bluuebunny/crossref_metadata_2025 huggingface dataset:
Re-Entrant Hexagons and Locked Turing–Hopf Fronts in the CIMA Reaction
Authors: Mosekilde E. , Larsen F. , Dewel G. , Borckmans P.
Published: September 2003

Aspects of the mode-interaction and pattern-selection processes in far-from-equilibrium chemical reaction–diffusion systems are studied through numerical simulation of the Lengyel–Epstein model. By varying the feed concentrations, a transition is observed in which hexagons are replaced by stripes and these again by inverted hexagons. The competition between Hopf oscillations and Turing stripes is investigated by following the propagation of a front connecting the two modes. In certain parameter regimes, mode-locking is found to occur. The front then moves an integer number of Turing stripes during an integer number of Hopf oscillations. This phenomenon can be seen as arising from depinning of the Turing front under influence of the Hopf mode.
Global Bifurcation Approximation in Controlling Chaotic Systems
Authors: Lee Byoung-Cheon , Kim Bong-Gyun , Wang Bo-Hyeun
Published: September 2003

In our previous research [Lee et al., 1995], we demonstrated that return map control and adaptive tracking method can be used together to locate, stabilize and track unstable periodic orbits (UPO) automatically. Our adaptive tracking method is based on the control bifurcation (CB) phenomenon which is another route to chaos generated by feedback control. Along the CB route, there are numerous driven periodic orbits (DPOs), and they can be good control targets if small system modification is allowed.

In this paper, we introduce a new control concept of global bifurcation approximation (GBA) which is quite different from the traditional local linear approximation (LLA). Based on this approach, we also demonstrate that chaotic attractor can be induced from a periodic orbit. If feedback control is applied along the direction to chaos, small erratic fluctuations of a periodic orbit is magnified and the chaotic attractor is induced. One of the special features of CB is the existence of irreversible orbit (IO) which is generated at the strong extreme of feedback control and has irreversible property. We show that IO induces a hysteresis phenomenon in CB, and we discuss how to keep away from IO.
Polarization Dynamical Phenomena in Gas Lasers with Weakly Anisotropic Cavities
Authors: Gudelev V. G. , Svirina L. P. , Zhurik Yu. P.
Published: September 2003

This paper presents the results of theoretical and experimental studies of a series of polarization dynamical phenomena in a single-mode standing-wave class-A laser with weakly anisotropic cavity at elliptically polarized eigenstates. The existence of spontaneous pulsations caused by the competition of active medium and empty cavity anisotropies is also proved.
Analysis of a Model Describing the Dynamics of Intracellular Ion Composition in Biological Cells
Authors: Van Mil H. G. J.
Published: September 2003

An electrophysiological model describing the dynamics of the intracellular ion concentration and the membrane potential (Vm) in biological cells is presented. The model links passive ion fluxes through channels of sodium, potassium and chloride to active ion fluxes generated by the sodium potassium pump. To model the interaction of Vm to the ionic fluxes Kirchhoff current law is used. Only one Vm-dependent permeability as represented by an inwardly rectifying potassium channel (IKR) is incorporated. It is shown that the resulting system of ordinary differential equations is degenerate. Decomposition of the system into noninteracting subsystems allows a dynamically independent description of the currents of sodium and potassium in relation to Vm. Physical and mathematical arguments for the decomposition into subsystems are presented. Analysis of the model show hysteresis properties that can account for the experimentally-observed bistability in skeletal and heart muscles fibers.
Edge of Chaos and Local Activity Domain of the Brusselator CNN
Authors: Dogaru Radu , Chua Leon O.
Published: September 2003

This paper presents an application of the local activity theory [Chua, 1998] to a specific reaction–diffusion cellular nonlinear network (CNN) with cells defined by a trimolecular model, called the Brusselator. Both the local activity domain and a subset called the "edge of chaos" are identified in the cell parameter space. Within these domains, various cell parameter points were selected to illustrate the effectiveness of the local activity theory in choosing the parameters for the emergence of complex (static and dynamic) patterns in a homogeneous lattice formed by coupled locally active cells.
The Central Barrier, Asymmetry and Random Phase in Chaotic Transport and Mixing by Rossby Waves in a Jet
Authors: Yang Huijun
Published: September 2003

The central barrier, asymmetry and random perturbation in transport and mixing by Rossby waves in a jet were investigated by simple kinematic model. Two complementary methods were used: A high-resolution Lagrangian Field Advection Model (FAM) and a finite-time Lyapunov exponent analysis. The present study revealed the following: (1) A central barrier can be formed in two Rossby waves without shear flow as well as in a jet, (2) the central barrier may occur in the region with maximum jet speed relative to the phase speed of the traveling wave, whereas the chaotic mixing most likely occurs near the critical lines; the central barrier widens as the phase speed of traveling waves relative to the jet speed increases, (3) asymmetry of wave-breaking is directly related to asymmetry of the critical line location in a jet, (4) the central barrier survives small random perturbations, (5) global bifurcation from a homoclinic orbit to a heteroclinic orbit and global chaos are two main mechanisms for the central barrier destruction. The results suggest that the small scale motions and random processes may not significantly affect the major character of Lagrangian transport and mixing by large-scale geophysical flow. Also potential vorticity mixing provides a unique kinematic and dynamic view of many features of the geophysical flow.
Validation and Calibration of Models for Reaction–Diffusion Systems
Authors: Dilão Rui , Sainhas Joaquim
Published: September 2003

Space and time scales are not independent in diffusion. In fact, numerical simulations show that different patterns are obtained when space and time steps (Δx and Δt) are varied independently. On the other hand, anisotropy effects due to the symmetries of the discretization lattice prevent the quantitative calibration of models. We introduce a new class of explicit difference methods for numerical integration of diffusion and reaction–diffusion equations, where the dependence on space and time scales occurs naturally. Numerical solutions approach the exact solution of the continuous diffusion equation for finite Δx and Δt, if the parameter γN=DΔt/(Δx)2 assumes a fixed constant value, where N is an odd positive integer parametrizing the algorithm. The error between the solutions of the discrete and the continuous equations goes to zero as (Δx)2(N+2) and the values of γN are dimension independent. With these new integration methods, anisotropy effects resulting from the finite differences are minimized, defining a standard for validation and calibration of numerical solutions of diffusion and reaction–diffusion equations. Comparison between numerical and analytical solutions of reaction–diffusion equations give global discretization errors of the order of 10-6 in the sup norm. Circular patterns of traveling waves have a maximum relative random deviation from the spherical symmetry of the order of 0.2%, and the standard deviation of the fluctuations around the mean circular wave front is of the order of 10-3.
Nonlinear Resonance in Basin Portraits of Two Coupled Swings Under Periodic Forcing
Authors: Ueda Yoshisuke , Ueda Yoshinori , Stewart H. Bruce , Abraham Ralph H.
Published: September 2003

A model of a simple electric power supply network involving two generators connected by a transmission network to a bus is studied by numerical simulation. In this model, the bus is supposed to maintain a voltage of fixed amplitude, but with a small periodic fluctuation in the phase angle. In such a case, traditional analysis using direct methods is not applicable. The frequency of the periodic fluctuation is varied over a range of values near a nonlinear resonance of the two-generator network. When the bus fluctuation frequency is away from resonance, the system has several attractors; one is a small-amplitude periodic oscillation corresponding to synchronized, quasi-normal operation (slightly swinging), while others are large amplitude periodic oscillations which, if realized, would correspond to one or both generators operating in a desynchronized steady state.

When the bus fluctuation frequency approaches resonance, a new periodic attractor with large amplitude oscillations appears. Although it does correspond to a synchronized steady state, this attractor has a disastrously large amplitude of oscillation, and represents an unacceptable condition for the network. Basin portraits show that this resonant attractor erodes large, complicated regions of the basin of the safe operating condition. Under conditions of small periodic fluctuation in bus voltage, this basin erosion would not be detected by traditional analysis using direct methods. Further understanding of such complicated basin structures will be essential to correctly predict the stability of electric power supply systems.
The Hénon and Heiles Problem in Three Dimensions.
Authors: Ferrer S. , Lara M. , Palacián J. , Juan J. F. San , Viartola A. , Yanguas P.
Published: September 2003

The second part of a research on the Hénon and Heiles system in three dimensions is presented. We focus on motions around the origin, where the system may be treated as a case of three perturbed isotropic harmonic oscillators. It is the only Hamiltonian of the family of axially symmetric cubic potentials in 1–1–1 resonance, which needs at least order four in the normalization to reach the features of the system. The fourth order normalized system is analyzed, considering orbits at any inclination. We study and classify the relative equilibria of the system finding pitchfork, centre-saddle and cusp bifurcations in the reduced orbit space.
Discretization Effect on a Sliding Mode Control System with Bang–Bang Type Switching
Authors: Yu Xinghuo
Published: September 2003

A complete analysis of various behaviors in discretization of a sliding mode control system is given. These behaviors are classified in three types: inherent periodic behaviors, convergent periodic behaviors and unstable behaviors. In particular, there are two classes of periodic behavior patterns: One class is a set of discrete points; the other a set of dense ellipses. These classes are determined by the sampling period which acts as an additional dimension of freedom to the discretized sliding mode control system. The relation between the sampling period and periodic behaviors is explored and the bifurcation point that distinguishes the stable periodic behaviors and irregular behaviors is given. The analysis is accompanied by various simulations.
Symmetric Ciphers Based on Two-Dimensional Chaotic Maps
Authors: Fridrich Jiri
Published: September 2003

In this paper, methods are shown how to adapt invertible two-dimensional chaotic maps on a torus or on a square to create new symmetric block encryption schemes. A chaotic map is first generalized by introducing parameters and then discretized to a finite square lattice of points which represent pixels or some other data items. Although the discretized map is a permutation and thus cannot be chaotic, it shares certain properties with its continuous counterpart as long as the number of iterations remains small. The discretized map is further extended to three dimensions and composed with a simple diffusion mechanism. As a result, a symmetric block product encryption scheme is obtained. To encrypt an N×N image, the ciphering map is iteratively applied to the image. The construction of the cipher and its security is explained with the two-dimensional Baker map. It is shown that the permutations induced by the Baker map behave as typical random permutations. Computer simulations indicate that the cipher has good diffusion properties with respect to the plain-text and the key. A nontraditional pseudo-random number generator based on the encryption scheme is described and studied. Examples of some other two-dimensional chaotic maps are given and their suitability for secure encryption is discussed. The paper closes with a brief discussion of a possible relationship between discretized chaos and cryptosystems.
Stable State Analysis of an Immune Network Model
Authors: Castellani G. C. , Giberti C. , Franceschi C. , Bersani F.
Published: September 2003

The paper analyzes a model of immune system developed by different authors (Perelson, De Boer, Weisbuch and others). The model describes interactions among B-lymphocytes. It does not consider antibodies as interaction intermediaries, although it uses a typical activation curve. The relevant parameters are: an influx term, a threshold value, a proliferation rate, and a decay parameter. The study of the n-dimensional extension of the model and a bifurcation analysis of the stationary states with respect to the influx parameter show that the influx value for which biologically acceptable solutions exist decreases as n increases. When the influx term is neglected the stationary states are obtained analytically and their stability is discussed. Moreover, it is discussed how the stable solutions can be considered as "selective states", that is, with only one high idiotypic concentration, when we suppose a complete connectivity.
Chaos: An Ecological Reality?
Authors: Upadhyay Ranjit Kumar , Iyengar S. R. K. , Rai Vikas
Published: September 2003

Deterministic chaos has been studied extensively in various fields. Some of the ideas emerging out of these studies have been put to novel applications. However, it is unknown whether natural ecological systems support chaotic dynamics. There is no concrete evidence which suggests that ecosystem evolution is chaotic in certain situations. This is very intriguing because ecosystems do possess all the necessary qualifications to be able to support such a dynamical behavior.

The present paper attempts to answer the above question with the help of a few systems modeling different but very common ecological situations. A new methodology for the analysis of a class of model ecological systems is presented. Simulation experiments suggest that natural terrestrial systems are not suitable candidates where one should look for chaos. Additionally, our study also points out that the failure of attempts to observe chaos in natural populations might have resulted because biological interactions are not conducive for such a behavior to be supported. The cause of these failures may not be the poor data quality or demerits in the analysis techniques.
Two Modified for Chaos Negative Impedance Converter Op Amp Oscillators with Symmetrical and Antisymmetrical Nonlinearities
Authors: Elwakil A. S. , Soliman A. M.
Published: September 2003

Two sinusoidal oscillator circuits, that employ an operational amplifier (op amp) as a current negative impedance converter (CNIC), are modified for chaos using a nonlinear resistor of anti-symmetrical current-voltage characteristics formed by a junction field effect transistor (JFET) operating in the triode region. The internal op amp dominant pole is found to contribute significantly to the chaotic nature of one circuit while the other circuit develops different chaotic attractors when cubic and fifth power odd symmetrical nonlinearities are used. Mathematical models of the two generators are presented. Experimental laboratory results, circuit simulations and numerical simulations of the mathematical models well agree and are included.
Control of Coupled Standard Map
Authors: Liu Zonghua , Chen Shigang
Published: September 2003

In this work, we extend the periodic impulsive method to high-dimensional conservative system, and use the coupled standard map as an example to illustrate how to control the high-dimensional Hamiltonian chaos. When the periodic pulse is applied to one variable of the system, different periodic windows, quasiperiodic orbit and some special structure can be stabilized, even the approximate KAM curve. And the largest Lyapunov exponent spectra corresponding to different initial points are given.
A Global Synchronization Theorem for a Class of Chaotic Systems
Authors: Wang Xiao Fan , Wang Zhi Quan
Published: September 2003

This Letter proposes a new synchronization theorem for a subclass of chaotic Lur'e systems. We take a specific state variable of the drive system as the driving signal. We prove that globally synchronization can be attained via the simple linear error feedback. The approach is illustrated using Chua's chaotic oscillator and a hyperchaotic oscillator.
Impulsive Synchronization of Chaotic Lur'e Systems by Measurement Feedback
Authors: Suykens J. A. K. , Yang T. , Chua L. O.
Published: September 2003

In this paper we consider impulsive control of master-slave synchronization schemes that consist of identical Lur'e systems. Impulsive control laws are investigated which make use of linear or nonlinear dynamic measurement feedback. A sufficient condition for global asymptotic stability is presented which is characterized by a set of matrix inequalities. Synchronization is proven for the error between the output signals. The method is illustrated on Chua's circuit and a hyperchaotic system with coupled Chua's circuits.
Braid Description of Few Body Dynamics
Authors: Clausen Sigmund , Helgensen Geir , Skjeltorp Arne T.
Published: September 2003

A few body system of magnetic holes set in motion by external ac magnetic fields is studied both experimentally and numerically. Notions from braid theory are used to describe the dynamics ina very compact manner. The time histroy of n magnetic holes moving in a plane is represented by an n-strand braid which enables us to extrat periodic orbits and to map out phase phase portraits. The transitions between different periodic modes of motion are either continuous or noncontinuous followed by strong hysteresis.
Determining the Minimum Embedding Dimensions of Input–Output Time Series Data
Authors: Cao Liangyue , Mees Alistair , Judd Kevin , Froyland Gary
Published: September 2003

Input–output dynamical systems are in many ways quite different from the autonomous systems that are usually modeled in dynamical system reconstruction. In this paper we investigate the problem of determining the embedding dimension of such systems from input and output data. A successful embedding is essential if one wishes to model the system, or to design a control law. We propose a variant of the well-known false nearest neighbors method, which we call the method of averaged false nearest neighbors. Our method has a simple interpretation and is easy to implement on a computer. We provide several numerical examples.
Modeling Noisy Time Series: Physiological Tremor
Authors: Timmer J.
Published: September 2003

Empirical time series often contain observational noise. We investigate the effect of this noise on the estimated parameters of models fitted to the data. For data of physiological tremor, i.e. a small amplitude oscillation of the outstretched hand of healthy subjects, we compare the results for a linear model that explicitly includes additional observational noise to one that ignores this noise. We discuss problems and possible solutions for nonlinear deterministic as well as nonlinear stochastic processes. Especially we discuss the state space model applicable for modeling noisy stochastic systems and Bock's algorithm capable for modeling noisy deterministic systems.
Attracting Basins of Certain Nonholomorphic Maps
Authors: Uchimura Keisuke
Published: September 2003

Attractive basins of a function [Formula: see text] are considered. The function Fc(z) is obtained by a perturbation of a "two-dimensional tent map" [Formula: see text]. We prove that the immediate attractive basins of the function F4/3(z) consist of six triangular regions which are subdivisions of a equilateral triangle by three medians.
Bifurcation and Chaos in Noninteger Order Cellular Neural Networks
Authors: Arena P. , Caponetto R. , Fortuna L. , Porto D.
Published: September 2003

In this paper a new class of Cellular Neural Networks (CNNs) is introduced. The peculiarity of the new CNN model consists in replacing the traditional first order cell with a noninteger order one. The introduction of fractional order cells, with a suitable choice of the coupling parameters, leads to the onset of chaos in a two-cell system of a total order of less than three. A theoretical approach, based on the interaction between equilibrium points and limit cycles, is used to discover chaotic motions in fractional CNNs.
Observations on the Onset and Propagation of Excitation Waves in Neural Tissue
Authors: Goldermann M. , Hanke W. , de Almeida A. C. Guimaraes , de Lima V. M. Fernandes
Published: September 2003

The onset and propagation of waves in an excitable medium were investigated using the retinal Spreading Depression (rSD). The rSD is an ideal tool for this purpose. The retina of chickent, which was used in all experiments, is a close to two-dimensional system, in which the wave can easily be observed by optical techniques in time and space. rSD waves can be elicited by a variety of stimuli. Between stimulus and onset of the wave a temporal delay is always present. We found that the wave velocity is a function of the duration of this delay. In this paper we show, that within this time increasing fluctuations occur of system parameters.
Strange Nonchaotic Attractors with Cellular Neural Networks
Authors: Zhu Zhiwen , Wang Shi , Leung Henry
Published: September 2003

In this paper, we investigate the existence of strange nonchaotic attractors in a nonautonomous cellular neural network (CNN). The network consists of two cells, each cell being driven by a sinusoidal input and the frequencies of two inputs being incommensurate. Numerical analyses based on Lyapunov exponent, Poincare map, double Poincare map, Fourier amplitude spectrum, and information dimension show the existence of strange nonchaotic attractors in a substantial parameter space. It appears that the CNN is the first dynamical system with separate excitations having the strange nonchaotic attractors.
Impulsive Control of Nonautonomous Chaotic Systems using Practical Stabilization
Authors: Yang Tao , Suykens Johan A. K. , Chua Leon O.
Published: September 2003

In this paper, we use the concept of practical stabilization of impulsive differential equations for controlling nonautonomous chaotic systems. Instead of controlling a chaotic system to a point as in the case of asymptotic stabilization, the aim of practical control is to stabilize a chaotic system into a small region of phase space. This method is useful to control a chaotic system into a prescribed region. We present the theory of controlling a nonautonomous chaotic system into a small region around the origin and illustrate the method on Duffing's oscillator.
Local Control of Chaotic Systems — A Lyapunov Approach
Authors: Richter Hendrik , Reinschke Kurt J.
Published: September 2003

In this paper a method for local control of an unstable equilibrium point in chaotic systems is presented. Linear state feedback to stabilize the equilibrium is employed which is only active in a bounded region around the desired point: the area of control action. Size and shape of the area of control action are determined by a Lyapunov function of the controlled chaotic system such that it belongs to the basin of attraction of the equilibrium point. We give the design procedure for both continuous-time and discrete-time systems.
Targeting Applying ε-Bounded Orbit Correction Perturbations
Authors: Baptista M. S.
Published: September 2003

A low-sized chaotic trajectory is used to compute epsilon-bounded orbit correction perturbations in order to rapidly target a trajectory from the vicinity of a starting point to a target. An algorithm that allows fast computation of a set of perturbations to be applied is presented, and its performance is tested in a higher-dimensional system, the kicked double rotor.
Feedback Anticontrol of Discrete Chaos
Authors: Chen Guanrong , Lai Dejian
Published: September 2003

In this paper, a simple feedback control design method earlier proposed by us for discrete-time dynamical systems is proved to be a mathematically rigorous approach for anticontrol of chaos, in the sense that any given discrete-time dynamical system can be made chaotic by the designed state-feedback controller along with the mod-operations.
Generalized Predictive Control of Discrete-Time Chaotic Systems
Authors: Park Kwang-Sung , Park Jin-Bae , Choi Yoon-Ho , Yoon Tae-Sung , Chen Guanrong
Published: September 2003

A generalized predictive control method based on an ARMAX model is suggested for chaos control in discrete-time systems. Both control performance and system sensitivity to initial conditions of this approach are compared with the conventional model-referenced adaptive control via numerical simulations. Simulation results show that this controller yields faster settling time, more accurate target tracking, and less initial sensitivity.
Synchronization of Self-Oscillations by Parametric Excitation
Authors: Astakhov V. , Shabunin A. , Anishchenko V.
Published: September 2003

This paper is devoted to the problem of synchronization of symmetrically coupled self-oscillators exhibiting chaos by means of chaos control technique. We use a nonfeedback method of control, in particular, high frequency periodic modulation of the coefficient of coupling. The model of Chua's circuits coupled via capacity is considered in this work. We study the possibility of synchronization in dependence on amplitude and frequency of modulation for various values of the parameters of the self-oscillators. The dependence of the threshold values of the amplitude of the synchronizing influence on coefficient is presented.
Fatou Components and a Problem of Bergweiler
Authors: Hua Xinhou , Yang Chung-Chun
Published: September 2003

For any transcendental meromorphic function, we shall study the relations between the components of the Fatou set and their images. This relates to a problem studied by Bergweiler [1993].
Applications of Chaotic Digital Code-Division Multiple Access (CDMA) to Cable Communication Systems
Authors: Yang Tao , Chua Leon O.
Published: September 2003

In this paper the technical details of chaotic digital code-division multiple access ((CD)2MA) communication systems used in cable communication systems are presented. The cable communication system may be a pure coaxial RF cable network, a hybrid fiber-coax network, or a pure optical fibre network for high-capacity data link. As an example of its many potential applications in cable communication systems, (CD)2MA is used to support the upstream digital data communications in cable TV systems occupying the very noisy 5–40 MHz portion of spectrum. Although the (CD)2MA proposed in this paper is only used to support current Internet services via cable TV networks, it can also be used to support the high-speed data-link provided in the 550–750 MHz band in hybrid fiber-coax networks.

(CD)2MA is a new communication framework which uses band-limited chaotic carriers insted of linear ones. For the purpose of generality, in this paper the band-limited chaotic carriers are approximated by groups of linear sub-carriers, which distribute within the same bandwidth with a fixed amplitude, random phases and uniformly distributed frequencies. The theoretical result of the performance of (CD)2MA is given. We also provide the simulation results of the bit-error-rate (BER) performances of a synchronous (CD)2MA used in cable communication systems. The results show that the (CD)2MA system has a better performance than the synchronous CDMA system proposed for the same cable communication system. Technical details of (CD)2MA are also presented for the future design of prototype systems. We present the framework of the whole (CD)2MA system including carrier syncronization, timing recovery and the details of nonlinear carrier generators.
Parametric Resonant Control of Chaos
Authors: Lima Ricardo , Pettini Marco
Published: September 2003

A concise account is given of the early motivations for introducing parametric methods to achieve control of chaos. The heuristic argument that made us think that this kind of method could have been successful is also given. A key study is then reviewed. This concerns a parametric perturbation of a damped and forced Duffing–Holmes oscillator in a chaotic regime. The theoretical analysis, based on the Melnikov treatment of homoclinic tangles, provides a clear understanding of the intimate mechanism that controls chaos. Numerical results confirm and extend the theoretical predictions. A brief discussion of an experimental test on a magneto-elastic device is finally presented.
Controlling Chaos with Parametric Perturbations
Authors: Fronzoni Leone , Giocondo Michele
Published: September 2003

We consider the effects of parametric perturbation on the onset of chaos in different dynamical systems. Favoring or suppression of chaos was observed depending on the phase or the frequency of the periodic perturbation. A lowering of the threshold of chaos was observed in an electronic device simulating a Josephson-Junction model and the suppression of chaos was obtained in a bistable mechanical device. We showed that in case of spatial instability in a sample of liquid crystal, the action of the parametric perturbation is to modify the velocity and the onset of the defects.

Considering that the emergence of defects precedes the threshold of spatio-temporal chaos, we infer that parametric perturbation can modify the threshold of chaos in this spatial dynamical system.
On Optimal Stabilization of Periodic Orbits via Time Delayed Feedback Control
Authors: Basso M , Genesio R. , Giovanardi L. , Tesi A. , Torrini G.
Published: September 2003

The paper considers the problem of designing time delayed feedback controllers to stabilize unstable periodic orbits of a class of sinusoidally forced nonlinear systems. This problem is formulated as an absolute stability problem of a linear periodic feedback system, in order to employ the well-known circle criterion. In particular, once a single test is verified by an unstable periodic orbit of the chaotic system, our approach directly provides a procedure for designing the optimal stabilizing controller, i.e. the one ensuring the largest obtainable stability bounds. Even if the circle criterion provides a sufficient condition for stability and therefore the obtained stability bounds are conservative in nature, several examples, as the one presented in this paper, show that the performance of the designed controller is quite satisfactory in comparison with different approaches.
Control of Chaotic Maps by Optimized Periodic Inputs
Authors: Mettin R.
Published: September 2003

It has been established that chaotic iterated maps can be transferred to a periodic motion by application of periodic signals. As a next step, we investigate the optimization of such signals with respect to a small norm. This method employs a cost function on the space of periodic inputs. By means of a direct optimization search in this space, the approach stabilizes periodicity with small forces. The results for increasing driving periods are compared.
Clustering Bifurcation and Spatiotemporal Intermittency in RF-Driven Josephson Junction Series Arrays
Authors: Xie Fagen , Cerdeira Hilda A.
Published: September 2003

We study the spatiotemporal dynamics of the underdamped Josephson junction series arrays (JJSA) which are globally coupled through a resistive shunting load and driven by an rf bias current. Clustering bifurcations are shown to appear. In particular, cluster-doubling induced period-doubling bifurcations and clustering induced spatiotemporal chaos are found. Furthermore, an interesting spatiotemporal intermittency is also found. These phenomena are closely related to the dynamics of the single cell.
Inhibition of Chaotic Escape by an Additional Driven Term
Authors: Balibrea Francisco , Chacón Ricardo , López Miguel Angel
Published: September 2003

In this paper, we are devoted to the problem of escaping from a potential well which is present in a great number of physical situations. We use the Helmholtz oscillator as a model for those situations and consider the behavior of the oscillator under an additional driven perturbation. The Melnikov analysis reveals it as an adequate method. Some comparisons are made with the perturbations of the oscillator on the linear and quadratic terms.
Simulation of Heartbeat Dynamics: A Nonlinear Model
Authors: Signorini Maria G. , di Bernardo Diego
Published: September 2003

The mathematical modeling of biological systems has proven to be a valuable tool by allowing experiments which would otherwise be unfeasible in a real situation. In this work we propose a system of nonlinear differential equations describing the macroscopic behavior of the cardiac conduction system. The model describes the interactoin between the SinoAtrial and AtrioVentricular node. Its very simple structure consists of two nonlinear oscillators resistively coupled.

The numerical analysis detects different kinds of bifurcations whose pathophysiological meanings are discussed. Moreover, the model is able to classify different pathologies, such as several classes of arrhythmic events, as well as to suggest hypothesis on the mechanisms that induce them. These results also show that the mechanisms generating the heartbeat obey complex laws. The model provides a wuite complete description of different pathological phenomena and its simplicity can be exploited for further studies on the control of cardiac dynamics.
Desynchronization Transitions in Rings of Coupled Chaotic Oscillators
Authors: Mariño I. P. , Pérez-Muñuzuri V. , Matías M. A.
Published: September 2003

Rings of chaotic oscillators coupled unidirectionally through driving are studied. While synchronization is observed for small sizes of the ring, beyond a certain critical size a desynchronizing transition occurs. In the two examples studied here the system exhibits a transition to periodic rotating waves for rings of Lorenz systems, while one finds a sort of chaotic rotating waves when Chua's circuit is used.
Suppression and Excitation of Chaos: The Example of the Glow Discharge
Authors: Braun Thomas
Published: September 2003

I report on the experimental observation of excitation and suppression of chaos through time dependent perturbations in the dynamical variable of a glow discharge. The interaction of the external signal with the dynamical system is explained in terms of the 1D map associated to the glow discharge. Numerical simulations are also performed with the logistic map. The proposed mechanism of exciting and/or suppressing chaos is in accordance with the OGY method of controlling chaos.
Fuzzy Control of Chaos
Authors: Calvo Oscar , Cartwright Julyan H. E.
Published: September 2003

We introduce the idea of the fuzzy control of chaos: we show how fuzzy logic can be applied to the control of chaos, and provide and example of fuzzy control used to control chaos in Chua's circuit.
Control of Chaos in Lasers by Feedback and Nonfeedback Methods
Authors: Glorieux Pierre
Published: September 2003

Analytical approaches of the theory of chaos control in class B lasers are presented in the cases of continuous delayed feedback and of subharmonic modulation. They are compared with experimental findings on a CO 2 laser and a Nd-doped fiber laser with modulated loss and pump respectively. In both cases, analytical theory allows one to predict the shift of the first period-doubling bifurcations, Numerical simulations show that subharmonic modulation may induce shifts, crises and new attractors in a laser with modulated parameters and that its phase relative to the main modulation allows one to control the laser dynamics. These results agree well with the experimental observations on control of chaos in CO 2 and fiber lasers.
Experimental Techniques for Controlling Chaos in Lasers
Authors: Meucci R. , Labate A. , Ciofini M.
Published: September 2003

This paper presents two control schemes for the chaotic dynamics of CO 2 laser with feedback which can be applied after the recognition of a leading frequency of the motion in the power spectrum. The first one is realized by means of a selective feedback loop which rejects all the frequency components except that of the leading cycle to be stabilized. The second one consists in a resonant sinusoidal modulation of the control parameter.
Instabilities and Tracking of Travelling Wave Patterns in a Three-Level Laser
Authors: Lu Weiping , Yu Dejin , Harrison Robert G.
Published: September 2003

Based on our earlier theoretical work on tracking periodic patterns into spatiotemporal chaotic regimes in spatially extended systems, we present in this article a case study of a high-aspect-ratio three-level laser. Following a detailed investigation into travelling wave solutions of the laser system and their stability conditions, we discuss ways of stabilising these solutions by local feedback algorithms. In numerical simulations, we choose Pyragus continuous delayed feedback algorithm to be the local feedback form and demonstrate that stable travelling wave solutions of the spatially extended three-level laser can be greatly extended to unstable regions in the presence of this feedback
Experimental Switchings in Bistability Domains Induced by Resonant Perturbations
Authors: Chizhevsky V. N. , Vilaseca R. , Corbalan R.
Published: September 2003

We show that a combination of a resonant perturbation which induces bistability in the system with the targeting technique based on the action of a short-lived pulse perturbation makes the nonfeedback control of nonlinear systems (not only in a chaotic state) more flexible and even competitive with OGY's method in the sense of fast switching between controlled orbits belonging to coexisting attractors. For different initial states we present several experimental and numerical examples of such a type of control, which does not require feedback system.
Self-Pulsing and Chaos in an Extended-Cavity Diode Laser with Intracavity Atomic Absorber
Authors: di Teodoro F. , Cerboneschi E. , Hennequin D. , Arimondo E.
Published: September 2003

An experimental investigation of the temporal dynamics of a diode laser subject to optical feedback from an external cavity containing a cell filled with cesium vapor has been performed. Peculiar dynamic regimes, such as self-pulsing, low-dimensional, and high-dimensional chaos, characterized by a new time scale, much longer than the time scales of all instabilities taking place in diode lasers under standard feedback conditions, have been identified.
Control of Turn-On in Class B Lasers
Authors: Porta P. A. , Hoffer L. M. , Grassi H. , Lippi G. L.
Published: September 2003

A very simple technique, which uses a succession of two different but constant levels in the pump parameter, is shown to be quite effective in controlling the turn-on transient of a class B laser. In particular,a drastic reduction in the delay time, as well as a lowering of the intensity overshoot under suitable conditions, has been observed both in numerical simulations and in experiments on a CO 2 laser. Such a straightforward, nonfeedback technique may have very promising applications in the realm of communications.
Synchronization of a Network of Chaotic Neurons Using Adaptive Control in Noisy Environment
Authors: Cazelles Bernard
Published: September 2003

The synchronization of chaotic systems have received an increasing interest in the last few years. In an attempt to understand some of the possible mechanisms of synchronization of neurons in a noisy environment, the present study extends a control method which is based on the Kalman filter. This adaptive control mechanism is able to modulate the frequency and the clustering behavior of a network of neurons and can thus make the network switch dynamically to different rhythmic activity, leading to different coding possiblity.
Control of Amplitude Turbulence in Delayed Dynamical Systems
Authors: Maza D. , Mancini H. , Boccaletti S. , Genesio R. , Arecchi T.
Published: September 2003

An experiment on Bénard–Marangoni time-dependent convection shows evidence of an amplitude turbulent regime in the temperature signal which is modeled by a delayed dynamical system. Application of a control procedure, which perturbs the value of the delay time, leads to the control of such dynamical regime, by suppression of phase defects and stabilization of the regular oscillations. The control technique is robust against the presence of large amounts of noise.
Pattern Formation and Spatial Chaos for Cellular Neural Networks with Asymmetric Templates
Authors: Shih Chih-Wen
Published: September 2003

The cellular neural networks with two kinds of two-parametered asymmetric templates are considered. The parameter space is partitioned into finitely many disjoint regions. In each region, the basic mosaic patterns are characterized. The feasible mosaic patterns correponding to the parameters in each region can then be determined. To exhibit the spatial complexity of the system, we estimate the entropy of mosaic patterns for parameters in the regime of spatial chaos. In light of this characterization, the effect from the symmetry of the template on pattern formation properties can be seen in detail. We also discuss the existence of some fundamental class of feasible local defect patterns. It is shown that the feasible local k-defect patterns of vertical type cannot exist if the connection weights are anti-symmetric in the vertical direction. Same conclusion also holds for the ones of horizontal type and horizontal direction.
Coding Scheme Based on Chaos Synchronization from Noninvertible Maps
Authors: Millerioux G. , Mira C.
Published: September 2003

This paper deals with a new coding scheme in digital implementation for secure communications. It is based on specific dynamic features generated by noninvertible maps. The main results are a global chaos synchronization, an exact synchronization without a residual error generated by the classical methods, a robustness with respect to channel disturbances. Chaos synchronization is obtained by introducting an observer model and the classical results of the control theory. Besides, this coding scheme introduces several "keys" required for decoding the initial information, which improves the security of communications.
Synchronization of Hyperchaotic Circuits via Continuous Feedback Control with Application to Secure Communications
Authors: Brucoli Michele , Cafagna Donato , Carnimeo Leonarda , Grassi Giuseppe
Published: September 2003

In this paper a synthesis technique for the synchronization of hyperchaotic circuits with application to secure communications is developed. It is well known that information-bearing signals can be considered as causes of perturbations, when a secure communication system based on a masking technique is implemented. Starting from this consideration, in this paper a feedback control scheme is developed to guarantee synchronization between transmitter and receiver. The control scheme involves as many state variables in the feedback as the number of information signals to be transmitted. After deriving the nonlinear dynamics of the synchronization error system, the feedback matrix is determined by finding a suitable Lyapunov function and by imposing the conditions which assure the global asymptotic stability of the origin of the error system. The method is illustrated by considering hyperchaotic circuits constituted by coupled Chua's oscillators, for which analytic expressions of the feedback gains are derived.
Bifurcation Sets of Continuous Piecewise Linear Systems with Two Zones
Authors: Freire Emilio , Ponce Enrique , Rodrigo Francisco , Torres Francisco
Published: September 2003

Planar continuous piecewise linear vector fields with two zones are considered. A canonical form which captures the most interesting oscillatory behavior is obtained and their bifurcation sets are drawn. Different mechanisms for the creation of periodic orbits are detected, and their main characteristics are emphasized.
The Multiple Scales Method, Homoclinic Bifurcation and Melnikov's Method for Autonomous Systems
Authors: Smith Peter
Published: September 2003

Melnikov's method is a well-established technique for detecting homoclinic bifurcation of perturbed autonomous or forced systems. This method uses a regular perturbation expansion in terms of a small parameter in the system. Whilst the approach correctly estimates the parameter values for the bifurcation and transverse intersections of separatrices and manifolds, it does not correctly represent solutions near the associated fixed point of the homoclinic orbit. For the autonomous case, a multiple scales method using matched inner and outer solutions is developed in this exposition which corrects this deficiency, whilst still confirming Melnikov's result to leading order.
Local Homeostasis Stabilizes a Model of the Olfactory System Globally in Respect to Perturbations by Input During Pattern Classification
Authors: Chang Hung-Jen , Freeman Walter J. , Burke Brian C.
Published: September 2003

A software model of the olfactory system is presented as a test bed for identifying and solving the problems of simulating the nonlinear dynamics of sensory cortex. Compression, normalization and spatial contrast enhancement of the input to the bulb, the input stage of the olfactory system, are done by input-dependent attenuation of forward and lateral transmission, and by modulation of the asymptotic maximum of the sigmoid function of bulbar neural populations. An implementation of these mechanisms in the model, constituting local homeostatic regulation at the input stage, stabilizes the model in respect to variations in analog input and to recovery from repeated input-induced state transitions. Both non-Hebbian habituation and Hebbian reinforcement constituting local homeostatic regulation are used to train the model. A spatially patterned analog input belonging to a previously learned class may then guide the system to an appropriate basin of attraction. These advances have improved the classification performance of the model but reveal a still unsolved problem: the prestimulus state is governed by a global attractor, but the learned states are governed by collections of local attractors, not the desired global states.
Slow-Fast Autonomous Dynamical Systems
Authors: Rossetto Bruno , Lenzini Thierry , Ramdani Sofiane , Suchey Gilles
Published: September 2003

In this paper, we consider a class of slow-fast autonomous dynamical systems, i.e. systems having a small parameter ∊ multiplying a component of velocity. At first, the singular perturbation method (∊ = 0+) is recalled. Then we consider the case ∊ ≠ 0. Starting from a working hypothesis and particularly in the case of a singular approximation, our purpose is to show that there exists slow manifolds which can be defined as the slow manifolds of a so-called tangent linear system. The method allowed us to plot the slow manifold and to go further into the qualitative study and the geometric characterization of attractors. As an example, we give the explicit slow manifold equation of the van der Pol limit cycle. The value of the parameter corresponding to bifurcations is computed. Other third order systems are also treated.

The method is extended to dynamical systems with no small parameter, and, therefore, which have no singular approximations, but have at least one real and negative eigenvalue in a large domain. It is numerically shown from the Lorenz model and from a laser model that there exists slow manifolds which can be defined as the slow manifods of a so-called tangent linear system, as in the previous cases. The implicit equation of these slow manifolds has been calculated too.