Landfill is fundamental to support incorportion into a Corrective Action Plan (CAP).
Riemannian theory of Hamiltonian chaos and Lyapunov exponents
Casetti, L; Pettini, M; Casetti, Lapo; Clementi, Cecilia; Pettini, Marco
1996-01-01
This paper deals with the problem of analytically computing the largest Lyapunov exponent for many degrees of freedom Hamiltonian systems. This aim is succesfully reached within a theoretical framework that makes use of a geometrization of newtonian dynamics in the language of Riemannian geometry. A new point of view about the origin of chaos in these systems is obtained independently of homoclinic intersections. Chaos is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of Jacobi equation for geodesic spread. Under general conditions ane effective stability equation is derived; an analytic formula for the growth-rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam beta model and to a chain of coupled rotators. An excellent agreement is found the theoretical prediction and the values of the Lyapunov exponent obtained by numerical simulations for both models.
Randomness versus deterministic chaos: Effect on invasion percolation clusters
Peng, Chung-Kang; Prakash, Sona; Herrmann, Hans J.; Stanley, H. Eugene
1990-10-01
What is the difference between randomness and chaos \\? Although one can define randomness and one can define chaos, one cannot easily assess the difference in a practical situation. Here we compare the results of these two antipodal approaches on a specific example. Specifically, we study how well the logistic map in its chaotic regime can be used as quasirandom number generator by calculating pertinent properties of a well-known random process: invasion percolation. Only if λ>λ*1 (the first reverse bifurcation point) is a smooth extrapolation in system size possible, and percolation exponents are retrieved. If λ≠1, a sequential filling of the lattice with the random numbers generates a measurable anisotropy in the growth sequence of the clusters, due to short-range correlations.
Deterministic chaos, fractals and quantumlike mechanics in atmospheric flows
Selvam, A M
1990-01-01
The complex spaciotemporal patterns of atmospheric flows that result from the cooperative existence of fluctuations ranging in size from millimetres to thousands of kilometres are found to exhibit long-range spacial and temporal correlations. These correlations are manifested as the self-similar fractal geometry of the global cloud cover pattern and the inverse power-law form for the atmospheric eddy energy spectrum. Such long-range spaciotemporal correlations are ubiquitous in extended natural dynamical systems and are signatures of deterministic chaos or self-organized criticality. In this paper, a cell dynamical system model for atmospheric flows is developed by consideration of microscopic domain eddy dynamical processes. This nondeterministic model enables formulation of a simple closed set of governing equations for the prediction and description of observed atmospheric flow structure characteristics as follows. The strange-attractor design of the field of deterministic chaos in atmospheric flows consis...
A Novel Memcapacitor Model and Its Application for Generating Chaos
Directory of Open Access Journals (Sweden)
Guangyi Wang
2016-01-01
Full Text Available Memristor and memcapacitor are new nonlinear devices with memory. We present a novel memcapacitor model that has the capability of capturing the behavior of a memcapacitor. Based on this model we also design a chaotic oscillator circuit that contains a HP memristor and the memcapacitor model for generating good pseudorandom sequences. Its dynamic behaviors, including equilibrium points, stability, and bifurcation characteristics, are analyzed in detail. It is found that the proposed oscillator can exhibit some complex phenomena, such as chaos, hyperchaos, coexisting attractors, abrupt chaos, and some novel bifurcations. Moreover, a scheme for digitally realizing this oscillator is provided by using the digital signal processor (DSP technology. Then the random characteristics of the chaotic binary sequences generated from the oscillator are tested via the test suit of National Institute of Standards and Technology (NIST. The tested randomness definitely reaches the standards of NIST and is better than that of the well-known Lorenz system.
Comparative study of variational chaos indicators and ODEs' numerical integrators
Darriba, Luciano A; Cincotta, Pablo M; Giordano, Claudia M
2012-01-01
The reader can find in the literature a lot of different techniques to study the dynamics of a given system and also, many suitable numerical integrators to compute them. Notwithstanding the recent work of Maffione et al. (2011a) for mappings, a detailed comparison among the widespread indicators of chaos in a general system is still lacking. Such a comparison could lead to select the most efficient algorithms given a certain dynamical problem. Furthermore, in order to choose the appropriate numerical integrators to compute them, more comparative studies among numerical integrators are also needed. This work deals with both problems. We first extend the work of Maffione et al. (2011) for mappings to the 2D H\\'enon & Heiles (1964) potential, and compare several variational indicators of chaos: the Lyapunov Indicator (LI); the Mean Exponential Growth Factor of Nearby Orbits (MEGNO); the Smaller Alignment Index (SALI) and its generalized version, the Generalized Alignment Index (GALI); the Fast Lyapunov Indi...
Catastrophic ice lake collapse in Aram Chaos, Mars
Roda, Manuel; Zegers, Tanja E; Oosthoek, Jelmer H P
2014-01-01
Hesperian chaotic terrains have been recognized as the source of outflow channels formed by catastrophic outflows. Four main scenarios have been proposed for the formation of chaotic terrains that involve different amounts of water and single or multiple outflow events. Here, we test these scenarios with morphological and structural analyses of imagery and elevation data for Aram Chaos in conjunction with numerical modeling of the morphological evolution of the catastrophic carving of the outflow valley. The morphological and geological analyses of Aram Chaos suggest large-scale collapse and subsidence (1500 m) of the entire area, which is consistent with a massive expulsion of liquid water from the subsurface in one single event. The combined observations suggest a complex process starting with the outflow of water from two small channels, followed by continuous groundwater sapping and headward erosion and ending with a catastrophic lake rim collapse and carving of the Aram Valley, which is synchronous with ...
Climate predictions: the chaos and complexity in climate models
Mihailović, Dragutin T; Arsenić, Ilija
2013-01-01
Some issues which are relevant for the recent state in climate modeling have been considered. A detailed overview of literature related to this subject is given. The concept in modeling of climate, as a complex system, seen through Godel's Theorem and Rosen's definition of complexity and predictability is discussed. It is pointed out to occurrence of chaos in computing the environmental interface temperature from the energy balance equation given in a difference form. A coupled system of equations, often used in climate models is analyzed. It is shown that the Lyapunov exponent mostly has positive values allowing presence of chaos in this systems. The horizontal energy exchange between environmental interfaces, which is described by the dynamics of driven coupled oscillators, is analyzed. Their behavior and synchronization, when a perturbation is introduced in the system, as a function of the coupling parameters, the logistic parameter and the parameter of exchange, was studied calculating the Lyapunov expone...
Reliability Modeling and Optimization Using Fuzzy Logic and Chaos Theory
Directory of Open Access Journals (Sweden)
Alexander Rotshtein
2012-01-01
Full Text Available Fuzzy sets membership functions integrated with logistic map as the chaos generator were used to create reliability bifurcations diagrams of the system with redundancy of the components. This paper shows that increasing in the number of redundant components results in a postponement of the moment of the first bifurcation which is considered as most contributing to the loss of the reliability. The increasing of redundancy also provides the shrinkage of the oscillation orbit of the level of the system’s membership to reliable state. The paper includes the problem statement of redundancy optimization under conditions of chaotic behavior of influencing parameters and genetic algorithm of this problem solving. The paper shows the possibility of chaos-tolerant systems design with the required level of reliability.
Smearing of chaos in sandwich pp-waves
Podolsky, J
1999-01-01
Recent results demonstrating the chaotic behavior of geodesics in non-homogeneous vacuum pp-wave solutions are generalized. Here we concentrate on motion in non-homogeneous sandwich pp-waves and show that chaos smears as the duration of these gravitational waves is reduced. As the number of radial bounces of any geodesic decreases, the outcome channels to infinity become fuzzy, and thus the fractal structure of the initial conditions characterizing chaos is cut at lower and lower levels. In the limit of impulsive waves, the motion is fully non-chaotic. This is proved by presenting the geodesics in a simple explicit form which permits a physical interpretation, and demonstrates the focusing effect. It is shown that a circle of test particles is deformed by the impulse into a family of closed hypotrochoidal curves in the transversal plane. These are deformed in the longitudinal direction in such a way that a specific closed caustic surface is formed.
Asymptotic chaos expansions in finance theory and practice
Nicolay, David
2014-01-01
Stochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface. In principle, they are well suited for pricing and hedging vanilla and exotic options, for relative value strategies or for risk management. In practice however, most SV models lack a closed form valuation for European options. This book presents the recently developed Asymptotic Chaos Expansions methodology (ACE) which addresses that issue. Indeed its generic algorithm provides, for any regular SV model, the pure asymptotes at any order for both the static and dynamic maps of the implied volatility surface. Furthermore, ACE is programmable and can complement other approximation methods. Hence it allows a systematic approach to designing, parameterising, calibrating and exploiting SV models, typically for Vega hedging or American Monte-Carlo. Asymptotic Chaos Expansions in Finance illustrates the ACE approach for single underlyings (suc...
Secure passive optical network based on chaos synchronization.
Jiang, Ning; Zhang, Chongfu; Qiu, Kun
2012-11-01
A physical-enhanced secure passive optical network (PON) based on chaos synchronization is proposed and numerically demonstrated. In this scheme, the chaotic output of an external-cavity semiconductor laser is used as the transmission carrier in both downstream and upstream directions, the chaos modulation technology is used to encrypt the downstream data, and the multiplexed subcarrier-modulation technology is adopted for the upstream transmission. Simulation results demonstrate that both the downstream data and the upstream data encrypted into the chaotic carriers can be successfully decrypted; moreover, the security of downstream can be enhanced by properly increasing the bit rate, and the upstream security can be maintained at a high level. The proposed PON affords secure all-optical access at the physical layer.
Computational complexity of symbolic dynamics at the onset of chaos
Lakdawala, Porus
1996-05-01
In a variety of studies of dynamical systems, the edge of order and chaos has been singled out as a region of complexity. It was suggested by Wolfram, on the basis of qualitative behavior of cellular automata, that the computational basis for modeling this region is the universal Turing machine. In this paper, following a suggestion of Crutchfield, we try to show that the Turing machine model may often be too powerful as a computational model to describe the boundary of order and chaos. In particular we study the region of the first accumulation of period doubling in unimodal and bimodal maps of the interval, from the point of view of language theory. We show that in relation to the ``extended'' Chomsky hierarchy, the relevant computational model in the unimodal case is the nested stack automaton or the related indexed languages, while the bimodal case is modeled by the linear bounded automaton or the related context-sensitive languages.
Chaos synchronization between two different 4D hyperchaotic Chen systems
Institute of Scientific and Technical Information of China (English)
Liu Yang-Zheng; Jiang Chang-Sheng; Lin Chang-Sheng; Jiang Yao-Mei
2007-01-01
This paper presents chaos synchronization between two different four-dimensional (4D) hyperchaotic Chen systems by nonlinear feedback control laws.A modified 4D hyperchaotic Chen system is obtained by changing the nonlinear function of the 4D hyperchaotic Chen system,furthermore,an electronic circuit to realize two different 4D hyperchaotic Chen systems is designed.With nonlinear feedback control method,chaos synchronization between two different 4D hyperchaotic Chen systems is achieved.Based on the stability theory,the functions of the nonlinear feedback control for synchronization of two different 4D hyperchaotic Chen systems is derived,the range of feedback gains is determined.Numerical simulations are shown to verify the theoretical results.
Intermittency and transient chaos from simple frequency-dependent selection.
Gavrilets, S; Hastings, A
1995-08-22
Frequency-dependent selection is an important determinant of the evolution of gametophytic self-incompatibility systems in plants, aposematic (warning) and cryptic coloration, systems of mimicry, competitive interactions among members of a population, mating preferences, predator-prey and host-parasite interactions, aggression and other behavioural traits. Past theoretical studies of frequency-dependent selection have shown it to be a plausible mechanism for the maintenance of genetic variability in natural populations. Here, through an analysis of a simple deterministic model for frequency-dependent selection, we demonstrate that complex dynamic behaviour is possible under a broad range of parameter values. In particular we show that the model exhibits not only cycles and chaos but also, for a more restricted set of parameters, transient chaos and intermittency: alterations between an apparently deterministic behaviour and apparently chaotic fluctuations. This behaviour, which has not been stressed within the population genetics literature, provides an explanation for erratic dynamics of gene frequencies.
Deterministic chaos at the ocean surface: applications and interpretations
Directory of Open Access Journals (Sweden)
A. J. Palmer
1998-01-01
Full Text Available Ocean surface, grazing-angle radar backscatter data from two separate experiments, one of which provided coincident time series of measured surface winds, were found to exhibit signatures of deterministic chaos. Evidence is presented that the lowest dimensional underlying dynamical system responsible for the radar backscatter chaos is that which governs the surface wind turbulence. Block-averaging time was found to be an important parameter for determining the degree of determinism in the data as measured by the correlation dimension, and by the performance of an artificial neural network in retrieving wind and stress from the radar returns, and in radar detection of an ocean internal wave. The correlation dimensions are lowered and the performance of the deterministic retrieval and detection algorithms are improved by averaging out the higher dimensional surface wave variability in the radar returns.
Control of complex dynamics and chaos in distributed parameter systems
Energy Technology Data Exchange (ETDEWEB)
Chakravarti, S.; Marek, M.; Ray, W.H. [Univ. of Wisconsin, Madison, WI (United States)
1995-12-31
This paper discusses a methodology for controlling complex dynamics and chaos in distributed parameter systems. The reaction-diffusion system with Brusselator kinetics, where the torus-doubling or quasi-periodic (two characteristic incommensurate frequencies) route to chaos exists in a defined range of parameter values, is used as an example. Poincare maps are used for characterization of quasi-periodic and chaotic attractors. The dominant modes or topos, which are inherent properties of the system, are identified by means of the Singular Value Decomposition. Tested modal feedback control schemas based on identified dominant spatial modes confirm the possibility of stabilization of simple quasi-periodic trajectories in the complex quasi-periodic or chaotic spatiotemporal patterns.
Coherence In Quantum Chaos, Stochastic Spacetime, And Collective Phenomena
Shiokawa, K
1998-01-01
Various manifestations of coherence properties in quantum and classical dynamics in open and closed systems are studied. Among many different issues and phenomena related to coherence, particular aspects are expounded by models chosen from quantum chaos, quantum optics, mesoscopic and high energy physics, and semiclassical relativity. I show how coherence in quantum and classical systems manifests itself in different forms and is enhanced, altered, and suppressed in the presence of chaos, randomness, boundary, and environment. Author's contributions start from the first time discussion of decoherence in quantum cat map and quantum kicked rotor. Wave propagation in stochastic spacetime is considered as that in random media by extending the analogy of spacetime metric with the refractive index of media...
Chaos control in an economic model via minimum entropy strategy
Energy Technology Data Exchange (ETDEWEB)
Salarieh, Hassan [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Tehran (Iran, Islamic Republic of)], E-mail: salarieh@mech.sharif.edu; Alasty, Aria [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Tehran (Iran, Islamic Republic of); National Research Institute for Science Policy (NRISP), Soheil Street, Shirazi Avenue, Tehran (Iran, Islamic Republic of)], E-mail: aalasti@sharif.edu
2009-04-30
In this paper, minimum entropy algorithm for controlling chaos, is applied to a Cournot duopoly with different constant marginal costs, as a discrete-time dynamical system which shows chaotic behavior. The ME control is implemented through delayed feedback. It is assumed that the equations of the dynamical system are not known, so the feedback gain cannot be obtained analytically from the system equations. In the ME method the feedback gain is obtained adaptively in such a way that the entropy of the system converges to zero, hence a fixed point of the system will be stabilized. Application of the proposed method with different economic control strategies is numerically investigated. Simulation results show the effectiveness of the ME method for controlling chaos in economic systems with unknown equations.
Chaos Control in Nonlinear Systems Using the Generalized Backstopping Method
Directory of Open Access Journals (Sweden)
A. R. Sahab
2008-01-01
Full Text Available One of the most important nonlinear systems for checking the abilities of control methods is chaos. In this study chaos in Lorenz system was used for checking abilities of new control method. This new method to control nonlinear systems was called Generalized Backstepping method because of its similarity to Backstepping but its abilities to control more systems than Backstepping. This new method was applied to Lorenz system in three ways: 1.Stabilized states of equations. 2. Track step response. 3. Track sinusoidal response. In every way, simulations proved abilities of method. Comparing this new method with Backstepping showed that in this method, states stabilize at zero in shorter time than Backstepping and input control is more limited. So new method not only is used in more systems but also has better response.
Adapting Predictive Feedback Chaos Control for Optimal Convergence Speed
Bick, Christian; Kolodziejski, Christoph
2012-01-01
Stabilizing unstable periodic orbits in a chaotic invariant set not only reveals information about its structure but also leads to various interesting applications. For the successful application of a chaos control scheme, convergence speed is of crucial importance. Here we present a predictive feedback chaos control method that adapts a control parameter online to yield optimal asymptotic convergence speed. We study the adaptive control map both analytically and numerically and prove that it converges at least linearly to a value determined by the spectral radius of the control map at the periodic orbit to be stabilized. The method is easy to implement algorithmically and may find applications for adaptive online control of biological and engineering systems.
Controlling chaos in unidimensional maps using macroevolutionary algorithms.
Marín, Jesús; Solé, Ricard V
2002-02-01
We introduce a simple search algorithm that explores the parameter of periodically perturbed discrete maps in order to find desired orbits through chaos control. The method has been applied to one-dimensional maps but is easily extendable to higher-dimensional systems. Here, we consider two types of chaos control involving proportional pulses in the system variables [Phys. Rev. Lett. 72, 1455 (1994)] and constant feedback [Phys. Rev. E 51, 6239 (1995)], the first case being presented in detail. It is shown that our method allows a rapid exploration of parameter space and the finding of high-fitness (i.e., controlled) solutions close to the target orbits, even when high periodicities are required.
Universality in chaos of particle motion near black hole horizon
Hashimoto, Koji; Tanahashi, Norihiro
2017-01-01
The motion of a particle near a horizon of a spherically symmetric static black hole is shown to possess a universal Lyapunov exponent of chaos bounded by its surface gravity. To probe the horizon, we introduce an electromagnetic or scalar force to the particle so that it does not fall into the horizon. There appears an unstable maximum of the total potential where the evaluated maximal Lyapunov exponent is found to be to the surface gravity of the black hole. This value is independent of the external forces, the particle mass and background geometry, and in this sense this Lyapunov exponent is universal. Unless there are other sources of chaos, the Lyapunov exponent is subject to an inequality λ ≤2 π TBH/ℏ, which is identical to the bound recently discovered by Maldacena, Shenker, and Stanford.
Universality in Chaos of Particle Motion near Black Hole Horizon
Hashimoto, Koji
2016-01-01
Motion of a particle near a horizon of a spherically symmetric black hole is shown to possess a universal Lyapunov exponent of a chaos provided by its surface gravity. To probe the horizon, we introduce electromagnetic or scalar force to the particle so that it does not fall into the horizon. There appears an unstable maximum of the total potential where the evaluated maximal Lyapunov exponent is found to be independent of the external forces and the particle mass. The Lyapunov exponent is universally given by the surface gravity of the black hole. Unless there are other sources of a chaos, the Lyapunov exponent is subject to an inequality $\\lambda \\leq 2\\pi T_{\\rm BH}/\\hbar$, which is identical to the bound recently discovered by Maldacena, Shenker and Stanford.
Quantum biology on the edge of quantum chaos.
Directory of Open Access Journals (Sweden)
Gabor Vattay
Full Text Available We give a new explanation for why some biological systems can stay quantum coherent for a long time at room temperature, one of the fundamental puzzles of quantum biology. We show that systems with the right level of complexity between chaos and regularity can increase their coherence time by orders of magnitude. Systems near Critical Quantum Chaos or Metal-Insulator Transition (MIT can have long coherence times and coherent transport at the same time. The new theory tested in a realistic light harvesting system model can reproduce the scaling of critical fluctuations reported in recent experiments. Scaling of return probability in the FMO light harvesting complex shows the signs of universal return probability decay observed at critical MIT. The results may open up new possibilities to design low loss energy and information transport systems in this Poised Realm hovering reversibly between quantum coherence and classicality.
Quantum biology on the edge of quantum chaos.
Vattay, Gabor; Kauffman, Stuart; Niiranen, Samuli
2014-01-01
We give a new explanation for why some biological systems can stay quantum coherent for a long time at room temperature, one of the fundamental puzzles of quantum biology. We show that systems with the right level of complexity between chaos and regularity can increase their coherence time by orders of magnitude. Systems near Critical Quantum Chaos or Metal-Insulator Transition (MIT) can have long coherence times and coherent transport at the same time. The new theory tested in a realistic light harvesting system model can reproduce the scaling of critical fluctuations reported in recent experiments. Scaling of return probability in the FMO light harvesting complex shows the signs of universal return probability decay observed at critical MIT. The results may open up new possibilities to design low loss energy and information transport systems in this Poised Realm hovering reversibly between quantum coherence and classicality.
From Hamiltonian chaos to complex systems a nonlinear physics approach
Leonetti, Marc
2013-01-01
From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach collects contributions on recent developments in non-linear dynamics and statistical physics with an emphasis on complex systems. This book provides a wide range of state-of-the-art research in these fields. The unifying aspect of this book is a demonstration of how similar tools coming from dynamical systems, nonlinear physics, and statistical dynamics can lead to a large panorama of research in various fields of physics and beyond, most notably with the perspective of application in complex systems. This book also: Illustrates the broad research influence of tools coming from dynamical systems, nonlinear physics, and statistical dynamics Adopts a pedagogic approach to facilitate understanding by non-specialists and students Presents applications in complex systems Includes 150 illustrations From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach is an ideal book for graduate students and researchers working in applied...
Hypersensitivity and chaos signatures in the quantum baker's maps
Scott, A J; Caves, C M; Schack, R; Brun, Todd A.; Caves, Carlton M.; Schack, Ruediger
2006-01-01
Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has lead to a number of different criteria being proposed for quantum chaos, including linear growth of entropy, exponential decay of fidelity, and hypersensitivity to perturbation. All of these accurately predict chaos in the classical limit, but it is not clear that they behave the same far from the classical realm. We investigate the dynamics of a family of quantizations of the baker's map, which range from a highly entangling unitary transformation to an essentially trivial shift map. Linear entropy growth and fidelity decay are exhibited by this entire family of maps, but hypersensitivity distinguishes between the simple dynamics of the trivial shift map and the more complicated dynamics of the other quantizations. This is supported by an analytical argument for short times and numerical evidence at later times.
Synchronization and suppression of chaos in non-locally coupled map lattices
Indian Academy of Sciences (India)
R M Szmoski; S E De S Pinto; M T Van Kan; A M Batista; R L Viana; S R Lopes
2009-12-01
We considered coupled map lattices with long-range interactions to study the spatiotemporal behaviour of spatially extended dynamical systems. 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 coupling strength which varies with the lattice in a power-law fashion. Depending on the range of the interactions, complete chaos synchronization and chaos suppression may be attained. Furthermore, we also calculated the Lyapunov dimension and the transversal distance to the synchronization manifold.
Effects on the upstream flood inundation caused from the operation of Chao Phraya Dam
Sutham Visutimeteegorn; Kanchit Likitdecharote; Suphat Vongvisessomjai
2007-01-01
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 trib...
Nonlinear Control of Beam Halo-Chaos in Accelerator-Driven Clean Nuclear Power System
Institute of Scientific and Technical Information of China (English)
FANG JinQing; CHEN GuanRong; ZHOU LiuLai; WENG JiaQiang
2002-01-01
Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applications in industry, medicine, and national defense. Some general engineering methods for chaos control have been developed in recent years, but they generally are unsuccessful for beam halo-chaos suppression due to many technical constraints. Beam halo-chaos is essentially a spatiotemporal chaotic motion within a high power proton accelerator. In this paper, some efficient nonlinear control methods, including wavelet function feedback control as a special nonlinear control method, are proposed for controlling beam halo-chaos under five kinds of the initial proton beam distributions (i.e., Kapchinsky-Vladimirsky, full Gauss,3-sigma Gauss, water-bag, and parabola distributions) respectively. Particles-in-cell simulations show that after control of beam halo-chaos, the beam halo strength factor is reduced to zero, and other statistical physical quantities of beam halo-chaos are doubly reduced. The methods we developed is very effective for suppression of proton beam halo-chaos in a periodic focusing channel of accelerator. Some potential application of the beam halo-chaos control in experiments is finally pointed out.
Experimental study of the effect of controlling signal on controlling chaos
Institute of Scientific and Technical Information of China (English)
李蓉; 祝恒江; 屈支林; 温孝东; 秦光戎; 胡岗
1995-01-01
A model of double-harmonious circuit for non-feedback control of chaos is introduced. A controlling signal is added to the coefficient for two-order term of the nonlinear differential equation The effect of controlling signal on controlling chaos is studied. By changing the controlling frequency fk and controlling strength Ik, chaos to period-doubling, period-adding and quasi-period state can be controlled. The effect of phase on controlling chaos is also discussed. A breathing phenomenon is observed and its mechanism is explained.
Obaid, Hafiz Muhammad; Khawar Islam, Muhammad; Obaid Ullah, Muhammad
2016-08-01
Broadband chaos can be generated by beating two wavelengths in a hybrid arrangement of Fabry-Perot (FP) Laser and Fiber ring cavity by injecting dual wavelengths. The bandwidth of generated chaos can be controlled by detuning different modes of FP Laser for beating. The bandwidth of generated chaos increased to many folds depending upon the injected strength and wavelength spacing matched to FP laser modes. The bandwidth enhancement in different simulation experiments conducted is optimized by varying different parameters of FP laser and cavity. The waveforms are analyzed and Lyapunov exponents are calculated in order to validate the existence of high bandwidth non-pulsating chaos.
An extension to chaos control via Lie derivatives: Fully linearizable systems.
Femat, Ricardo
2002-12-01
The technique of using Lie derivatives to control chaos introduced by Kocarev et al. [Chaos, Solitons Fractals 9, 1359-1366 (1998)] is extended in this contribution. Here, by using Lie derivatives in an extended space state, it is proved that chaos can be practically suppressed via feedback in spite of the Lie derivative being ill-posed at the reference. The main idea is to construct a dynamically equivalent system. In this way, the chaotic system can be practically stabilized around any point of singularity x(0). The Lorenz equation is used as an illustrative example to show the application in the chaos control context. (c) 2002 American Institute of Physics.
Controlling chaos and synchronization for new chaotic system using linear feedback control
Energy Technology Data Exchange (ETDEWEB)
Yassen, M.T. [Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)] e-mail: mtyassen@yahoo.com
2005-11-01
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.
Energy Technology Data Exchange (ETDEWEB)
Ge Zhengming [Department of Mechanical Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan (China)]. E-mail: zmg@cc.nctu.edu.tw; Lee, Ching-I [Department of Mechanical Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan (China)
2005-03-01
Chaos, control, anticontrol and synchronization of chaos for an autonomous rotational machine system with a hexagonal centrifugal governor and spring for which time-delay effect is considered are studied in the paper. By applying numerical results, phase diagram and power spectrum are presented to observe periodic and chaotic motions. Linear feedback control and adaptive control algorithm are used to control chaos effectively. Linear and nonlinear feedback synchronization and phase synchronization for the coupled systems are presented. Finally, anticontrol of chaos for this system is also studied.
Chaos analysis and chaotic EMI suppression of DC-DC converters
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
Coherence and Chaos in Integrable PDEs (Partial Differential Equations)
1991-03-01
01 Aug 88 to 30 Sep 9n 4. AMSUB"=S. PUNOUUS NU"蕁 COHERENCE AND CHAOS IN INTEGRABLE PDEs ( PARTIAL DIFFERENTIAL EQUATIONS ) AFOSR-83-0195 _61102F... Differential Equations , Parts 1 and 2; Lectures in Appl. Math. 23, edited by Basil Nicolaenko, Darrel Holm, and and J. Mac Hyman (American Mathematical...Coherent Structures, edited by David Campbell, Alan C. Newell, R. Schrieffer, and Harvey Segur, Physica 18D (1986). 4. Nonlinear Systems of Partial
Doubly excited helium. From strong correlation to chaos
Energy Technology Data Exchange (ETDEWEB)
Jiang, Yuhai
2006-03-15
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{sub 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{sub 5} to I{sub 9} and I{sub 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{sub 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{sub 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.)
Chaos detection tools: The LP-VIcode and its applications
Darriba, L. A.; Maffione, N. P.; Cincotta, P. M.; Giordano, C. M.
A very important topic in galactic dynamics is the detection of instabilities of a given system and the possible appearance of chaos. Such a chaotic bahaviour can be detected and studied by means of variational chaos in- dicators (CIs). The CIs are based on the study of the evolution of initial deviation vectors, which makes these techniques specially sensitive to in- dicate the presence of chaos. Notwithstanding their special sensitiveness to identify chaos, the CIs are still good alternatives to determine also the resonance web. On the other hand, the so-called spectral analysis methods are based on the study of some quantity (e.g. the frequency) on a single orbit, which turns these techniques very efficient for the determination of the resonant struc- ture of the system. The analysis of the interaction among chaotic and regular components as well as the determination of the resonant structure of the Hamiltonian leads to a deeper understanding of the system's dynamics. Despite the advan- tages of the simultaneous application of both types of techniques, many researchers keep applying only one of them. Herein, we present an alpha version of a program coded in Fortran, the LP-VIcode. Although the code is in a developing stage, it can compute several CIs, and here we apply it together with the Frequency Modified Fourier Transform (FMFT) (Sidlichovský & Nesvorný 1996) to study the stationary space (Schwarzchild 1993) of an average realistic Hamiltonian model (Muzzio et al. 2005). Using the LP-VIcode, in Maffione et al. (2011b) and Darriba et al. (sub- mitted) the authors suggest an efficient package of CIs to study a general Hamiltonian. Here the research is extended to show that the complemen- tary use of the LP-VIcode and the spectral analysis methods is highly rec- ommended to study a realistic Hamiltonian model.
Chaos, archetypes, and the all-integrating field.
Harle, Rob
2010-01-01
This essay explores the notion that the fundamental ontology of the universe is an all-integrating field. The process of chaos operates within this field as do other phenomena such as gravity and electromagnetic force. I argue that there are 'no objects only events', that is, dynamic continual process is the basic building block of all existence. My accompanying artworks illustrate these principles using the beauty of computer generated fractals combined with digitally manipulated, figurative images.