M lefranc, S. Boccaletti, B. Gluckman, C. Grebogi, J. K¨ Urths, L. Pecora

Part II

Poster contribution

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Statistical monitoring of atrial fibrillation? [1]

Guillaume Attuel1, Patrick Attuel3, Nicolas Derval2, & Jean-Michel Haissaguerre

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2

3CND McGIll, 3655 Promenade Sir William Osler, Montreal, Quebec H3G 1Y6, Canada

Hopital Haut-Leveque Avenue de Magellan 33604 Pessac CEDEX, CHU Bordeaux, France

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5CMC Parly II, 21 rue Mouxouris 78150 le Chesnay, Versailles, France [e-mail]

It is an open question, whether complex fragmented activity during fibrillation in the atrium, might characterise the stage of the pathology. Eventually, this could be used as genuine monitoring during ablation. We adress it by analysing the statistical properties of human’s endocavitary electrograms during ablation. Particular attention is given to the fluctuations of the potential, which are in general not considered as relevant, for lack of clear interpretation. We believe that these are prototypical of non-equilibrium fluctuations, and that interpretation can be confidently envisaged from their statistical properties. A recent theoretical clarification on the probability distribution functions is a basic guideline for the study

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Some natural geological systems possibly related to the Liesegang phenomenon [2]

Rabih Sultan1& Abdel-Fattah Abdel-Rahman2

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2Department of Chemistry, American University of Beirut, Beirut, Lebanon

Department of Geology, American University of Beirut, Beirut, Lebanon [e-mail]

The Liesegang phenomenon is the display of parallel bands of precipitate formed periodically when coprecipitate ions interdiffuse in a gel medium. Spectacular textural features occurring in geodes, agates, malachites, as well as in some mineral bands that characterize stratigraphic units of some rock formations have been reported in the literature as examples of naturally appearing Liesegang patterns. In this contribution, we attempt to raise questions related to the possible presence of an explanation of whether the mechanism of the Liesegang phenomenon can be considered as a viable mechanism to produce similar features observed at a small (mm) scale of strongly zoned feldspar crystals, as well as at large (km) scale magma chambers. Questions such as: Could zonations characteristic of some large scale circular zoned plutons and anorogenic ring complexes that typically range in size from two to ten km be somehow related to the Liesegang phenomenon at a magma chamber level? Could cyclic layering in large mafic/ultramafic layered intrusions represent a natural expression of the Liesegang mechanism? Could features observed in orbicular granites at hand sample (cm) scale be related to the Liesegang mechanism? We examine whether Liesegang systems, which exhibit spatial oscillations due to periodic precipitation obtained through the coupling of the precipitation reaction with diffusion are applicable to small-scale, as well as large-scale self-organization geological features.

For geochemical self-organization to operate via a Liesegang-type mechanism, a necessary condition is that the system be transiently out of equilibrium as established by the Brussels school led by I. Prigogine. The dynamical equations describing the evolution of the system are nonlinear, and involve the coupling of chemical reaction kinetics to the laws of transport processes. Such a complex underlying dynamics provides a clearly different scenario from mere seasonal variations, believed to be functional in, say, sedimentary layering. Patterns in banded iron or goethite formation were shown to have been differentiated from an initially uniform sediment. Marl/limestone alternations arise from a diagenetic self-organization mechanism, coupled to a very limited external trigger. A requirement for maintaining the system out of equilibrium during the formation process is that free energy be constantly dissipated. Such conditions are fulfilled in a host of examples in geological processes. Local perturbations in T and P, as well as mass exchange near the contact zone between the magma and a neighboring solid induce changes in the free energy. Stresses experienced by metamorphic and sedimentary rocks drive alterations in the free energy of neighboring grains.

In this study, we analyze a wide spectrum of geological patterns and examine the viability of the prevailing conditions of their formation, in relation with the various requirements for the growth of Liesegang structures.

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Pattern formation and chaotic dynamics in a three-way catalytic reactor with cross-flow [3]

Martin Kohout1, Otto Hadac1, Jaromir Havlica2, & Igor Schreiber

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2Department of Chemical Engineering, Center for Nonlinear Dynamics of Chemical and Biological Systems, Institute of Chemical Technology, Prague, Technicka 5, 166 28 Prague 6, Czech Republic,

Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, Rozvojova 135, 165 02 Prague 6, Czech Republi

[e-mail]

A three-way catalytic converter (TWC) is the most common reactor for detoxification of automobile exhaust gases. This catalytic reactor is typically operated with periodic variation of inlet oxygen concentration. In the TWC carbon monoxide, hydrocarbons and nitrogen oxides are transformed into carbon dioxide, nitrogen and water vapor. Dynamics of models describing this complex catalytic reaction set taking place in a cross-flow tubular reactor are examined.

We begin with a detailed kinetic model proposed for three-way catalytic converters. In an effort to relate resulting patterns to specific pathways in the mechanism we select two reaction subsystems combining CO oxidation with oxidation of C2H2and with NOxreduction. The ability of these two subsystems to generate nonlinear dynamical effects is examined first by neglecting transport phenomena and studying a lumped (CSTR) system with the use of stoichiometric network and bifurcation analysis.

Spatiotemporal behavior due to reaction kinetics combined with transport processes have been further studied in tubular reactor with cross-flow (TFR). Based on knowledge of the lumped dynamics, the observed spatiotemporal patterns are classified as phase waves, travelling front and pulse waves and chaotic spatiotemporal patterns. Their dependence on input parameters is systematically studied and their relation to different unstable reaction pathways is discussed.

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Pattern formation under interacting Turing-Hopf instability [4]

Jorge Carballido-Landeira & Alberto P ´ erez Mu ˜ nuzuri

Nonlinear Physics Group, Dpt. of Condensed Physics Matter, University of Santiago de Compostela, Spain [e-mail]

Belousov-Zhabotinsky reaction (BZ) was confined in a reverse microemulsion (BZ-AOT system). BZ nanodroplets are surrounded by an anionic surfactant (aerosol OT) in a pool of oil (octane). This system displays a huge variety of spatiotemporal patterns including Turing patterns, Bulk Oscillations, Outwardly and Inwardly Spirals Waves, localized structures, spatiotemporal chaos, among others. Special emphasis is placed in patterns obtained when two or more different instabilities can interact. As examples, oscillatory Turing patterns, Dash Waves or Segmented Waves are patterns involving interacting instabilities. Our objective is focused in the understanding of the complex patterns formed when the system undergoes a transition from Turing to Hopf instability. In this way the system bridges the gap exhibiting moving Spots, and Sparkling Waves, which resemble the remarks that unexplored interacting instabilities could offer a rich array of patterns, some of them already predicted theoretically.

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Synchrony and precision of chaotic electrochemical oscillators: effects of temperature and coupling [5]

Istv ´ an Z. Kiss & Mahesh Wickramasinghe

Saint Louis University, Department of Chemistry, 3501 Laclede Avenue, St. Louis, MO 63123 [e-mail]

In a network of complex dynamical systems (e.g., oscillatory circuits in the brain), the identification of connection topology is a challenging task. Synchronization theories play a pivotal role in understanding the communication between rhythmic elements. We study the role of precision chaotic oscillations on dynamics of single and small networks of electrochemical oscillators in order to gain insight into the features of chemical reactivity of a corrosion process.

The effects of temperature on complexity features of a single chaotic electrochemical oscillator are investigated using the anodic electrodissolution of nickel in sulfuric acid. The precision of chaotic oscillation is characterized by phase diffusion coefficient (D). It is shown that reduced phase diffusion coefficient (D/frequency) exhibits Arrhenius type dependency on temperature with apparent activation energy of 108 kJ/mol. The reduced Lyapunov exponent of the attractor exhibits no considerable dependency on temperature. These results suggest that the precision of electrochemical oscillations deteriorates with temperature and the variation of phase diffusion coefficient does not necessarily correlate with that of Lyapunov exponent. Modeling studies qualitatively simulate the behavior observed in the experiments: the precision of oscillations in the chaotic Ni dissolution model can be tuned by changes of a time scale parameter of an essential variable, which is responsible for development of chaotic behavior.

For studies on effect of coupling on precision, three locally coupled phase coherent chaotic oscillators (A-B-C) are considered first in nickel electrodissolution. As the interaction strength is increased among the electrodes, an onset of synchronization is observed where the frequencies become identical. Transition to synchronization was found to be accompanied by enhanced phase fluctuations that deteriorate the precision of the oscillations. By partial synchrony analysis of the phases of the oscillators, the direct (between A-B and B-C) and the indirect (between A-C) coupling can be identified and thus the network topology can be deduced.

Coupling experiments were also carried out at high temperature (35 oC) with three non-phase-coherent oscillators. In this system traditional phase definition using Hilbert-transform fails. With phase obtained through derivative Hilbert transform approach it is shown that enhanced phase fluctuation close to synchronization transition can also be observed.

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Coincidences in chemical kinetics [6]

Gregory Yablonsky1, Denis Constales2, & Guy Marin

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2

33450 Lindell Blvd, Saint Louis Boulevard, Parks College, Department of Chemistry, St. Louis MO 63103, USA

Department of Mathematical Analysis, Ghent University, Galglaan 2, B-9000, Ghent, Belgium

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0Laboratory for Chemical Technology, Ghent University, Krijgslaan 281 (S5), Ghent, Belgium [e-mail]

New properties of intersections and coincidences of transient concentration curves were discovered and are presented analytically using classical mechanisms, in particular the consecutive mechanism, as examples. We identify six different special points, and analyze and classify the 6 possible (out of 612 combinations) patterns of concentration peak and intersection times and values that distinguish the parameter subdomains and sometimes can eliminate the mechanism. This developed theory is tested on examples (multi-step radioactive decay, isomerization reaction). The mathematical analysis relies on a combination of elementary and symbolic techniques, special functions and numerical approximations

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Complex dynamics in mass-coupled flow-through chemical reactors with a pH-oscillatory reaction [7]

Lenka Schreiberova, Oldrich Pesek, Petra Simcikova, & Igor Schreiber

Institute of Chemical Technology, Prague, Department of Chemical Engineering [e-mail]

Reaction between hydrogen peroxide and thiosulfate catalyzed by Cu2+ ions (HPTCu) in an isothermal stirred flow-through reactor is an autocatalytic chemical oscillator with large amplitude pH variations. In these pH regulated reactions the concentration of hydrogen ions plays a critical role in the dynamical behaviour of system. The oxidation reduction reaction between H2O2 and S2O32- in the presence of catalytic amount of Cu2+ has been shown to exhibit a rich variety of dynamical behavior if it is carried out in a continuous flow stirred tank reactor (CSTR). Dynamics of the system in one CSTR was initially examined by Orban and Epstein (1987). They found that pH of the system corresponds to: steady state I (SSI) with pH = 7-9, steady state II (SSII) with pH = 5, steady state III (SSIII) with pH = 3.5 and oscillations. In addition, the steady states may coexist and the system will operate at one of the alternative attractors depending on its history. In our earlier work we found that there are also parameter regions, where the system is excitable to pulsed addition of selected chemical species. In this work we report on experiments in a cascade of two reaction cells coupled via an opening for mass transfer. In particular, we studied synchronization between two oscillators. The change of dynamical behavior is monitored by a pH electrode in each reactor as the flow rate k0 is stepwise varied. The recorded time series are used to construct one parameter diagrams where the dependence of pH in both reactors on the flow rate (reciprocal residence time) in the first reactor is represented. The system can be found in a combination of the four aforementioned dynamical regimes, the state of system depends on direction of changes of flow rate thus its history and the reactors influence each other. Series of experiments for various coupling strength are summarized in bifurcation diagrams, which are plotted in the parameter plane of the flow rate and mass transfer coefficient. These diagrams show that the coupling causes disappearance of bistability between SS II and SS I in the first reactor and an extinction of oscillations in the second reactor, where oscillations are replaced by SS III. The studied system serves as a representative model for more complex biochemical and biological systems that are frequently pH-sensitive and can be represented as coupled subsystems.

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Violin sounds are chaotic [8]

Masanori Shiro, Yoshito Hirata, & Kazuyuki Aihara

Ce602 Institute of Industrial Science, the University of Tokyo, 4-6-1 KOMABA MEGURO-KU, TOKYO 153-8505, JAPAN [e-mail]

Among sounds of many instruments, sounds of strings have one of the most complicated patterns. For example, the sounds of a violin show complicated twisted orbits. Since these orbits looked like a strange attractor, we wondered whether or not the sounds of violin are of deterministic chaos, which is a question we will answer in this talk.

Until now, many physicists have tried to model the sounds of strings. Although a number of researches have constructed mathematical models of strings, there are few researches that have analyzed real data observed from string instruments such as violins. Here, we make clear the nonlinear properties of violin sounds using methods of nonlinear time series analysis.

Although there are many definitions of deterministic chaos, their common requirement is sensitive dependence on initial conditions. As for an index of sensitive dependence on initial conditions, the maximal Lyapunov exponent is often used. We estimated the maximal Lyapunov exponent using the method of Kantz and found that it is positive. The positive maximal Lyapunov exponent is a sign of deterministic chaos.

However, there are some concerns that random time series may also exhibit a positive maximal Lyapunov exponent. To eliminate these concerns, we used 4 different surrogate tests with the Wayland statistic as a test statistic. The results show that violin sounds are nonlinear and have determinism beyond pseudo-periodicity. Our results show that violin sounds are likely to be of deterministic chaos.

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2

Chaotic oscillator from a PMSM model using DS [9]

Luis Nestor Coria1;2, Konstantin E Starkov2, Arturo Sotelo1, Ivan Contreras1, Ramon Ramirez1, & Paul Valle

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2Instituto Tecnologico de Tijuana. Blvd. Industrial s/n, Mesa de Otay, Tijuana, BC, Mexico.

_x= 20(bx+ 200 yz); _y= 20(y200 xz+ cz); _z= 20(a(yz) + 200  xy):

TMS320C6713 digital signal processors,” International Journal of Applied Engineering Research, vol. 2, no. 3, pp. 545– 556, 2007.

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3CITEDI-IPN. Av. del Parque 1310, Mesa de Otay, Tijuana, BC, Mexico. [e-mail]

Dynamical properties of chaotic systems suggest complexity for a physical implementation. This paper presents a chaotic oscillator using the TMS320C6713 DSP. The implemented chaotic oscillator corresponds to a scaled version of the model of a permanent-magnet synchronous motor (PMSM) that presents chaos for some values of its parameters, this model was presented and discussed in [1] and is given by the following equations:

Traditionally, a chaotic oscillator is implemented with analog components, but this has changed because of many benefits provided by a DSP [2]. Time series of all state variables of the chaotic oscillator with DSP were obtained and three different metods were applied in order to establish its chaotic properties. We found: 1) The largest positive Lyapunov exponent; 2) Poincare map; and 3) Fourier Transform. Chaotic signals can be used in data encription [3], [4], and generate chaos like behavior in some physical application where it is desired [5], and so on. This work was supported by SEP-CONACYT project 78890 and DGEST project TIJ-IET-2009-217, MEXICO.

References

1. Z. Jing, C. Yuc, and G. Chen, “Complex dynamics in a permanent-magnet synchronous,” Chaos, Solitons and Fractals, vol. 22(4), pp. 831–848, 2004.

2. P. Lapsley, DSP Processor Fundamentals. IEEE Press, 1997. 3. H. Xiao and W. Zeng, “A hard disk encryption system realized by the digital signal processor,” International Conference on

Computational Intelligence and Security, vol. 2, pp. 312–314, 2009. 4. R. Saravanan, T. Sivaramakrishnan, and K. Ramamoorthy, “A new approach on discrete chaotic cryptography using

5. S. Ye, K. Chau, and N. Shuangxia, “Chaoization of a single-phase induction motor for washing machines,” in Industry Applications Conference, 2006. 41st IAS Annual Meeting., IEEE. IEEE, 2006, pp. 855 – 860

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Detecting recursive and non recursive filters using chaos [10]

Tom Carroll

Code 6362, Naval Research Lab, Washington, DC 20375 USA [e-mail]

Filtering a chaotic signal through a recursive (or IIR) filter has been shown to increase the dimension of the chaos under certain conditions. Filtering with a non recursive (or FIR) filter should not increase dimension, but it has been shown that if the FIR filter has a long tail, measurements of actual signals may appear to show a dimension increase. I simulate IIR and FIR filters that correspond to naturally occurring resonant objects, and I show that using dimension measurements, I can distinguish the filter type. These measurements could be used to detect resonances using radar, sonar or radar signals, or to determine if a resonance is due to an IIR or an FIR filter. I am also able to detect a very broad resonance with a narrow bandwidth signal.

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Numerical design of robust estimators for box-photochemistry system [11]

Mark Pinsky & Hyun Cho

Department of Mathematics and Statistics, University of Nevada.Reno. Reno NV 89557, USA [e-mail]

Various uncertainties jeopardize numerical forecasts of various atmospheric-chemistry models which stimulate efforts to improve the accuracy of numerical forecasts by integrating limited observations and simulations. This paper presents a numerical approach to the design of feedback controlled robust estimators for multidimensional nonlinear models that are frequently used to describe photochemical reactions. Parameters of feedback control, which deliver robust tracking of directly immeasurable system states, are found via off-line minimization of error function assessing mismatches between trial and actual system trajectories. This assures efficient online simulation of complex estimator system. Extensive numerical tests show that these estimators provide rapid and robust tracking of solutions to photochemistry systems. These systems accumulate significant uncertainties in their parameters and initial values under the most conservative assumption that a concentration of single reacting specie is only measurable. We also assure our approach using the Lyapunov function method and consider its application to the problem of noise removal if available data is corrupted by noise.

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On the unique reconstruction of a signal from its recurrence plot [12]

Aloys Sipers1, Paul Borm1, & Ralf Peeters

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2Centre of Research Life Sciences, Zuyd University,The Netherlands

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6Maastricht University, The Netherlands [e-mail]

Recurrence plots are two-dimensional representations of high-dimensional trajectories of dynamical systems. Patterns in recurrence plot carry information on the underlying trajectories and can be studied and analyzed for detection and classification purposes. From the literature it is known that a recurrence plot determines its underlying trajectory up to isometry. Here we consider trajectories that are obtained from a one-dimensional signal with the time-delay embedding method. We address the question to which extent a recurrence plot determines the underlying signal. First we show that a recurrence plot determines the power spectrum of this signal. Then we provide conditions on the embedding dimension and the time-delay which imply uniqueness of the underlying signal (up to a sign factor). A worked example from EEG analysis illustrates how this theory allows one to understand the limitations that apply to the interpretation of a recurrence plot. We consider a measured EEG signal containing a so-called Mu rhythm, i.e. exhibiting an m-shaped morphology with frequencies between 8 Hz and 12 Hz. We show that for some values of the embedding dimension and time-delay, another signal with a different morphology can be constructed which yields the same recurrence plot. This induces ambiguity in the interpretation of the associated recurrence plot. We also show how to avoid this phenomenon by appropriately choosing the embedding dimension and time-delay parameters to guarantee uniqueness of the corresponding pattern in the recurrence plot

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