bluuebunny/crossref_metadata_2025 huggingface dataset:
Ferroelectric Systems with Controlled Chaos
Authors: Habel R. , Beige H.
Published: September 2003

A practically implemented control of a chaotic system in the frequency range of 1…20 kHz is described. We use a ferroelectric crystal as a nonlinear capacitance in a series resonance circuit. So the circuit shows all features of nonlinear systems like period doubling, chaos or periodic windows. The required control of the chaotic state can be carried out as fast as necessary by using an analogous electronic device.
Combating Noise and Other Channel Distortions in Chaotic Communications
Authors: Milanović Veljko , Syed Khalid M. , Zaghloul Mona E.
Published: September 2003

A novel scheme is proposed for chaotic communications which is robust to noise and amplitude fluctuations in the channel. The scheme implements spread spectrum communication of binary data utilizing synchronized discrete-time chaotic systems. The chaotic signals of the transmitter are used as spreading codes, while the synchronized chaotic outputs of the receiver despread the signal, thereby recovering the message. The improved synchronization algorithm and the implementation of spread spectrum communications techniques result in reliable performance in the presence of considerable signal distortions in the channel. The method is implemented with a chaotic logistic map and also with a piecewise-linear map of a chaotic neuron. In both cases, average bit-error-rates were computed for varied signal-to-noise ratio, using additive white Gaussian noise. The proposed scheme also offers high privacy because of the non-periodicity of the chaotic spreading sequences.
Strange Nonchaotic Attractors of Chua's Circuit with Quasiperiodic Excitation
Authors: Zhu Zhiwen , Liu Zhong
Published: September 2003

This paper focuses attention on strange nonchaotic attractor of Chua's circuit with two-frequency quasiperiodic excitation. Existence of the attractor is confirmed by calculating several characterizing quantities such as Lyapunov exponents, Poincaré maps, double Poincaré maps and so on. Two basic mechanisms are described for the development of the strange nonchaotic attractor from two-frequency quasiperiodic state (torus solution). One of them is torus-doubling bifurcation followed by a smooth transition from the torus attractor to the strange nonchaotic attractor; and another is that the torus does not undergo period-doubling bifurcation at all; instead, the torus attractor gradually becomes wrinkled, and eventually becomes strange but nonchaotic.
Communication Systems via Chaotic Signals from a Reconstruction Viewpoint
Authors: Itoh Makoto , Wu Chai Wah , Chua Leon O.
Published: September 2003

In this paper, we study communication systems, modulators, and demodulators using chaotic systems from the perspective of reconstruction of attractors. We consider a two-step approach to the recovery of information signals from chaotic modulation. To recover the information signal modulated by a chaotic dynamical system, the first step is to reconstruct the chaotic attractor given a subset of the state variables. The second step is to reconstruct the information signal from the chaotic attractors. Two main techniques to accomplish this are the Takens reconstruction theorem and the chaotic synchronization theorem. In general, a combination of these two techniques are needed to recover the information signal. We show a systematic way to reconstruct an attractor and the injected signal exactly from a scalar observable for a subclass of Lur'e systems. We illustrate this approach using several examples. Extensions to discrete-time systems are also presented.
The Dynamics of a Piecewise Linear Map and its Smooth Approximation
Authors: Aharonov D. , Devaney R. L. , Elias U.
Published: September 2003

The paper describes the dynamics of a piecewise linear area preserving map of the plane, F: (x, y) → (1 - y - |x|, x), as well as that portion of the dynamics that persists when the map is approximated by the real analytic map Fε: (x, y) → (1 - y - fε(x), x), where fε(x) is real analytic and close to |x| for small values of ε. Our goal in this paper is to describe in detail the island structure and the chaotic behavior of the piecewise linear map F. Then we will show that these islands do indeed persist and contain infinitely many invariant curves for Fε, provided that ε is small.
Map Dynamics Study of the Lorenz Equations
Authors: Michielin Olivier , Phillipson Paul E.
Published: September 2003

The Lorenz equations [Lorenz, 1963], in addition to a strange attractor, display sequences of periodic and aperiodic orbits. Approximate one-dimensional map solutions are heuristically constructed, supplementing previous symbolic dynamics studies, which closely reproduce these sequences. A relatively simple solution reproduces the sequence topology to good accuracy. A second more refined solution reproduces to higher accuracy both the topology and scale of the attractor. The second solution is sufficiently accurate to predict periodic orbits not previously observed and difficult to extract directly from computer solution of the Lorenz equations.
Constructing Permutations that Approximate Lebesgue Measure Preserving Dynamical Systems Under Spatial Discretization
Authors: Kloeden P. E. , Mustard J.
Published: September 2003

A discrete-time dynamical system can sometimes display quite different dynamical behavior under spatial discretization. Systems generated by maps for which the Lebesgue measure is invariant are, however, robust in the sense that they can be approximated by permutations on a uniform lattice. A fast algorithm to construct such permutations is presented here and its implementation is illustrated with several examples of well–known one and two dimensional systems.
Synchronization through Compound Chaotic Signal in Chua's Circuit and Murali–Lakshmanan–Chua Circuit
Authors: Murali K. , Lakshmanan M.
Published: September 2003

In this letter the idea of synchronization of chaotic systems is further extended to the case where all the drive system variables are combined to obtain a compound chaotic drive signal. An appropriate feedback loop is constructed in the response system to achieve synchronization among the variables of drive and response systems. We apply this method of synchronization to the familiar Chua's circuit and Murali–Lakshmanan–Chua circuit equations.
Strange Nonchaotic Trajectories on Torus
Authors: Kapitaniak T. , Chua L. O.
Published: September 2003

In this letter we have shown that aperiodic nonchaotic trajectories characteristic of strange nonchaotic attractors can occur on a two-frequency torus. We found that these trajectories are robust as they exist on a positive Lebesgue measure set in the parameter space.
Induced Hysteresis-Free Transitions in a Bistable System (Experimental Verification)
Authors: Raab Volker , Postnov Dmitry
Published: September 2003

A new concept has recently been developed to facilitate transitions between the two stable states of a bistable dynamical system. The transitions therein take place without loss of stability (hysteresis). In this letter the experimental feasibility of the proposed method is shown by means of an analog circuit. Bifurcation diagrams are being determined experimentally with this circuit.
Optimal Control of a Chaotic Map: Fixed Point Stabilization and Attractor Confinement
Authors: Piccardi C. , Ghezzi L. L.
Published: September 2003

Optimal control is applied to a chaotic system. Reference is made to a well-known one-dimensional map. Firstly, attention is devoted to the stabilization of a fixed point. An optimal controller is obtained and compared with other controllers which are popular in the control of chaos. Secondly, allowance is made for uncertainty and emphasis is placed on the reduction rather than the suppression of chaos. The aim becomes that of confining a chaotic attractor within a prescribed region of the state space. A controller fulfilling this task is obtained as the solution of a min-max optimal control problem.
On Bifurcations of Periodic Orbits in the van der Pol-Duffing Equation
Authors: Belyakova G. V. , Belyakov L. A.
Published: September 2003

Various routes to chaos are demonstrated on an example of the periodically forced van der Pol-Duffing equation.
On the Integrability and Chaotic Behavior of an Ecological Model
Authors: Joy M. P.
Published: September 2003

A three-species food chain model is studied analytically as well as numerically. Integrability of the model is studied using Painlevé analysis while chaotic behavior is studied using numerical techniques, such as calculation of Lyapunov exponents, plotting the bifurcation diagram and phase plots. We correct and critically comment on the wrong results reported recently on this ecological model, in a paper by Rai "1995".
Determination of Fatigue Crack Paths
Authors: Pook L. P.
Published: September 2003

The complete solution of the problem of a fatigue crack growing from an initial crack includes determination of the crack path. Macroscopic aspects of the main features of the path taken by a growing fatigue crack in a metallic material are reasonably well understood in a qualitative sense. However, the governing equations are highly nonlinear, and are only partially understood. Microstructural irregularities have a significant effect on fatigue crack path behaviour. The nonlinear dynamics concept of attractor (in a physical rather than a state space sense) as a line or surface to which a fatigue crack path trends, appears to be helpful in providing a unified view of crack path behaviour. If the attractor for a particular configuration is known, then the crack path can be estimated. At present attractors have to be obtained intuitively on the basis of experience.
A Model for the Action of External Current onto Excitable Tissue
Authors: Biktashev V. N. , Holden A. V. , Zhang H.
Published: September 2003

We outline a mathematical model of the action of an external electric current on excitable tissue, which considers the action of the current on different parts of the cell membrane within an ODE description. This model is intuitively clear and numerically efficient, and is used to predict and compute the defibrillation threshold for cardiac tissue.
Heart Muscle as a Reaction–Diffusion Medium: The Roles of Electric Potential Diffusion, Activation Front Curvature, and Anisotropy
Authors: Winfree A. T.
Published: September 2003

This tutorial, the third in a series about electrical dynamics in the heart, reviews laboratory experiments and numerical experiments about a reaction–diffusion partial-differential equation model commonly used to interpret electrophysiological propagation in normal heart muscle. It aims to sort out ostensibly contradictory impressions competing in current literature about the nature, magnitude, and dynamical consequences of activation front curvature within such a uniformly anisotropic tissue, insofar as such idealizations represent normal heart muscle. It is shown that activation fronts do not generally propagate along the perpendicular, and do not attach perpendicularly to no-flux boundaries, and that "critical radius" is a tricky concept except in isotropic media. Much is found to depend, even qualitatively, on the numerical value of the electric diffusion coefficient for normal heart muscle, to which values spanning two orders of magnitude are imputed in the literature. A "correct" value is tentatively identified which seems to lie securely inside the continuum range, so things are rather simpler than they may have appeared (except in diverse cases of unspecifiable abnormality in living specimens and in models). This tutorial is intended as much to provoke inquiry as to lay it to rest: The reader looking for solvable problems will find many unsolved here, with a rich current reference list leading to more.
Stationary Stochastic Processes and Fractal Data Compression
Authors: Barnsley Michael F. , Deliu Anca , Xie Ruifeng
Published: September 2003

It is shown that the invariant measure of a stationary nonatomic stochastic process yields an iterated function system with probabilities and an associated dynamical system that provide the basis for optimal lossless data compression algorithms. The theory is illustrated for the case of finite-order Markov processes: For a zero-order process, it produces the arithmetic compression method; while for higher order processes it yields dynamical systems, constructed from piecewise affine mappings from the interval [0, 1] into itself, that may be used to store information efficiently. The theory leads to a new geometrical approach to the development of compression algorithms.
Robustness of Synchronized Chaotic Oscillations
Authors: Rulkov Nikolai F. , Sushchik Mikhail M.
Published: September 2003

In this paper we address the issue of robustness of synchronized chaotic oscillations in coupled systems. One frequently observes in physical experiments that synchronized chaotic oscillations are occasionally interrupted by brief incidents of unsynchronized behavior. By numerical simulations we show that, under certain circumstances, the regime of synchronized chaos is very sensitive to even small noise and to slightest differences between parameters of coupled systems. As a result of such sensitivity, these small perturbations lead to non-steady, "bursting" synchronization. Using experiments with nonlinear electronic circuits and analytical and numeric analyzes of their ODE model, we study certain bifurcations associated with fixed points and limit cycles in the synchronized chaotic attractor. We establish the connection between these bifurcations and the appearance of the outbursts of unsynchronized behavior. We illustrate a mechanism of formation of complicated invariant sets of trajectories that are associated with the dynamics during such outbursts.
Master-Slave Synchronization of Lur'e Systems
Authors: Suykens J. A. K. , Vandewalle J.
Published: September 2003

In this paper we present a sufficient condition for master-slave synchronization of Lur'e systems. The scheme makes use of linear full static state feedback. The criterion is based on a Lur'e–Postnikov Lyapunov function for global asymptotic stability of the error system. The condition is basically the same as the one for global asymptotic stability of the Lur'e system, controlled with linear state feedback. The design of the feedback matrix is done by solving a constrained nonlinear optimization problem. The method is illustrated on the synchronization of Chua's circuit.
Stability of Synchronized States in One Dimensional Networks of Second Order PLLS
Authors: Tanaka Hisa-Aki , de Sousa Vieira Maria , Lichtenberg Allan J. , Lieberman Michael A. , Oishi Shin'ichi
Published: September 2003

Synchronous distributed timing clocks are the basic building blocks in digital communication systems. Conventional systems mainly employ a tree-like network of cascaded timing clocks for synchronous clocking. On the other hand, decentralized synchronous networks of timing clocks, which have been proposed from a very early stage of the digital communication, are gaining attention in the consumer communication networks and also recently in large, high-performance digital systems (such as multiprocessors) clocking. In this paper, we present a theoretical study of synchronous networks of timing clocks consisting of locally connected second order phase-locked loops (PLLs). We find a close connection between the stability properties of the first and second order networks. The particular examples of one way and two way nearest neighbor coupling, with a lag-lead filter and a triangular phase detector (PD) are analyzed in detail. Both the synchronized in-phase solution and the wave-like "mode-lock" solution are examined. A criterion is found for the stability of the one-way coupled network while the two-way coupled network is found to be always stable.
When is OGY Control More Than Just Pole Placement
Authors: Obradovic Dragan , Lenz Henning
Published: September 2003

Deterministic chaotic systems give rise to very complex dynamical behavior in spite of the fact that they are usually of very low dimension. The exceptionally high sensitivity to changes in initial conditions makes dealing with these systems non-trivial due to inherent measurement errors and limited numerical precision. Within a chaotic attractor it is usually possible to identify unstable point attractors and unstable periodic orbits. One of the widely accepted techniques for stabilizing unstable point attractors and periodic orbits is the so called OGY controller method developed by Ott, Grebogi, and Yorke. In the case of stabilizing an unstable point attractor within the chaotic map, the OGY controller effectively forces the system to move on the corresponding stable manifold in the state-space. On the other hand, it can be shown that this strategy coincides with the design of a full state feedback controller that places the unstable eigenvalues of the state matrix of the locally linearized system at zero while keeping the location of the stable eigenvalues unchanged. When the stabilization of the original, open-loop system is the only goal, the OGY approach does not offer any advantage over other stabilizing control actions such as pole placement to arbitrary but stable eigenvalue locations. In addition, neither OGY nor arbitrary pole placement explicitly deal with the problem of noise sensitivity. Hence, when the original chaotic system is noise corrupted, it is not clear if the OGY approach is even close to being optimal with respect to noise cancelation with "acceptable" control action. Although the answer to this question is negative in the general case, there are situations where the optimal system behavior is achieved. The contribution of this paper is twofold. The first contribution is the rigorous discussion of the relationship between the OGY approach and the pole placement and the extension of the OGY method to stabilization of systems with more than one unstable eigenvalue. The second contribution of the paper is the proof that the OGY control approach to the equilibrium point stabilization in the presence of persistent, magnitude bounded process noise is actually optimal when the system performance is measured by the l∞-norm of the control signal. The proof is based on properties of the optimal l1-norm controller design and on the parameterization of all stabilizing controllers for a given linear system.
Chaos in Robot Control Equations
Authors: Lankalapalli Shrinivas , Ghosal Ashitava
Published: September 2003

The motion of a feedback controlled robot can be described by a set of nonlinear ordinary differential equations. In this paper, we examine the system of two second-order, nonlinear ordinary differential equations which model a simple two-degree-of-freedom planar robot, undergoing repetitive motion in a plane in the absence of gravity, and under two well-known robot controllers, namely a proportional and derivative controller and a model-based controller. We show that these differential equations exhibit chaotic behavior for certain ranges of the proportional and derivative gains of the controller and for certain values of a parameter which quantifies the mismatch between the model and the actual robot. The system of nonlinear equations are non-autonomous and the phase space is four-dimensional. Hence, it is difficult to obtain significant analytical results. In this paper, we use the Lyapunov exponent to test for chaos and present numerically obtained chaos maps giving ranges of gains and mismatch parameters which result in chaotic motions. We also present plots of the chaotic attractor and bifurcation diagrams for certain values of the gains and mismatch parameters. From the bifurcation diagrams, it appears that the route to chaos is through period doubling.
Optimal Axle Distance of a Railway Bogie
Authors: Galvanetto U. , Briseghella L. , Bishop S. R.
Published: September 2003

The dynamics of a railway bogie are investigated by utilizing methods of nonlinear dynamic as system theory. The railway bogie model is that introduced by Cooperrider and further developed by Kaas-Petersen. "Principal" and "secondary" attractors are defined and periodic and chaotic attractors are described. A "qualitative" distinction of secondary attractors is introduced according to the robustness of the attractors with respect to random perturbations. The results suggest the possible existence of an optimal axle distance between two wheel sets.
Orbits Embedded in IFS Attractors
Authors: Bahar Sonya
Published: September 2003

It has recently been shown that a modified iterated function system (IFS) is capable of generating closed orbits which undergo bifurcation and transition to a chaotic regime as control parameters are varied [Bahar, 1995, 1996]. Here we discuss a technique for isolating orbits embedded in chaotic attractors generated by an IFS algorithm, and develop a symbolic classification based on the folding patterns of the embedded orbits.
Adaptive Evolutionary Optimization of Team Work
Authors: Buchholtz Volkhard , Pöschel Thorsten
Published: September 2003

We discuss a new optimization strategy, which considerably improves the effectivity of evolutionary algorithms applied to a certain class of optimization problems. The basic principle is to solve first a simpler related problem, which is constructed by introducing additional degrees of freedom to the landscape. Starting from the solution in this simplified landscape we remove stepwise the added degrees of freedom. Our optimization strategy is demonstrated for a sample problem.
Complexity and Predictability of the Heartbeat Time Series in Transplanted Subjects
Authors: Balocchi Rita , Barbi Michele , Carpeggiani Clara , Chillemi Santi , Di Garbo Angelo , Michelassi Claudio
Published: September 2003

Physiological fluctuations in heart rate, known as "sinus arrhythmia", are due to the influence of the autonomic nervous system on the sinus node, modulated by baroreceptor activity and respiration. Reduction in heart rate variability (HRV) correlated to age or disease has been reported by several investigators, together with its importance as prognostic indicator in pathophysiological situations.

In this paper the heart rhythm is investigated in heart transplanted subjects, an apparently opposite condition with respect to normal hearts as for the influence of the autonomic system. Selected segments of the (first difference) interbeat interval time series are analyzed with an efficient approach [Sugihara, 1994] able to evaluate both the short term predictability and the nonlinearity of these data. Moreover, other more qualitative methods are used to better characterize the experimental sequences.

The results indicate that these time series only occasionally exhibit some degree of predictability, as assessed by this metric. A careful examination of the predictability behavior, by means of surrogate data, reveals that it cannot be interpreted as evidence of nonlinearity. Rather, a stochastic-like dynamics seems to characterize the transplanted hearts.
Convective Instabilities in Homeotropic Nematic Liquid Crystals: Experimental Results in Thick Layers
Authors: Salán J. , Fernández-Vela J. , Gonzalez-Viñas W. , Soria S.
Published: September 2003

Experimental results are presented for Rayleigh–Bénard convection in thick horizontal layers of Homeotropic Nematic Liquid Crystal heated from below under external magnetic fields. New results are shown about the subcritical bifurcation in the oscillatory and steady convective regimes. Also, a more accurate estimation of the codimension-two point is made. The frequencies of the oscillatory solutions and other nonlinear effects are measured.
Phase- and Center-Manifold Reductions for Large Populations of Coupled Oscillators with Application to Non-Locally Coupled Systems
Authors: Kuramoto Yoshiki
Published: September 2003

In the first half of this paper, some general ideas will be developed on how to approach mathematically large systems of coupled limit-cycle oscillators. Two representative reduction techniques, namely, the phase reduction and the center-manifold reduction will be presented for a prototypal system of biological cell assembly with periodic activity. The evolution equation derived through each reduction method is further classified into three groups according to the range of the oscillator coupling (i.e. local, global and intermediate). As a consequence, six classes of model equations are obtained. In the second half of the paper, some new results from our recent study on non-locally coupled oscillators will be reported, and the generation of anomalous turbulent fluctuations obeying a power law will be discussed in some detail.
Analytical Solution of the Logistic Equation
Authors: Rabinovich S. , Berkolaiko G. , Buldyrev S. , Shehter A. , Havlin S.
Published: September 2003

An analytical solution for the well-known quadratic recursion, also known as the logistic map, is presented. Our derivation makes use of the analogy between this equation and Galton–Watson processes. The latter can be treated in a linear way using the transfer matrix technique. The solution is represented as a power of an appropriate transfer matrix.
Second Order Phase Transition in a Highly Chaotic Hamiltonian System with Many Degrees of Freedom
Authors: Yamaguchi Yoshiyuki Y.
Published: September 2003

Second order phase transition is numerically investigated in a Hamiltonian system with many degrees of freedom. Slow relaxations of power type are observed for some initial conditions at critical energy of phase transition. This is consisent with a result of a phenomenological theory of statistical mechanics. On the other hand, the slow relaxations show that the system stays in non-equilibrium states for a while, and that phenomenon does not agree with a result of the theory. To understand the slow relaxation, theories for perturbed systems cannot be applied since near the critical energy the system is highly chaotic rather than nearly integrable. The thresholds of the highly chaotic systems is different from the critical energy of phase transition.
Chaos Induced Transition
Authors: Shimizu Toshihiro , Morioka Nozomi
Published: September 2003

To study the coherent nature of chaos, two models are proposed. Model 1 is a simple nonlinear system [Formula: see text] and Model 2 is a linear harmonic oscillator [Formula: see text], which are driven by a chaotic force f(t). The chaotic force f(t) is defined by [Formula: see text] for nτ < t ≤ (n + 1)τ(n = 0, 1, 2, …), where yn+1 is a chaotic sequence of a map F(y; r) with the bifurcation parameter r: yn+1 = F(yn; r) (-0.5 ≤ yn ≤ 0.5) and ŷn = yn - < y0>. In Model 1 the relaxation process of this system and the τ- and r-dependence of the stationary distribution of x are discussed. It is shown that the small change of the bifurcation parameter r causes the drastic change of the stationary distribution. In Model 2, resonance phenomena are investigated near the period 3 window of the logistic map, in particular, in the intermittent chaos region and the period doubling region. The theoretical results are shown to be in a good agreement with numerical ones, which have been done for the logistic map as F(y; r).
Diffusive Interaction Leading to Dephasing of Coupled Neural Oscillators
Authors: Han Seung Kee , Kurrer Christian , Kuramoto Yoshiki
Published: September 2003

It is usually believed that strong diffusive coupling in one of the dynamical variables is well-suited for imposing synchronization of oscillators. But it was recently shown that weak diffusive coupling, counter-intuitively, can lead to dephasing of coupled neural oscillators.

In this paper, we investigate how diffusively coupled oscillators become dephasing. For this we study a system of coupled neural oscillators on a limit cycle generated through a homoclinic bifurcation. We examine the asymptotic behavior of diffusive coupling as the control parameter approaches the critical value for which the homoclinic bifurcation occurs. In this study, we show that the gradient of phase velocity near the limit cycle is essential in generating dephasing through diffusive interaction.
Chaotic Bursting Behavior of Coupled Neural Oscillators
Authors: Han Seung Kee , Park Seon Hee , Yim Tae Gyu , Kim Seunghwan , Kim Seunghwan
Published: September 2003

Recently it was shown that dephasing of diffusively coupled neural oscillators leads to a new class of bursting phenomena, where neural oscillators switch between high and low oscillation amplitudes.

To analyze this behavior we study a system of three-coupled neurons, which is the most simple one that shows chaotic bursting behavior. For the intermediate values of coupling constant kc, the chaotic bursting behavior occurs. For a quantitative analysis of chaotic bursting, we introduce three mean activities of oscillators. From the Poincaré sections we find a period-doubling route to chaos. We illustrate the busting behavior in terms of competition of the single oscillator behavior with the collective one arising from the diffusive coupling of oscillators.
Generation of Periodic Orbits from Chaotic Attractors of Weakly Coupled Diode Resonators
Authors: Shin Jong Cheol , Kwun Sook-Il , Kim Youngtae
Published: September 2003

We have designed coupled diode resonators to study the effect of small perturbations due to weak symmetric coupling on chaotic dynamics. Our experiment clearly demonstrated that chaos of the diode resonators was suppressed so that chaotic motions were converted into periodic ones with small modifications to the attractor when an appropriate coupling signal perturbed the diode resonators. Many unstable periodic orbits were stabilized and they were very stable depending on the dynamical properties of the coupling signals. Our results suggest that coupling of signals belonging to the same class is effective in controlling chaos.
Control Bifurcation Structure of Return Map Control in Chua's Circuit
Authors: Lee Byoung-Cheon , Lee Ki-Hak , Wang Bo-Hyeun
Published: September 2003

We demonstrate that return map control and adaptive tracking can be used together to locate, stabilize, and track unstable periodic orbits (UPOs). Through bifurcation studies as a function of some control parameters of return map control, we observe the control bifurcation (CB) phenomenon which exhibits another route to chaos. Nearby an UPO there are a lot of driven periodic orbits (DPOs) along the CB route. DPOs are not embedded in the original chaotic attractor, but they are generated artificially by driving the system slightly in a direction with feedback control. Based on the CB phenomenon, our adaptive tracking algorithm searches for the location and the exact control condition of the UPO by minimizing feedback perturbations. We discuss the universality of the CB phenomenon and the possibility of immediate control which does not require much prior analysis of the system.
An Overall View of Stochastic Resonance
Authors: Gitterman Moshe , Weiss George H.
Published: September 2003

We describe some universal features of dynamical systems that exhibit stochastic resonance. Examples of such systems show that stochastic resonance appears as the result of the interaction between an externally imposed rate and stochastic characteristics of the dynamic systems which are not restricted to be nonlinear.
Nonequilibrium Phenomena in Globally Coupled Phase Oscillators: Noise-Induced Bifurcations, Clustering, and Switching
Authors: Park Seon Hee , Kim Seunghwan , Han Seung Kee
Published: September 2003

The Nonequilibrium phenomena in a class of globally coupled phase oscillators systems with multiplicative noise are studied. It is shown that at the critical value of the noise intensity the systems undergo a phase transition and converge to clustered states. We also show that the time delay in the interaction between oscillators gives rise to the switching phenomena of clusters. These phenomena are noise-induced effects which cannot be seen in the deterministic systems or in the simple additive noise models.
Bifurcation and Chaos in a Periodically Driven Quartic Oscillator at Relativistic Energies
Authors: Kim Sang Wook , Lee Hai-Woong
Published: September 2003

The classical dynamics of a damped quartic oscillator driven by a sinusoidal force is investigated, with particular attention to the effects that arise when the motion of the oscillator becomes relativistic. Bifurcation diagrams constructed numerically indicate that, as relativistic effects become strong, chaotic behavior exhibited by the oscillator in the nonrelativistic limit at large force amplitude is replaced by a period-1 regular motion. At relativistic energies, therefore, a transition from chaos to a regular motion occurs as the force amplitude is increased beyond a critical value. The transition is seen to occur abruptly with a slight increase of the force amplitude from below to above the critical value. The sudden destruction of the chaotic attractor is probably triggered by the mechanism of crisis.
Analog Techniques for Modeling and Controlling the Mackey-Glass System
Authors: Namajūnas A. , Pyragas K. , Tamaševičius A.
Published: September 2003

An analog circuit which models an infinite-dimensional dynamical system is described. It provides an easy and rapid way to simulate periodic and chaotic behaviors in a delay differential equation, the Mackey-Glass mathematical model. Several methods of controlling unstable steady states are considered. Analog techniques for stabilizing non-zero stationary point in the Mackey-Glass system are developed.
The Scientist in the Sandbox: Time-Dependence, Fractals and Waves
Authors: Behringer R. P.
Published: September 2003

Granular materials exhibit a rich variety of dynamical behavior, much of which is poorly understood. Fractal-like stress chains, convection, a variety of wave dynamics, including waves which resemble capillary waves, 1/f noise, and fractional Brownian motion provide examples. Although granular materials consist of collections of interacting particles, there are important differences between the dynamics of a collection of grains and the dynamics of a collection of molecules. In particular, the ergodic hypothesis is generally invalid for granular materials, so that ordinary statistical physics does not apply. Fluctuations on laboratory scales in such quantities as the stress can be very large — as much as an order of magnitude greater than the mean. Below is a brief review of some of the theoretical approaches to granular flow followed by a discussion of several recent experiments. These experiments focus on complex structures and fluctuations in the flow of granular materials in a hopper or in simple shear flow. The experimental work at Duke has been carried out in collaboration with a number of investigators, including G. W. Baxter, R. Leone, H. K. Pak, E. Van Doorn, C. O'Hern, and B. Miller. Elsewhere in this issue, Pak et al. discuss experiments to characterize and better understand the convective flows which occur when granular materials are shaken with accelerations exceeding that of gravity.
Coherence and Complexity in Condensed Matter: Josephson Junction Arrays
Authors: Domínguez D. , Bishop A. R. , Grønbech-Jensen N.
Published: September 2003

The importance of the mesoscopic bridge between microscopic and mesoscopic descriptions of complex, nonlinear-nonequilibrium extended dynamical systems is illustrated in a condensed matter context through three-dimensional Josephson junction arrays. Large-scale Langevin molecular dynamics is used to study novel transformer and melting effects, emphasizing the central roles of topological excitations (flux vortex lines) in determining mesoscopic patterns and dynamics — through flux line creation, annihilation, interaction and statistical mechanics.
Hydrodynamical Effects of Chemical Waves in Quasi-Two-Dimensional Solution in Belousov–Zhabotinsky Reaction
Authors: Inomoto Osamu , Kai Shoichi , Ariyoshi Takayuki , Inanaga Shoji
Published: September 2003

The evidence was studied that the chemical wave accompanied by hydrodynamic instability showed some noteworthy characteristics in a quasi-two-dimensional shallow layer of the unstirred excitable Belousov–Zhabotinsky (BZ) reaction. This chemical wave has been known as the "Big Wave" or the "Hydrochemical Soliton", which showed soliton-like properties. We clarified properties of the wave using an optical technique (Mach–Zehnder interferometry). The Big Wave acceleratingly propagated with large velocity, and simultaneously caused flow in the bulk of the solution as well as large surface deformation (~ 5μm). We proposed that the main mechanism of this wave was chemically coupled Marangoni instability, which was induced by the gradient of surface tension due to the thermal and/or material inhomogeneity in the BZ solution.
Lagrangian Chaos in the Stokes Flow Between Two Eccentric Rotating Cylinders
Authors: Atobe Takashi
Published: September 2003

Chaotic motion of the fluid particles in the Stokes flow between two eccentric cylinders rotating alternately is investigated numerically, analytically and experimentally. We examine the dependence of the motion of the fluid particles on the eccentricity ε, focusing on an equilibrium point of the Poincaré plot. When the bifurcation of the equilibrium point from the elliptic to the hyperbolic type occurs at ε = εb, the area of the chaotic region takes a maximum around εb. The results from the perturbation analysis show good agreement with the numerical results. The orbital instability of the motion of the fluid particles is also investigated experimentally. The orbital instability is visualized by injected dye in the "return experiment", in which the two cylinders are rotated alternately by N periods in the first half, and then rotated in its time reversal way for N periods in the second half. The dye starting from the regular region of the numerically computed Poincaré plot of particle positions after every period returns well to its initial position even for large N. However, the deviation of the dye starting from the chaotic region of the Poincaré plot from its initial position is large and rapidly increases with N.
Ambient Gases and Heaping Instability of Granular Materials Under Vertical Vibration
Authors: Pak Hyuk K. , Van Doorn E. , Behringer Robert P.
Published: September 2003

We consider layers of non-cohesive granular materials lying on a vertically vibrating surface. Above a threshold acceleration, Γ = Γc internal convective motion begins, and the free surface of the granular material becomes unstable to the formation of a heap. As Γ increases further, there are several higher order instabilities, traveling surface waves, subharmonic bifurcations, and bubbling. We find that for particles of diameter d ≤ 1 mm, the pressure P of the surrounding gas plays a key role in the instabilities. We propose criteria to determine when gas effects are relevant.
Structural Criticality of Dynamical Glass State in a Spatially Extended Dynamical System
Authors: Hata Hiroki , Yabe Kimitoshi
Published: September 2003

Many periodic attractors frequently coexist in the phase space of a spatially extended dynamical system, and such a state is called the dynamical glass state [Fujisaka et al., 1993]. We study numerically the dynamical glass state of a coupled map system and find that the measure of the structurally critical attractors (just before the bifurcation points) is large. Hence, the global basin structure of the dynamical glass state is "critical". And the dynamical glass state is observed in a finite region in the parameter space, therefore almost all the trajectories made from random initial states focus on the structurally critical attractors without tuning any control parameters in the region. This interesting new property and the relaxation process from an initial state to one of the final attractors are reported.
Numerical and Analytical Study of Nonlinear Electronic Circuits
Authors: Bitton G. , Balberg I. , Gomez M. , Weisz S. Z.
Published: September 2003

We have carried out a comprehensive study of the dynamics of nonlinear electronic circuits. As model circuits we have used the simple model proposed by Matsumato et al., and the more realistic model proposed by Brorson et al. In our study we have determined the bifurcation diagrams, the return maps, the Lyapunov exponents and the fractal dimensions which characterize the nonlinear behavior of these circuits. In order to get an insight into the physics of the circuits' operation we have computed the average charge, the average current and the average capacitance of the nonlinear circuits, and concluded that the most fundamental physical process that governs the behavior of these circuits is the mode locking of the circuit to the external drive source.
Spectral Analysis of the Flow of a Neutralized Electron Beam
Authors: Summers Danny , Matsumoto Hiroshi , Ohnishi Takafumi
Published: September 2003

The flow of a neutralized electron beam in the classical Pierce beam–plasma system is examined. The system comprises two grounded electrodes containing a stationary background population of neutralizing ions, and electrons are steadily injected with speed V0 from the left-hand electrode at which the charge density is maintained constant. According to cold fluid theory, the system is governed by a single dimensionless parameter α = Lωp/V0, where L is the separation of the electrodes and ωp the plasma frequency. We cast the governing partial differential equations of the cold fluid model in general spectral form, and, by the technique of Galerkin truncation, we reduce the system to low-order systems of ordinary differential equations. Specifically, we reduce the Pierce system to four-dimensional and six-dimensional systems. We examine the nonlinear dynamics of the electron flow, and we find that the nature of the long-term oscillations can be critically dependent on both the value of the parameter α and the initial conditions. While oscillations are typically quasi-periodic, chaotic behavior is also common. For instance, chaotic oscillations in the four-dimensional system can be induced, for any value of α in the range 2.6π ≤ α ≤ 3π, by a suitable choice of initial conditions. That the initial conditions in the Pierce beam–plasma system can play a significant role in influencing the long-term behavior is a main result of our study. We compare our results with computer simulations of the full system, and conclude that whether or not the complex nonlinear dynamics of the Pierce system can be captured in a low-order ordinary differential system remains a challenging question.
Chaos in Ionic Transport Through Membranes
Authors: Grzywna Zbigniew J. , Siwy Zuzanna
Published: September 2003

The chaotic nature of ionic current through nuclear filters has been detected and analyzed by means of Liapunov exponents and bifurcation diagrams. The "crowd model" describing the nonlinear behavior of single channel ionic current, based on the family of logistic maps, has been formulated and applied to analysis of the patch clamp recordings. Some characteristic features of the system read out from the bifurcation diagrams of the two-parameter logistic map, and also from the extended Hodgkin–Huxley theory have been presented. The relation between the logistic difference schemes (and, at the same time, the class of logistic differential equations) and the logistic maps as well as some possibilities of using the crowd model to biological membranes have also been shown.
DNA Transcription Mechanism with a Moving Enzyme
Authors: Juhi-Lian Ting Julian
Published: September 2003

Previous numerical investigations of a one-dimensional DNA model with an extended modified coupling constant by transcripting enzyme are integrated to longer time and demonstrated explicitly the trapping of breathers by DNA chains with realistic parameters obtained from experiments. Furthermore, collective coordinate method is used to explain a previously observed numerical evidence that breathers placed far from defects are difficult to trap, and the motional effect of RNA-polymerase is investigated.
Analog Neural Network Model Produces Chaos Similar to the Human EEG
Authors: Bondarenko Vladimir E.
Published: September 2003

The self-organization processes in an analog asymmetric neural network with the time delay were considered. It was shown that in dependence on the value of coupling constants between neurons the neural network produced sinusoidal, quasi-periodic or chaotic outputs. The correlation dimension, largest Lyapunov exponent, Shannon entropy and normalized Shannon entropy of the solutions were studied from the point of view of the self-organization processes in systems far from equilibrium state. The quantitative characteristics of the chaotic outputs were compared with the human EEG characteristics. The calculation of the correlation dimension ν shows that its value is varied from 1.0 in case of sinusoidal oscillations to 9.5 in chaotic case. These values of ν agree with the experimental values from 6 to 8 obtained from the human EEG. The largest Lyapunov exponent λ calculated from neural network model is in the range from -0.2 s -1 to 4.8 s -1 for the chaotic solutions. It is also in the interval from 0.028 s -1 to 2.9 s -1 of λ which is observed in experimental study of the human EEG.
Significance of the Tent Map Bifurcations in Continuous Media
Authors: Moon H. T. , Kim M. J.
Published: September 2003

This study provides an incidence where the dynamics of pattern selection is described by the bifurcations of a tent map. This study also shows that the tent map bifurcations in nonlinear systems are structurally stable, implying experimental observability.
Dynamics of Granular Compaction
Authors: Hayakawa Hisao , Hong Daniel C.
Published: September 2003

We investigate the way the disordered granular materials organize themselves in a vibrating bed, the intensity of which is given by the dimensionless parameter Γ. Based on the recognition that an assembly of mono-disperse and cohesionless granular materials is a collection of spinless hard sphere Fermions, we first demonstrate that the time averaged steady state density profile for weak excitation with Γ ≈ 1 is given by the Fermi distribution. This is consistent with the observed experimental data and the results of Molecular dynamics. We then present a dynamic model to study the dynamics of granular compaction, namely the dynamic evolution of the initial state ultimately relaxing toward this steady state. Our preliminary investigation reveals that the relaxation is exponential, which is not inconsistent with the available experimental data for low Γ.
Synthesis of Topologically Conjugate Chaotic Nonlinear Circuits
Authors: Itoh Makoto
Published: September 2003

In this letter, we present a method for synthesizing topologically conjugate chaotic nonlinear circuits. One advantage of our approach is that numerous results from classic circuit synthesis theory can be directly applied to generate a large variety of distinct but equivalent high-dimensional chaotic circuits.
Torus Destruction and Chaos–Chaos Intermittency in a Commodity Distribution Chain
Authors: Sosnovtseva O. , Mosekilde E.
Published: September 2003

The destruction of two-dimensional tori T2 and the transitions to chaos are studied numerically in a high-dimensional model describing the decision making behavior of human subjects in a simulated managerial environment (the beer production-distribution model). Two different routes from quasiperiodicity to chaos can be distinguished. Intermittency transitions between chaotic and hyperchaotic attractors are characterized, and transients in which the "system pursues the ghost" of a vanished hyperchaotic attractor are studied.