bluuebunny/crossref_metadata_2025 huggingface dataset:
SILICON SUPPORT VECTOR MACHINE WITH ON-LINE LEARNING
Authors: GENOV ROMAN , CHAKRABARTTY SHANTANU , CAUWENBERGHS GERT
Published: May 2003

Training of support vector machines (SVMs) amounts to solving a quadratic programming problem over the training data. We present a simple on-line SVM training algorithm of complexity approximately linear in the number of training vectors, and linear in the number of support vectors. The algorithm implements an on-line variant of sequential minimum optimization (SMO) that avoids the need for adjusting select pairs of training coefficients by adjusting the bias term along with the coefficient of the currently presented training vector. The coefficient assignment is a function of the margin returned by the SVM classifier prior to assignment, subject to inequality constraints. The training scheme lends efficiently to dedicated SVM hardware for real-time pattern recognition, implemented using resources already provided for run-time operation. Performance gains are illustrated using the Kerneltron, a massively parallel mixed-signal VLSI processor for kernel-based real-time video recognition.
A MEMORYLESS REVERSE CONVERTER FOR THE 4-MODULI SUPERSET {2n - 1, 2n, 2n + 1, 2n + 1 - 1}
Authors: VINOD A. P , PREMKUMAR A. BENJAMIN
Published: May 2003

This paper presents a residue number system to binary converter in the four moduli set {2n - 1, 2n, 2n + 1, 2n + 1 - 1}, valid for even values of n. This moduli set is an extension of the popular set {2n - 1, 2n + 1}. The number theoretic properties of the moduli set of the form 2n ± 1 are exploited to design the converter. The main challenge of dealing with fractions in Residue Number System is overcome by using the fraction compensation technique. A hardware implementation using only adders is also proposed. When compared to the common three moduli reverse converters, this four moduli converter offers a larger dynamic range and higher parallelism, which makes it useful for high performance computing.
AN ALTERNATIVE PROOF OF MODIFIED-BOOTH RECODING ALGORITHM BASED ON NUMBER-DOMAIN TRANSFORMATIONS
Authors: RAO VISHWAS M. , NOWROUZIAN BEHROUZ
Published: May 2003

In this letter, the nonredundant radix-4 representation of two's complement numbers is exploited to develop an alternative proof for the modified-Booth recoding algorithm. This proof is established by showing that the modified-Booth recoding algorithm essentially amounts to successive transformations of the number from its two's complement to its nonredundant radix-4 representation and from its nonredundant radix-4 to its modified radix-4 signed-digit representation. The salient feature of these transformations is that the digits in the resulting modified radix-4 signed-digit number take on values from the same balanced digit-set, placing in evidence the main principle and motivation behind the modified-Booth recoding algorithm.
PERFORMANCE OF SCALABLE SHARED-MEMORY ARCHITECTURES
Authors: MOTLAGH BAHMAN S. , DeMARA RONALD F.
Published: May 2003

Analytical models were developed and simulations of memory latency were performed for Uniform Memory Access (UMA), Non-Uniform Memory Access (NUMA), Local-Remote-Global (LRG), and RCR architectures for hit rates from 0.1 to 0.9 in steps of 0.1, memory access times of 10 to 100 ns, proportions of read/write access from 0.01 to 0.1, and block sizes of 8 to 64 words. The RCR architecture provides favorable performance over UMA and NUMA architectures for all ranges of application and system parameters. RCR outperforms LRG architectures when the hit rates of the processor cache exceed 80%and replicated memory exceed 25%. Thus, inclusion of a small replicated memory at each processor significantly reduces expected access time since all replicated memory hits become independent of global traffic. For configurations of up to 32 processors, results show that latency is further reduced by distinguishing burst-mode transfers between isolated memory accesses and those which are incrementally outside the working set.
FAST ALGORITHMS FOR GENERALIZED DISCRETE HARTLEY TRANSFORM
Authors: BI GUOAN , LIAN SHOUTIAN
Published: May 2003

Based on the prime factor decomposition, this paper presents fast algorithms for type-III generalized discrete Hartley transform (GDHT). When N = p*q, where p and q are mutually prime, the length-N GDHT can be decomposed into p length-q type-III GDHT and q length-p type-III discrete cosine transform (DCT). The proposed algorithms achieve a substantial reduction of the number of additions and multiplications and possess a regular computational structure. In particular, a simple index mapping method is proposed to minimize the overall implementation complexity and cost.
NOVEL TEST GENERATION ALGORITHM FOR COMBINATION CIRCUITS
Authors: RAAHEMIFAR K. , AHMADI M.
Published: May 2003

It has been known for many years that combinational circuits have a Complete Test Set (CTS) which is capable of detecting all single and multiple faults. In this paper, we attempt to find CTS systematically. Our algorithm finds a test set which detects all single and multiple stuck-at faults in combinational circuits. This test set is obtained without probing internal nodes, using fault simulation or fault enumeration. It is shown that the test set is independent of logic circuit structure and dependent to the mapping function, number of inputs, outputs, and fanout stems. An upper-bound and lower-bound figures for the number of test vectors required to obtain 100% fault coverage are provided. This number is a small fraction of the entire solution space. A number of recommendations are made to improve the testability of a logic circuit.
IMPLEMENTATION OF A LONG RANGE LRF BY AUTOMATIC MULTI-MODE MEASUREMENT SCHEME
Authors: PARNICHKUN MANUKID , SAMADI VIRAPHAN
Published: May 2003

A long range Laser Range Finder (LRF) is proposed and developed in this paper. A mathematical model, which relates object distance and Position Sensitive Detector (PSD) voltage output is investigated. LRF is a single point optical triangulation instrument, which detects distance information quickly and easily without touching the object being measured. It can be used in real-time control application. This kind of instrument is available in today's market, however, it is limited to a short range application only (maximum range of about 400 mm). The nonlinearity is inherent in this kind of instrument, resulting the sensitivity and accuracy change with the distance nonlinearly. Sensitivity and accuracy becomes worse abruptly when distance to the object being measured is longer than a limited range. The proposed long range LRF is developed to achieve a longer operation range of about 1 m or more. To improve the instrument accuracy at long range, automatic multi-mode measurement scheme is introduced and implemented. The PSD output voltage is selected properly from a corrected mode. Then, it is shifted and scaled depending on the mode of operation before feeding to analog to digital converter-(ADC) automatically. This automatic multi-mode measurement scheme has shown the ability to make the accuracy finer considerably depending on the number of mode being used.
DIRECTED ONE-TIME PASSWORD AUTHENTICATION SCHEME BASED UPON DISCRETE LOGARITHM
Authors: TANG SHAOHUA
Published: May 2003

A new kind of one-time password authentication scheme, directed one-time password authentication scheme, is presented in this paper. The distinguished feature of the directed authentication scheme is that only the specified verifier can validate the verifiee's genuine identity, without the help of this specified verifier, anyone else cannot verify it. One strong directed one-time password authentication scheme based on discrete logarithm is proposed in this paper and the security and performance of which are also analyzed.
MULTISPLITTING WAVEFORM RELAXATION FOR SYSTEMS OF LINEAR INTEGRAL-DIFFERENTIAL-ALGEBRAIC EQUATIONS IN CIRCUIT SIMULATION
Authors: JIANG YAO-LIN , CHEN RICHARD M. M.
Published: May 2003

The multisplitting technique introduced by D. P. O'Leary and R. E. White is applied to treat the waveform relaxation solutions for systems of linear integral-differential-algebraic equations in circuit simulation. The convergence condition of the multisplitting waveform relaxation method which can contain overlapping is established for the continuous-time case. The convergence rates of the relaxation-based method for different multisplittings are compared from the view-point of spectral radii of splitting matrices in systems. Numerical experiments are provided to confirm the new theoretical results.
INDUCTION-ORIENTED VERIFICATION OF REPLICATED ARCHITECTURES DESCRIBED IN VHDL
Authors: PIERRE LAURENCE
Published: May 2003

This paper is concerned with the application of theorem proving techniques to the formal proof of hardware. More precisely, we aim at providing a methodology for applying provers like Nqthm or Acl2 to the formal verification of parameterized replicated circuits. Nqthm (the Boyer–Moore theorem prover) and its successor Acl2 are induction-based systems; their formalisms are respectively a simplified Lisp-like language and Common Lisp. Hence, the circuits we consider must be given a purely functional representation. Moreover, our work puts the emphasis on the integration of formal proof techniques in CAD (Computer Aided Design) environments which support Hardware Description Languages in which replication is expressed by iteration. Therefore, we associate with the iterative statement of the VHDL language a functional semantics that guarantees an easy translation from VHDL to Nqthm/Acl2 while simplifying the subsequent inductive proofs. The approach has been successfully applied to one-dimensional as well as two-dimensional structures.
NONLINEAR COOPERATIVE DYNAMICS OF LIVING NEURONS
Authors: RABINOVICH MIKHAIL I. , VARONA PABLO , ABARBANEL HENDRY D. I.
Published: May 2003

There is a substantial body of experimental evidence that neurons often produce oscillations to achieve their functional goals. They thus behave as dynamical systems despite the fluctuations we observe due to environmental noise and imperfections in their construction. In observations of neural behavior these oscillations can appear "intrinsic" as in the rhythmical pulsing of Central Pattern Generators (CPGs) or the oscillations can arise in response to a stimulus as in the actions of projection neurons in olfactory operation or even in the dynamical response of cortex neurons. When assemblies of neurons perform oscillations, their collective behavior is determined in an essential way by both the nonlinear dynamics of the individuals in the assembly and by the architecture of the neural circuitry.

The neurons inside an assembly can synchronize, possibly with an evident time lag, to produce particular patterns which control the rhythmic muscular activity of an animal, as in CPG operation. The component neurons may compete with each other in a dynamical fashion to solve the problem of pattern recognition, as in the cortex. They may collectively produce rich spatiotemporal behavior in response to specific forms of stimulus from sensory systems.

This is a review of these phenomena which are discussed in language familiar in the description of nonlinear dynamical systems including synchronization and competition. We illustrate our ideas with data from experiment and model simulations for both individual neurons and assemblies of neurons.
EXPERIMENTAL DEFINITION OF THE BASIN OF ATTRACTION FOR CHUA'S CIRCUIT
Authors: PEGNA GUIDO , MARROCU RITA , TONELLI ROBERTO , MELONI FRANCO , SANTOBONI GIOVANNI
Published: May 2003

In this paper we study the experimental determination of the basin of attraction for the Chua's circuit by means of an electronic device that is able to select initial voltages and to show the early stages of the subsequent trajectory on the oscilloscope. The results are shown and discussed in cases of multistability of periodic and chaotic solutions.
CHAOS IN THE REORIENTATION PROCESS OF A DUAL-SPIN SPACECRAFT WITH TIME-DEPENDENT MOMENTS OF INERTIA
Authors: IÑARREA M. , LANCHARES V.
Published: May 2003

We study the spin-up dynamics of a dual-spin spacecraft containing one axisymmetric rotor which is parallel to one of the principal axes of the spacecraft. It will be supposed that one of the moments of inertia of the platform is a periodic function of time and that the center of mass of the spacecraft is not modified. Under these assumptions, it is shown that in the absence of external torques and spinning rotors the system possesses chaotic behavior in the sense that it exhibits Smale's horseshoes. We prove this statement by means of the Melnikov method.

The presence of chaotic behavior results in a random spin-up operation. This randomness is visualized by means of maps of the initial conditions with final nutation angle close to zero. This phenomenon is well described by a suitable parameter that measures the amount of randomness of the process. Finally, we relate this parameter with the Melnikov function in the absence of the spinning rotor and with the presence of subharmonic resonances.
MODELING CHAOTIC DYNAMICS WITH DISCRETE NONLINEAR RATIONAL MODELS
Authors: CORRÊA M. V. , AGUIRRE L. A. , MENDES E. M. A. M.
Published: May 2003

This paper investigates the application of discrete nonlinear rational models, a natural extension of the well-known polynomial models. Rational models are discussed in the context of two different problems: reconstruction of chaotic attractors from a time series and the estimation of static nonlinearities from dynamical data. Rational models are obtained via black box identification techniques which only need a relatively short data set. A simple modified algorithm is proposed to handle the noise thus providing a solution to one of the greatest obstacles for estimating rational models from real data. The suggested algorithm and related ideas are tested and discussed using Rössler's equations, real data collected from an implementation of Chua's circuit, logistic map, sine-map with cubic-type nonlinearities, tent map and a map of a feedback buck switching regulator model.
CONTROLLING CHAOS AND THE INVERSE FROBENIUS–PERRON PROBLEM: GLOBAL STABILIZATION OF ARBITRARY INVARIANT MEASURES
Authors: BOLLT ERIK M.
Published: May 2003

The inverse Frobenius–Perron problem (IFPP) is a global open-loop strategy to control chaos. The goal of our IFPP is to design a dynamical system in ℜnwhich is: (1) nearby the original dynamical system, and (2) has a desired invariant density. We reduce the question of stabilizing an arbitrary invariant measure, to the question of a hyperplane intersecting a unit hyperbox; several controllability theorems follow. We present a generalization of Baker maps with an arbitrary grammar and whose FP operator is the required stochastic matrix.
PARTIAL SYNCHRONIZATION IN A SYSTEM OF COUPLED LOGISTIC MAPS
Authors: TABOROV A. V. , MAISTRENKO Yu. L. , MOSEKILDE E.
Published: May 2003

Clustering (or partial synchronization) in a system of globally coupled chaotic oscillators is studied by means of a model of three coupled logistic maps. For this model we determine the regions in parameter space where total and partial synchronization take place, examine the bifurcations through which total synchronization (one-cluster dynamics) breaks down to give way to two- and three-cluster dynamics, and follow the subsequent transformations of the various asynchronous periodic, quasiperiodic and chaotic states. Different forms of riddling of the basins of attraction for the fully synchronized state are observed, and we discuss the mechanisms through which they arise.
NONLINEAR DYNAMICS OF DRIVEN SINGLE-ELECTRON TUNNELING JUNCTIONS
Authors: YANG TAO , CHUA LEON O.
Published: May 2003

In this paper we investigate the nonlinear dynamics of circuits made of single-electron tunneling junctions (SETJ) driven by a sinusoidal pump and biased by a DC voltage source. The mathematical model of an isolated SETJ circuit is a first-order nonautonomous impulsive differential equation. The tunneling effect of each SETJ can be realistically modeled by the impulsive effect of the junction voltage, which we choose to be the state variable of our circuit model. Based on this model we present theoretical results on the stability of the periodic and almost periodic solutions of driven SETJs. Our theoretical results show there are two phase states in each isolated SETJ circuit, which corresponds to two phase-shifted periodic solutions of our model. We present theoretical and numerical results of return maps of an isolated SETJ circuit. Our results also show that if the tunneling events are equipotentially almost periodic then the attractors generated by two-coupled SETJs will be confined to the vicinity of some periodic orbits. This result provides a foundation for implementing robust logic operations in nanoelectronics.
SELF-ORGANIZATION IN NONRECURRENT COMPLEX SYSTEMS
Authors: ARENA PAOLO , CAPONETTO RICCARDO , FORTUNA LUIGI , RIZZO ALESSANDRO , LA ROSA MANUELA
Published: May 2003

In this paper, systems formed by networks of simple nonlinear cells are studied. Using lattice models, some of the fundamental features of complex systems such as self-organization and pattern formation are illustrated. In the first part of this work, a lattice of identical Chua's circuit is used to experimentally study its global spatiotemporal dynamics, according to the variation of some macroparameters, like the coupling coefficient or the neighboring dimension. The second part of the paper deals with the remarkable improvements regarding regularization and pattern formation, obtained in networks of nonlinear systems by introducing some spatial diversity, especially generated by deterministic, unpredictable dynamics. Simulation results show that synchronization and self-organization occur in networks with a few nonlocally connected cells, with irregular topology and small spatial diversity.
ADAPTIVE BACKSTEPPING CONTROL OF A CLASS OF CHAOTIC SYSTEMS
Authors: GE S. S. , WANG C. , LEE T. H.
Published: May 2003

This paper is concerned with the control of a class of chaotic systems using adaptive backstepping, which is a systematic design approach for constructing both feedback control laws and associated Lyapunov functions. Firstly, we show that many chaotic systems as paradigms in the research of chaos can be transformed into a class of nonlinear systems in the so-called nonautonomous "strict-feedback" form. Secondly, an adaptive backstepping control scheme is extended to the nonautonomous "strict-feedback" system, and it is shown that the output of the nonautonomous system can asymptotically track the output of any known, bounded and smooth nonlinear reference model. Finally, the Duffing oscillator with key constant parameters unknown, is used as an example to illustrate the feasibility of the proposed control scheme. Simulation studies are conducted to show the effectiveness of the proposed method.
DELAYED CONTROL OF A MOORE–GREITZER AXIAL COMPRESSOR MODEL
Authors: AERNOUTS WERNER , ROOSE DIRK , SEPULCHRE RODOLPHE
Published: May 2003

Several feedback control laws have appeared in the literature concerning the stabilization of the nonlinear Moore–Greitzer axial compression model. Motivated by magnitude and rate limitations imposed by the physical implementation of the control law, Larsen et al. studied a dynamic implementation of the S-controller suggested by Sepulchre and Kokotović. They showed the potential benefit of implementing the S-controller through a first-order lag: while the location of the closed-loop equilibrium achieved with the static control law was sensitive to poorly known parameters, the dynamic implementation resulted in a small limit cycle at a very desirable location, insensitive to parameter variations.

In this paper, we investigate the more general case when the control is applied with a time delay. This can be seen as an extension of the model with a first-order lag. The delay can either be a result of system constraints or be deliberately implemented to achieve better system behavior. The resulting closed-loop system is a set of parameter-dependent delay differential equations. Numerical bifurcation analysis is used to study this model and investigate whether the positive results obtained for the first-order model persist, even for larger values of the delay.
A HARTMAN-GROBMAN THEOREM FOR SOME PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS
Authors: BENKHALTI R. , EZZINBI K.
Published: May 2003

We show that the flow of some partial functional differential equations has a global attractor. As a conseqsuence we prove that the flow near a hyperbolic equilibrium is equivalent to its variational equation.
SYNCHRONIZATION DEFECT LINES
Authors: GORYACHEV ANDREI , KAPRAL RAYMOND , CHATÉ HUGUES
Published: May 2003

Spatially distributed reaction–diffusion media where the local dynamics exhibits complex oscillatory or chaotic dynamics are investigated. Spiral waves in such complex-oscillatory or excitable media contain synchronization defect lines which separate domains of different oscillation phases and across which the phase changes by multiples of 2π. Such synchronization defect lines arise from the need to reconcile the rotation period of a one-armed spiral wave with the oscillation period of the local dynamics. We analyze synchronization defect lines and show how to classify them and enumerate their types. In certain parameter regions the spatially distributed system exhibits line defect turbulence arising from the nucleation, growth and destruction of defect lines. The transitions to line defect turbulence may be characterized by power law behavior of order parameters and may be described as nonequilibrium phase transitions.
ALGORITHMS AND VISUALIZATION FOR SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS
Authors: CHEN GOONG , ZHOU JIANXIN , NI WEI-MING
Published: May 2003

In this paper, we compute and visualize solutions of several major types of semilinear elliptic boundary value problems with a homogeneous Dirichlet boundary condition in 2D. We present the mountain–pass algorithm (MPA), the scaling iterative algorithm (SIA), the monotone iteration and the direct iteration algorithms (MIA and DIA). Semilinear elliptic equations are well known to be rich in their multiplicity of solutions. Many such physically significant solutions are also known to lack stability and, thus, are elusive to capture numerically. We will compute and visualize the profiles of such multiple solutions, thereby exhibiting the geometrical effects of the domains on the multiplicity. Special emphasis is placed on SIA and MPA, by which multiple unstable solutions are computed. The domains include the disk, symmetric or nonsymmetric annuli, dumbbells, and dumbbells with cavities. The nonlinear partial differential equations include the Lane–Emden equation, Chandrasekhar's equation, Henon's equation, a singularly perturbed equation, and equations with sublinear growth. Relevant numerical data of solutions are listed as possible benchmarks for other researchers. Commentaries from the existing literature concerning solution behavior will be made, wherever appropriate. Some further theoretical properties of the solutions obtained from visualization will also be presented.
GENERIC HOPF BIFURCATION FROM LINES OF EQUILIBRIA WITHOUT PARAMETERS III: BINARY OSCILLATIONS
Authors: FIEDLER BERNOLD , LIEBSCHER STEFAN , ALEXANDER J. C.
Published: May 2003

We consider discretized systems of hyperbolic balance laws. Decoupling of the flow, associated with a central difference scheme, can lead to binary oscillations — even and odd numbered grid points, separately, provide time-evolutions of two distinct, different, separate profiles.

Investigating the stability of this decoupling phenomenon, we encounter Hopf-like bifurcations in the absence of parameters. With some computer-algebra assistance, we describe the qualitative behavior near these bifurcation points. In particular we observe distinct even/odd profiles which oscillate periodically in time and, for arbitrarily fine discretization, exhibit preferred, nonzero phase relationships between adjacent discretization points.
THE SPATIOTEMPORAL PRISONER'S DILEMMA
Authors: NEMES LÁSZLÓ , CHUA LEON O.
Published: May 2003

A novel platform, the cellular neural network universal machine (CNN-UM) model is proposed to simulate the spatial prisoner's dilemma (SPD) game introduced in [Nowak & May, 1992]. The application of CNN is motivated by both its high conformity with the modeled natural phenomena (analog dynamics) and its superior speed enabling the exploration of the SPD's vast parameter space. Several models are shown as examples of CNN implementation. In particular, a synchronously updated model is introduced using strategy based on best individual strategy (BIS). A new synchronous model is shown based on better average strategy (BAS). Stemming from the CNN implementation of synchronous SPD an asynchronous model has been developed employing BIS, and the survival of clusters of cooperating individuals is demonstrated. This seems to contradict the view elaborated in [Huberman & Glance 1993] claiming that the viability of cooperation is an artifact of synchronous updating in SPD.
CELLULAR NEURAL NETWORKS: LOCAL PATTERNS FOR GENERAL TEMPLATES
Authors: HSU CHENG-HSIUNG , JUANG JONQ , LIN SONG-SUN , LIN WEN-WEI
Published: May 2003

This work investigates the mosaic local patterns for cellular neural networks with general templates. Our results demonstrate that the set of templates can be divided into many finite regions. In each region, the same family of local patterns can be generated. Conversely, our results further demonstrate that some templates can realize a family of local patterns which can be linearly separated by a hyperplane in the configuration space. This study also proposes algorithms for verifying the linear separability for a given family of local patterns and, when it is separable, for obtaining the associated template.
MOSAIC SOLUTIONS AND SPATIAL ENTROPY FOR A CLASS OF NEURAL NETWORK MODELS
Authors: JENNINGS BARBARA , VAN VLECK ERIK S.
Published: May 2003

In this article, we present a lattice differential equation model for a class of neural networks. A subset of the equilibrium solutions called mosaic equilibrium solutions is defined. Existence and stability theorems are proved for mosaic equilibrium solutions. Regions of stability are defined and spatial entropy calculations, as a measure of the complexity of the system, are presented that give insights into the effects of spatial coupling.
POINCARÉ MAPPING OF CONTINUOUS RECURRENT NEURAL NETWORKS EXCITED BY TEMPORAL EXTERNAL INPUT
Authors: SATO SHOZO , GOHARA KAZUTOSHI
Published: May 2003

This paper presents qualitative analyses of the dynamics of continuous-time recurrent neural networks (RNNs) with continuous temporal external input. We show how to analyze continuous-time RNNs using Poincaré mapping. We introduce an input space in which the external input is parametrized, and define the product space which consists of the input space and the phase space. We numerically examine the bifurcation caused by changing the external input in the product space. It is shown that the network dynamics can be considered as rapid transitions in the bifurcation diagram. From the bifurcation viewpoint, the learning process of the RNN can be considered as a process to adjust the bifurcation diagram in order to satisfy a given input–output relation. We also numerically investigate the network behavior against the noise of the external input, and show the qualitative conditions for robustness.
SCENE SEGMENTATION OF THE CHAOTIC OSCILLATOR NETWORK
Authors: ZHAO L. , MACAU E. E. N. , OMAR N.
Published: May 2003

A chaotic oscillatory correlation network for scene segmentation is presented. It is a two-dimensional array with locally coupled chaotic elements. It offers a mechanism to escape from the synchrony–desynchrony dilemma. As a result, this model has unbounded capacity of segmentation. Chaotic dynamics and chaotic synchronization in the model are analyzed. Desynchronization property is guaranteed by the definition of chaos. Computer simulations confirm the theoretical prediction.
DYNAMICS OF THREE COUPLED EXCITABLE CELLS WITH D3 SYMMETRY
Authors: SIGMAN M. , MINDLIN B. G.
Published: May 2003

We study the solutions of a system of three coupled excitable cells with D3 symmetry. The system has two parameters, one controls the local dynamics of each cell and the other the strength of the coupling. We find and describe self-sustained collective oscillations. Periodic solutions appear in global bifurcations, typically after the collapse of fixed points heteroclinically connected. The symmetries of these periodic solutions are the same as the ones expected in periodic solutions which appear in local (Hopf) bifurcations.
PIECEWISE-LINEAR CHAOTIC SYSTEMS WITH A SINGLE EQUILIBRIUM POINT
Authors: YANG TAO , CHUA LEON O.
Published: May 2003

As a unique paradigm for chaos, the various versions of Chua's circuits and equations consists of a three-dimensional autonomous system with a three-segment piecewise-linear function which gives rise to three equilibrium points. This paper considers the possibility of simplifying the system configurations of piecewise-linear chaotic systems based on the structures of Chua's systems. We study a new class of piecewise-linear three-dimensional autonomous system with a three-segment piecewise-linear function. However, unlike Chua's systems, the systems we study in this paper have only single equilibrium points. To find chaotic attractors from this class of systems, we use a systematic random-search process to search the parameter space. The searching process consists of three stages. For the first stage, we simply count the number of points on a Poincaré section and find candidates for chaotic attractors. At the second stage, Lyapunov exponents are calculated for selecting chaotic attractors from the candidates. Finally, bifurcation diagrams constructed around the located chaotic attractors are used to find different types of chaotic attractors. Many qualitatively different chaotic attractors of this class of systems had been found and presented in this paper. Another method to simplify the configurations of a piecewise-linear chaotic system is to reduce the number of segments of the piecewise-linear function. We have developed some chaotic systems with a two-segment piecewise-linear function and which gives rise to two equilibrium points. Many color illustrations of chaotic attractors and bifurcation diagrams are presented.
ABUNDANCE OF TRAVELING WAVES IN COUPLED CIRCLE MAPS
Authors: QIN WEN-XIN
Published: May 2003

In this paper we study the existence of traveling waves with any rational velocity in coupled circle maps. We introduce an induced map, then a traveling wave with velocity p/q corresponds to a fixed point of the induced map. Moreover, the stability of a traveling wave is equivalent to that of the corresponding fixed point. Space translational system is chaotic on the set of traveling waves with rational velocities. In addition, time evolution operator exhibits sensitivity-like behavior with respect to initial conditions. By investigating the spatial periodicity of traveling waves, we obtain infinitely many space-time periodic structures. We also consider spatial asymptoticity of these traveling waves, which leads to the existence of fronts, defect solutions and soliton-like solutions. The abundance of traveling waves may be regarded as a signature of the spatial-temporal complexity in extended systems.
SPATIAL ENTROPY OF ONE-DIMENSIONAL CELLULAR NEURAL NETWORK
Authors: LIN SONG-SUN , YANG TZI-SHENG
Published: May 2003

This work investigates the global mosaic pattern and spatial entropy for one-dimensional cellular neural network (CNN). A novel method is developed to partition the parameter space into finitely many regions. The CNNs, with parameters in each region, have the same global pattern. An algorithm is also presented to evaluate the spatial entropy.
THE EFFECT OF THE FORCING FUNCTION ON DISRUPTION OF A PHASE-LOCKED LOOP (PLL)
Authors: BOOKER S. M. , SMITH P. D. , BRENNAN P. , BULLOCK R.
Published: May 2003

In this paper we compare the disruption of a second-order type II phase-locked loop (PLL) by two different waveforms: a sinusoid and a sawtooth. The choice of these two waveforms results from a novel approach to the problem of determining an appropriate forcing function for studying the disruption of such systems. It is shown that the sawtooth is the better disruptor for low frequencies of modulation, i.e. in the regime of physical interest. Analytical, numerical and experimental results are reported which support this conclusion. The paper presents the first results of a sawtooth modulated PLL, which viewed as a nonsmooth dynamical system with a nonsmooth forcing function is a problem of considerable theoretical interest. This paper demonstrates that forcing functions can be designed for nonlinear dynamical systems which are well suited to the study of certain aspects of the system dynamics, and significantly better than the conventional choice of a simple sinusoid.
ON THE CONSTRUCTION OF TRANSFORMATIONS OF LINEAR HAMILTONIAN SYSTEMS TO REAL NORMAL FORMS
Authors: BUTCHER ERIC A. , SINHA S. C.
Published: May 2003

A technique for constructing the transformations to real Hamiltonian normal forms of linear Hamiltonian systems via permutation matrices is presented. In particular, a method is shown for obtaining the symplectomorphism between the symplectic basis of the real Jordan form to the standard symplectic basis in which the real Hamiltonian normal form resides. All possible degeneracies are accounted for since the algebraic and geometric multiplicities of nonsemisimple eigenvalues are not restricted, including the "difficult" cases of zero and imaginary eigenvalues. Since the normal forms are not unique, several possible arrangements of the suggested transformations are given which result in the various normal forms derived previously as well as in a few new ones for degenerate cases which have not appeared before.
FEEDBACK CONTROL OF THE CHEMOTHERAPY OF HIV
Authors: ALVAREZ-RAMIREZ JOSE , MERAZ MONICA , VELASCO-HERNANDEZ JORGE X.
Published: May 2003

Using a model which describes the interaction of the immune system with the human immunodeficiency virus (HIV), we introduce a feedback control strategy of chemotherapy in an early treatment setting, where the control represents the percentage of effect chemotherapy has on the viral production. We seek to regulate the viral count by manipulating the percentage of effect chemotherapy has on the viral production. We show via numerical simulations that the proposed feedback control strategy can handle strong uncertainties in the HIV dynamics induced by imperfect modeling and sampled/delayed cell measurements.
ORDERING CHAOS IN CHUA'S CIRCUIT: A SAMPLED-DATA FEEDBACK AND DIGITAL REDESIGN APPROACH
Authors: GUO SHU-MEI , SHIEH LEANG S. , CHEN GUANRONG , ORTEGA MARITZA
Published: May 2003

In this paper, we develop and apply some digital design and redesign techniques for ordering the chaotic Chua's circuit. The idea of using sampled-data feedback for controlling the circuit was previously suggested [Yang & Chua, 1998], which relies on small sampling periods. We show how this sampled-data feedback control method can be significantly improved, so that large sampling times are allowed, for the same purpose of ordering the nonlinear circuit, from anywhere within the chaotic attractor towards a predesired periodic cycle of the circuit.
MENTAL CONDITIONS REFLECTED BY THE CHAOS OF PULSATION IN CAPILLARY VESSELS
Authors: SUMIDA TAKEO , ARIMITU YOITCHI , TAHARA TAKASHI , IWANAGA HIROAKI
Published: May 2003

The presence of deterministic chaos has been clarified experimentally in the time series of pulsation of capillary vessels [Tsuda et al., 1992]. In this paper, first we reconfirmed the nonlinearity of the time series of pulsation of capillary vessels with surrogate data testing. Second, we investigated the characteristics of chaos of capillary data on normal subjects in different states of the autonomic nervous system and on psychiatric patients. As a result, the chaotic fluctuations decreased for the state of sympathetic dominance of normal subjects. On the contrary, the chaotic fluctuations increased for the state of parasympathetic predominance of normal subjects. We also found that the chaotic fluctuations decreased in the symptomatic phase of psychiatric patients. Interpretation of this fact is as follows.

Psychiatric patients in symptomatic phase are in a condition of poor flexibility of emotion and motivated behavior in the limbic system. This condition affects the regulation of the autonomic nervous system in the hypothalamus. So it is easy to fall into the imbalance of the autonomic nervous system even with slight stress. Furthermore, in the attractor of capillary chaos we found two parts that showed the role of origin of stimulation of the sympathetic nervous system and that of stimulation of the parasympathetic nervous system, respectively. The geometrical change of topology was caused by the interplay of two parts. From our study we concluded that chaos of pulsation in capillary vessels reflected mental conditions through the autonomic nervous system.
ANALYTICAL ESTIMATES OF THE EFFECT OF NONLINEAR DAMPING IN SOME NONLINEAR OSCILLATORS
Authors: TRUEBA JOSÉ L. , RAMS JOAQUÍN , SANJUÁN MIGUEL A. F.
Published: May 2003

This paper reports on the effect of nonlinear damping on certain nonlinear oscillators, where analytical estimates provided by the Melnikov theory are obtained. We assume general nonlinear damping terms proportional to the power of velocity. General and useful expressions for the nonlinearly damped Duffing oscillator and for the nonlinearly damped simple pendulum are computed. They provide the critical parameters in terms of the damping coefficient and damping exponent, that is, the power of the velocity, for which complicated behavior is expected. We also consider generalized nonlinear damped systems, which may contain several nonlinear damping terms. Using the idea of Melnikov equivalence, we show that the effect of nonlinear dissipation can be equivalent to a linearly damped nonlinear oscillator with a modified damping coefficient.
FAST MULTIFRACTAL ANALYSIS BY RECURSIVE BOX COVERING
Authors: FEENY B. F.
Published: May 2003

A fractal can be generated by using recursion, and a fractal set of data can be analyzed in the same way. This paper discusses a box-counting algorithm which exploits self-similarity via recursion. The speed of the algorithm is O(n), where n is the number of points in the set. The algorithm is applied to multifractal analysis of the binomial multiplicative process. The algorithm does not involve sorting the floating-point summation; a brief examination of the sorting issue is presented. Scattering for negative q, characteristic of box-counting algorithms, is encountered, and is explained for the simple case of a uniform 1-D set.
DISCRETE-TIME CHAOTIC SYSTEMS: APPLICATIONS IN SECURE COMMUNICATIONS
Authors: LIAN KUANG-YOW , CHIANG TUNG-SHENG , LIU PETER
Published: May 2003

The general design for dead-beat and asymptotic synchronizers for a large class of discrete-time chaotic systems is proposed. According to whether the form of the transmitter output (drive signal) is linear, nonlinear or the sum of two, different system structures for synchronization discussions are held. Secure communications is then applied taking into consideration to which state in the transmitter masks the message. Examples of different secure communication schemes are discussed, with a comparison given of the various schemes based on the performance of the receivers ability to recover the message. To accomodate the uncertainty existing in the transmitter parameters, an extended Kalman filter (EKF) algorithm is utilized to estimate both the parameters and states when the message is already embedded. To overcome the problem of high error rates of recovered messages while simultaneously estimating parameters, two alternative methods, namely linear output scheme and indirect scheme, are presented to improve the performance. Numerical simulations for secure communications illustrate a binary signal as the message is recovered and recognizable at the receiver's end.
EFFECTS OF A PARAMETER MISMATCH ON THE SYNCHRONIZATION OF TWO COUPLED CHAOTIC OSCILLATORS
Authors: YANCHUK SERGIY , MAISTRENKO YURI , LADING BRIAN , MOSEKILDE ERIK
Published: May 2003

Considering two identical, coupled Rössler systems, the paper first examines the bifurcations through which low-periodic orbits embedded into the synchronized chaotic state lose their transverse stability and produce the characteristic picture of riddled basins of attraction. The paper hereafter addresses the issue of the robustness of the synchronized chaotic state to a mismatch of the parameter values between the two subsystems. It is shown that the synchronized state is shifted away from the symmetric manifold, and the magnitude of this shift is expressed in terms of the coupling strength and the mismatch parameter. Finally, the paper illustrates how similar phenomena can be observed in a system of two coupled chaotic oscillators describing the spiking behavior of biological cells.
MANIPULATED SYNCHRONIZATION: BEAM STEERING IN PHASED ARRAYS
Authors: HEATH TED , WIESENFELD KURT , YORK ROBERT A.
Published: May 2003

We consider a relatively new application of mutually interacting, synchronized oscillators. The idea is to intentionally introduce variations among the elements to induce phase shifts between the oscillators. Though often unwanted, in certain instances these phase shifts are highly desirable: We discuss how to manipulate array parameters in order to steer and scan the beam emanating from radiating arrays.
PHASE SYNCHRONIZATION OF CHAOS IN A PLASMA DISCHARGE TUBE
Authors: ROSA EPAMINONDAS , PARDO WILLIAM B. , TICOS CATALIN M. , WALKENSTEIN JONATHAN A. , MONTI MARCO
Published: May 2003

Experimental phase synchronization of chaos is demonstrated for a plasma discharge tube subject to a high dc voltage (800–900 V), and paced with a low amplitude (less than 1 V) wave generator.
EXPERIMENTAL OBSERVATION OF LAG SYNCHRONIZATION IN COUPLED CHAOTIC SYSTEMS
Authors: TAHERION SAEED , LAI YING-CHENG
Published: May 2003

Chaotic lag synchronization is a subtle dynamical phenomenon in which the states of two mutually coupled, nonidentical chaotic oscillators follow each other with a fixed time delay. We investigate to what extent lag synchronization can be observed in laboratory experiments. Our measurements indicate that due to the influence of noise, lag synchronization appears to occur intermittently in time. Numerical confirmation and a heuristic explanation to the observed intermittent behavior are given.
QUANTIFICATION OF SYNCHRONIZATION PROCESSES BY COHERENCE AND PHASE AND ITS APPLICATION IN ANALYSIS OF ELECTROPHYSIOLOGICAL SIGNALS
Authors: SCHACK BÄRBEL , RAPPELSBERGER PETER , ANDERS CHRISTOPH , WEISS SABINE , MÖLLER EVA
Published: May 2003

Neuronal activity during information processing and muscle activity are generally characterized by oscillations. Mostly, widespread areas are involved and electrophysiological signals are measured on different sites of the cortex or of the muscle.

In order to investigate functional relationships between different components of multidimensional electrophysiological signals, coherence and phase analyses turned out to be useful tools. These parameters allow the investigation of synchronization phenomena with regard to oscillations of defined frequencies or frequency bands.

Coherence and phase are closely connected spectral parameters. Coherence may be understood as a measure of phase stability. Whereas coherence describes the amount of common information with regard to oscillations within certain frequency bands, the corresponding phase, from which time delays of these oscillations can be computed, hints at the direction of information transfer through oscillation.

Coherence and phase analysis of surface EMG during continuous activity of deep and superficial muscles show distinct differences due to volume conduction properties of myoelectrical signals. Superficial activity therefore is characterized by significant coherence and stable phase relationships, which, additionally, can be used to determine motor unit action potential (MUAP) propagation velocity along the fibre direction without application of invasive methods. Deep muscle activity lacks significant coherence.

Mental processes can be very brief and cooperation between different areas may be highly dynamic. For this reason in addition to usual Fourier estimation of coherence and phase, a two-dimensional approach of adaptive filtering was developed to estimate coherence and phase continuously in time. Statistical and dynamic properties of instantaneous phase are discussed.

In order to demonstrate the value of this method for studying higher cognitive processes the method was applied to EEG recorded during word processing. During visual presentation of abstract nouns an information transfer through the propagation of oscillations from visual areas to frontal association areas in the α1-frequency band could be verified within the first 400 ms. In contrast, in case of auditory presentation positive phases from the temporal electrode locations T3 and T4 towards the occipital areas appear within the time interval of 300 ms–600 ms. The α1-band predominately seems to reflect sensory processing and attention processes.
FEEDBACK SYNCHRONIZATION USING POLE-PLACEMENT CONTROL
Authors: TONELLI ROBERTO , LAI YING-CHENG , GREBOGI CELSO
Published: May 2003

Synchronization in chaotic systems has become an active area of research since the pioneering work of Pecora and Carroll. Most existing works, however, rely on a passive approach: A coupling between chaotic systems is necessary for their mutual synchronization. We describe here a feedback approach for synchronizing chaotic systems that is applicable in high dimensions. We show how two chaotic systems can be synchronized by applying small feedback perturbations to one of them. We detail our strategy to design the control based on the pole-placement method, and give numerical examples.
CHAOTIC PHASE SYNCHRONIZATION BASED ON BINARY COUPLING SIGNALS
Authors: PARLITZ ULRICH , WEDEKIND IMMO
Published: May 2003

It is shown that phase synchronization of chaotic dynamical systems can be achieved using a binary coupling signal that takes only two possible values. This phenomenon is demonstrated using analog electronic implementations of the Rössler system and Chua's oscillator.