bluuebunny/crossref_metadata_2025 huggingface dataset:
ON INTEGRABILITY OF DIFFERENTIAL EQUATIONS DEFINED BY THE SUM OF HOMOGENEOUS VECTOR FIELDS WITH DEGENERATE INFINITY
Authors: CHAVARRIGA J. , GARCÍA I. A. , GINÉ J.
Published: April 2003

The paper deals with polynomials systems with degenerate infinity from different points of view. We show the utility of the projective techniques for such systems, and a more detailed study in the quadratic and cubic cases is carried out. On the other hand, some results on Darboux integrability in the affine plane for a class of systems are given. In short we show the explicit form of generalized Darboux inverse integrating factors for the above kind of systems. Finally, a short proof of the center cases for arbitrary degree homogeneous systems with degenerate infinity is given, and moreover we solve the center problem for quartic systems with degenerate infinity and constant angular speed.
NUMERICAL BIFURCATION ANALYSIS OF DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY
Authors: LUZYANINA TATYANA , ENGELBORGHS KOEN , ROOSE DIRK
Published: April 2003

In this paper we apply existing numerical methods for bifurcation analysis of delay differential equations with constant delay to equations with state-dependent delay. In particular, we study the computation, continuation and stability analysis of steady state solutions and periodic solutions. We collect the relevant theory and describe open theoretical problems in the context of bifurcation analysis. We present computational results for two examples and compare with analytical results whenever possible.
DISCONTINUOUS BIFURCATIONS OF CHAOTIC ATTRACTORS IN FORCED OSCILLATORS BY GENERALIZED CELL MAPPING DIGRAPH (GCMD) METHOD
Authors: HONG LING , XU JIANXUE
Published: April 2003

Discontinuous bifurcations of chaotic attractors are investigated by means of Generalized Cell Mapping Digraph (GCMD) method. The two categories of discontinuous bifurcations of chaotic attractors are found in typical systems described by dissipative ordinary differential equations, namely catastrophic and explosive bifurcations. For the case of a catastrophe, the two different types, namely a regular saddle and a chaotic saddle catastrophe, are studied, in particular, the subtle distinction between them can be explicitly observed in phase portrait. We show that a regular saddle catastrophe results from a collision between a chaotic attractor and a regular saddle on its smooth basin boundary. In such a case the chaotic attractor is suddenly destroyed as the parameter passes through a critical value, leaving behind a nonattracting chaotic saddle in the place of the original chaotic attractor in phase space. We demonstrate that a chaotic saddle catastrophe results from a collision between a chaotic attractor and a chaotic saddle in its fractal basin boundary. In such a case the chaotic attractor is suddenly destroyed as the parameter passes through a critical value, simultaneously the chaotic saddle also undergoes an abrupt enlargement in its size, namely, the chaotic attractor is converted into a new incremental portion of the chaotic saddle after the collision. For the case of an explosion, a chaotic saddle explosion is studied, in which there is a sudden increase in the size of a chaotic attractor as the parameter passes through a critical value. We demonstrate that at the chaotic saddle explosion the chaotic attractor collides with a chaotic saddle already existent when the explosion occurs. This chaotic saddle is an invariant and nonattracting set. We also investigate the origin and evolution of the chaotic saddle. A locally refining process of Generalized Cell Mapping (GCM) method is developed to refine persistent and transient self-cycling sets. The refining procedures of persistent and transient self-cycling sets are respectively given on the basis of their definitions in the cell state space.
PEAKONS AND THEIR BIFURCATION IN A GENERALIZED CAMASSA–HOLM EQUATION
Authors: LIU ZHENGRONG , QIAN TIFEI
Published: April 2003

Camassa and Holm [1993] recently derived a new dispersive shallow water equation known as the Camassa–Holm equation. They showed that it also has solitary wave solutions which have a discontinuous first derivative at the wave peak and thus are called "peakons".

In this paper, from the mathematical point of view, we study the peakons and their bifurcation of the following generalized Camassa–Holm equation [Formula: see text] with a>0, k∈ℝ, m∈ℕ and the integral constants taken as zero. Using the bifurcation method of the phase plane, we first give the phase portrait bifurcation, then give the integral expressions of peakons through the bifurcation curves and the phase portraits, and finally obtain the peakon bifurcation parameter value and the number of peakons. For m=1, 2, 3, we give the explicit expressions for the peakons. It seems that the bifurcation method of phase planes is good for the study of peakons in nonlinear integrable equations.
BIFURCATIONS ON ELLIPTIC FUNCTIONS
Authors: BALIBREA FRANCISCO , CHACÓN RICARDO , LÓPEZ MIGUEL ÁNGEL
Published: April 2003

In this paper we are dealing with the dynamical properties of the Jacobian elliptic functions, cosine-amplitude and sine-amplitude. Seen as one parameter dynamical systems, they present a flip type bifurcation at the origin. In fact they are particular cases of some general families of functions holding sufficient conditions we call degenerate.
NEWTON'S METHOD AND MORSE INDEX FOR SEMILINEAR ELLIPTIC PDEs
Authors: NEUBERGER JOHN M. , SWIFT JAMES W.
Published: April 2003

In this paper we primarily consider the family of elliptic PDEs Δu+f(u) = 0 on the square region Ω=(0, 1)×(0, 1) with zero Dirichlet boundary condition. Following our previous analysis and numerical approximations which relied on the variational characterization of solutions as critical points of an "action" functional, we consider Newton's method on the gradient of that functional. We use a Galerkin expansion, in eigenfunctions of the Laplacian, to find solutions of arbitrary Morse index. Taking f′(0) to be a bifurcation parameter, we analyze the bifurcations from the trivial solution, u≡0, using symmetry arguments and our numerical algorithm. The Morse index of the approximated solutions is provided and support is found concerning several existence and nodal structure conjectures. We discuss the applicability of this method to find critical points of functionals in general.
ON CRITICAL CURVES IN TWO-DIMENSIONAL ENDOMORPHISMS
Authors: CATHALA J. C.
Published: April 2003

Properties of the critical curves of noninvertible maps are studied using the representation of the plane in the form of sheets. In such a representation, every sheet is associated with a well-defined determination of the inverse map which leads to a foliation of the plane directly related to fundamental properties of the map. The paper describes the change of the plane foliation occurring in the presence of parameter variations, leading to a modification of the nature of the map by crossing through a foliation bifurcation. The degenerated map obtained at the foliation bifurcation is characterized by the junction of more than two sheets on a critical curve segment. Examples illustrating these situations are given.
SELF-SIMILAR STRUCTURE OF RESCALED EVOLUTION SETS OF CELLULAR AUTOMATA I
Authors: HAESELER F. v. , PEITGEN H.-O. , SKORDEV G.
Published: April 2003

The self-similarity properties of the orbits of a class of cellular automata are deciphered by matrix substitutions, hierarchical iterated function systems and appropriate scaling procedure.
AUTOMATIC DETECTION OF SLIGHT CHANGES IN NONLINEAR DYNAMICAL SYSTEMS USING MULTIRESOLUTION ENTROPY TOOLS
Authors: TORRES M. E. , AÑINO M. M. , GAMERO L. G. , GEMIGNANI M. A.
Published: April 2003

The continuous multiresolution entropy, which combines advantages stemming from both classical entropy and wavelet analysis, has shown to be sensitive to dynamical complexity changes. The addition of classical statistical changes detection tools gives rise to a new tool that allows their automatic detection. In this paper, a new tool for the automatic detection of slight parameter changes in nonlinear dynamical systems from the analysis of the corresponding time series is proposed. The relevance of the approach, together with its robustness in the presence of moderate noise, is discussed in numerical simulations and it is applied to biological signals.
SURROGATE DATA PATHOLOGIES AND THE FALSE-POSITIVE REJECTION OF THE NULL HYPOTHESIS
Authors: RAPP P. E. , CELLUCCI C. J. , WATANABE T. A. A. , ALBANO A. M. , SCHMAH T. I.
Published: April 2003

It is shown that inappropriately constructed random phase surrogates can give false-positive rejections of the surrogate null hypothesis. Specifically, the procedure erroneously indicated the presence of deterministic, nonlinear structure in a time series that was constructed by linearly filtering normally distributed random numbers. It is shown that the erroneous identification was due to numerical errors in the estimation of the signal's Fourier transform. In the example examined here, the introduction of data windowing into the algorithm eliminated the false-positive rejection of the null hypothesis. Additional guidelines for the use of surrogates are considered, and the results of a comparison test of random phase surrogates, Gaussian scaled surrogates and iterative surrogates are presented.
SELF-SIMILAR STRUCTURE OF RESCALED EVOLUTION SETS OF CELLULAR AUTOMATA II
Authors: HAESELER F. v. , PEITGEN H.-O. , SKORDEV G.
Published: April 2003

The description of the rescaled evolution set of p-Fermat cellular automata developed in the first part of this paper is applied for the calculation of the Hausdorff dimension of this set. The scaling procedure is analyzed and an appropriate scaling sequence for cellular automata with states in the integers modulo m is given. New proof of the main theorem of the first part of the paper is presented for the linear cellular automata with states in the integers modulo a power of prime number.
WAVE AND BASIN STRUCTURE IN SPATIALLY COUPLED MAGNETO-ELASTIC BEAM SYSTEM — TRANSITIONS BETWEEN COEXISTING WAVE SOLUTIONS
Authors: HIKIHARA TAKASHI , TORII KENTARO , UEDA YOSHISUKE
Published: April 2003

Standing and traveling waves are well-known phenomena of the coupled ordinary differential equations in many fields. The wave solutions of the coupled system are considered to be similar to the partial differential equation of the system. In this paper, the waves which appear in a coupled magneto-elastic beam system are discussed theoretically and numerically. The physical system is continuous elastically and discrete magnetically. There are several classes of models describing the system behavior. The Galerkin method is one of the powerful methods used to analyze the dynamics of the spatially distributed structure. The numerical solutions appearing in the coupled ordinary differential equation must show the spatially discrete characteristics even in the distributed system. However, most of the results obtained in the coupled systems are not more than the numerical approximation of the related partial differential equations. The large number of oscillators are given for the approximation. In this paper, the relationship between the coupled magneto-elastic beam system and the modified KdV equation is established by using the long wave approximation. However, in the short wavelength range, the approximation to the partial differential equation has no physical rationality. Therefore, the analysis of the difference–differential equation provides an important place of knowledge filling up the gap between the characteristics of the physical model and the numerical approximation.
DYNAMICAL SYSTEMS OF DIFFERENT CLASSES AS MODELS OF THE KICKED NONLINEAR OSCILLATOR
Authors: KUZNETSOV A. P. , TURUKINA L. V. , MOSEKILDE E.
Published: April 2003

Using the nonlinear dissipative kicked oscillator as an example, the correspondence between the descriptions provided by model dynamical systems of different classes is discussed. A detailed study of the approximate 1D map is undertaken: the period doubling is examined and the possibility of non-Feigenbaum period doubling is shown. Illustrations in the form of bifurcation diagrams and sets of iteration diagrams are given, the scaling properties are demonstrated, and the tricritical points (the terminal points of the Feigenbaum critical curves) in parameter space are found. The congruity with the properties of the corresponding 2D map, the Ikeda map, is studied. A description in terms of tricritical dynamics is found to be adequate only in particular areas of parameter space.
STATE-SPACE SELF-TUNING CONTROL FOR NONLINEAR STOCHASTIC AND CHAOTIC HYBRID SYSTEMS
Authors: GUO SHU-MEI , SHIEH LEANG-SAN , LIN CHING-FANG , CHANDRA JAGDISH
Published: April 2003

This paper presents a new state-space self-tuning control scheme for adaptive digital control of continuous-time multivariable nonlinear stochastic and chaotic systems, which have unknown system parameters, system and measurement noises, and inaccessible system states. Instead of using the moving average (MA)-based noise model commonly used for adaptive digital control of linear discrete-time stochastic systems in the literature, an adjustable auto-regressive moving average (ARMA)-based noise model with estimated states is constructed for state-space self-tuning control of nonlinear continuous-time stochastic systems. By taking advantage of a digital redesign methodology, which converts a predesigned high-gain analog tracker/observer into a practically implementable low-gain digital tracker/observer, and by taking the non-negligible computation time delay and a relatively longer sampling period into consideration, a digitally redesigned predictive tracker/observer has been newly developed in this paper for adaptive chaotic orbit tracking. The proposed method enables the development of a digitally implementable advanced control algorithm for nonlinear stochastic and chaotic hybrid systems.
ADAPTIVE BACKSTEPPING CONTROL OF UNCERTAIN LORENZ SYSTEM
Authors: WANG C. , GE S. S.
Published: April 2003

In this paper, we consider the problem of controlling chaos in the well-known Lorenz system. Firstly we show that the Lorenz system can be transformed into a kind of nonlinear system in the so-called general strict-feedback form. Then, adaptive backstepping design is used to control the Lorenz system with three key parameters unknown. By exploiting the property of the system, the resulting controller is singularity free, and the closed-loop system is stable globally. Simulation results are conducted to show the effectiveness of the approach.
BIFURCATIONS IN ONE DEGREE-OF-VIBRATION QUANTUM BILLIARDS
Authors: PORTER MASON A. , LIBOFF RICHARD L.
Published: April 2003

We classify the local bifurcations of one dov quantum billiards, showing that only saddle-center bifurcations can occur. We analyze the resulting planar system when there is no coupling in the superposition state. In so doing, we also consider the global bifurcation structure. Using a double-well potential as a representative example, we demonstrate how to locate bifurcations in parameter space. We also discuss how to approximate the cuspidal loop using AUTO as well as how to cross it via continuation by detuning the dynamical system. Moreover, we show that when there is coupling, the resulting five-dimensional system — though chaotic — has a similar underlying structure. We verify numerically that both homoclinic orbits and cusps occur and provide an outline of an analytical argument for the existence of such homoclinic orbits. Small perturbations of the system reveal homoclinic tangles that typify chaotic behavior.
SELF-OSCILLATIONS AND SLIDING IN RELAY FEEDBACK SYSTEMS: SYMMETRY AND BIFURCATIONS
Authors: BERNARDO MARIO DI , JOHANSSON KARL HENRIK , VASCA FRANCESCO
Published: April 2003

This paper is concerned with the bifurcation analysis of linear dynamical systems with relay feedback. The emphasis is on the bifurcations of the system periodic solutions and their symmetry. It is shown that, despite what has been conjectured in the literature, a symmetric and unforced relay feedback system can exhibit asymmetric periodic solutions. Moreover, the occurrence of periodic solutions characterized by one or more sections lying within the system discontinuity set is outlined. The mechanisms underlying their formation are carefully studied and shown to be due to an interesting, novel class of local bifurcations.
ON TWO MECHANISMS OF THE DOMAIN STRUCTURE OF VENTRICULAR FIBRILLATION
Authors: BIKTASHEV V. N. , HOLDEN A. V. , MIRONOV S. F. , PERTSOV A. M. , ZAITSEV A. V.
Published: April 2003

Analysis of optically recorded irregular electrical wave activity on the surface of the heart during experimentally induced fibrillation reveals a strong local temporal periodicity. The spatial distribution of the dominant temporal frequencies of excitation has a domain organization. The domains are large (≈1 cm 2) and they persist for minutes. We demonstrate that these data can be reproduced in a two-dimensional excitable medium governed by the FitzHugh–Nagumo equations with a spatial inhomogeneity. We identified two potential mechanisms that may contribute to the observed experimental dynamics: coexistence of stable spiral waves with noncommensurate frequencies of rotation, and Wenckebach-like frequency division from a single spiral source due to inhomogeneity. The number of domains is not an index of the number of wave sources. Both mechanisms reproduce the uniformity of the dominant frequency within individual domains and sharp boundaries between domains. The possibility of distinguishing between different mechanisms using Lissajous figures is discussed.
BIFURCATIONS IN SYNAPTICALLY COUPLED BVP NEURONS
Authors: TSUMOTO K. , YOSHINAGA T. , KAWAKAMI H.
Published: April 2003

We investigate bifurcations of periodic solutions in model equations of two and three Bonhöffer–van der Pol (BVP) neurons coupled through the characteristics of synaptic transmissions with a time delay. Bifurcations of the coupled BVP neurons are compared with bifurcations of synaptically coupled Hodgkin–Huxley neurons. We obtained a parameter set of the BVP system, such that the two systems are qualitatively very similar from a bifurcational point of view. This study is a base for the analysis of synaptically coupled neurons with a large number of coupling strategies.
THE HISTORIC STRATEGIST
Authors: ALONSO-SANZ RAMÓN , MARTÍN M. CARMEN , MARTÍN MARGARITA
Published: April 2003

The basic aim of this paper is to extend earlier work on assessing the effect of considering previous results (history) in the evolutionary dynamics of the spatial formulation of the Prisoner's Dilemma. In the simpler historic models considered earlier, players did not elaborate strategies. In the present work one-dimensional strategies are followed by the players. Both synchronous and asynchronous updating schemes have been taken into account. It is concluded here that the essential result found in the no-strategies scenario remains valid when keeping historic memory of payoffs, moves and of the strategies themselves: history induces a preserving effect.
LASER EXPERIMENTS AND THEORETICAL MODELING FOR THE DIAGNOSIS OF BIFURCATION SEQUENCES OF AN OSCILLATING ELECTRODE REACTION
Authors: KARANTONIS ANTONIS , SHIOMI YUKA , NAKABAYASHI SEIICHIRO
Published: April 2003

The existence of stable and unstable attractors is investigated experimentally for an electrochemical system consisting of a ring iron electrode immersed in sulfuric acid solution. The applied potential is considered as the bifurcation parameter whereas an external resistance is considered as a second parameter of the system. The stable and unstable states of the system are revealed by combining steady state and laser perturbation experiments with the bifurcation characteristics. A structure of the steady state curve is proposed that can predict the experimental dynamical response. The system is modeled by considering the electrode potential and the concentration of one of the ionic species as dynamical variables. The resulting boundary value problem is studied numerically and a comparison between the experimental and theoretical results is performed. It is shown that the model can predict most of the experimental behavior in a good qualitative agreement.
EXPERIMENTAL EVIDENCE ON THE STRUCTURE AND EVOLUTION OF THE PENTA–HEPTA DEFECT IN HEXAGONAL LATTICES DUE TO BÉNARD–MARANGONI CONVECTION
Authors: AFENCHENKO V. O. , EZERSKY A. B. , NAZAROVSKY A. V. , VELARDE M. G.
Published: April 2003

Evidence is provided to show that the penta–hepta defect in a Bénard convective hexagonal lattice arises as a result of the attraction of two dislocations having opposite topological charges and belonging to different modes. The dislocations approach each other along a corridor connecting those topological charges. Fields of long–living penta–hepta defects have been analyzed. The comparison of experimental results with recent numerical calculations and solutions obtained analytically shows good qualitative agreement.
BIFURCATIONS OF ONE-DIMENSIONAL REACTION–DIFFUSION EQUATIONS
Authors: LI CHANGPIN , CHEN GUANRONG
Published: April 2003

Bifurcations of a class of one-dimensional reaction–diffusion equations of the form u″+μu-uk=0, where μ is a parameter, 2≤k∈Z+, with boundary value condition u(0)=u(π)=0, are investigated. Using the singularity theory based on the Liapunov–Schmidt reduction, some characterization results are obtained.
COMPUTATION OF SIMPLEST NORMAL FORMS OF DIFFERENTIAL EQUATIONS ASSOCIATED WITH A DOUBLE-ZERO EIGENVALUE
Authors: YUAN Y. , YU P.
Published: April 2003

In this paper a method is presented for computing the simplest normal form of differential equations associated with the singularity of a double zero eigenvalue. Based on a conventional normal form of the system, explicit formulae for both generic and nongeneric cases are derived, which can be used to compute the coefficients of the simplest normal form and the associated nonlinear transformation. The recursive algebraic formulae have been implemented on computer systems using Maple. The user-friendly programs can be executed without any interaction. Examples are given to demonstrate the computational efficiency of the method and computer programs.
MULTIFRACTAL SPECTRUM AND THERMODYNAMICAL FORMALISM OF THE FAREY TREE
Authors: PIACQUADIO M. , CESARATTO E.
Published: April 2003

Let (Ω, μ) be a set of real numbers to which we associate a measure μ. Let α≥0, let Ωα={x∈Ω/α(x)=α}, where α is the concentration index defined by Halsey et al. [1986]. Let fH(α) be the Hausdorff dimension of Ωα. Let fL(α) be the Legendre spectrum of Ω, as defined in [Riedi & Mandelbrot, 1998]; and fC(α) the classical computational spectrum of Ω, defined in [Halsey et al., 1986]. The task of comparing fH, fCand fLfor different measures μ was tackled by several authors [Cawley & Mauldin, 1992; Mandelbrot & Riedi, 1997; Riedi & Mandelbrot, 1998] working, mainly, on self-similar measures μ. The Farey tree partition in the unit segment induces a probability measure μ on an universal class of fractal sets Ω that occur in physics and other disciplines. This measure μ is the Hyperbolic measure μℍ, fundamentally different from any self-similar one. In this paper we compare fH, fCand fLfor μℍ.
TIME-FREQUENCY ANALYSIS OF CLASSICAL TRAJECTORIES OF POLYATOMIC MOLECULES
Authors: VELA-AREVALO LUZ V. , WIGGINS STEPHEN
Published: April 2003

We present a new method of frequency analysis for Hamiltonian Systems of 3 degrees of freedom and more. The method is based on the concept of instantaneous frequency extracted numerically from the continuous wavelet transform of the trajectories. Knowing the time-evolution of the frequencies of a given trajectory, we can define a frequency map, resonances, and diffusion in frequency space as an indication of chaos. The time-frequency analysis method is applied to the Baggott Hamiltonian to characterize the global dynamics and the structure of the phase space in terms of resonance channels. This 3-degree-of-freedom system results from the classical version of the quantum Hamiltonian for the water molecule given by Baggott [1988]. Since another first integral of the motion exists, the so-called Polyad number, the system can be reduced to 2 degrees of freedom. The dynamics is therefore simplified and we give a complete characterization of the phase space, and at the same time we could validate the results of the time-frequency analysis.
SYNCHRONIZATION OF CHAOTIC SYSTEMS: A GENERALIZED HAMILTONIAN SYSTEMS APPROACH
Authors: SIRA-RAMÍREZ HEBERTT , CRUZ-HERNÁNDEZ CÉSAR
Published: April 2003

A reapproach to chaotic systems synchronization is presented from the perspective of passivity-based state observer design in the context of Generalized Hamiltonian systems including dissipation and destabilizing vector fields. The synchronization and lack of synchronization of several well-studied chaotic systems is reexplained in these terms.
AN INVERSE SYSTEM APPROACH FOR CHAOTIC COMMUNICATIONS
Authors: ALVAREZ-RAMIREZ JOSE , PUEBLA HECTOR , SOLIS-DAUN JULIO
Published: April 2003

In this paper, an inverse system approach for communications using chaotic signals is presented. In this approach, the transmitter contains a chaotic oscillator with an input that is modulated by the information signal. The receiver is a linear asymptotic approximation to the inverse system and contains an integral feedback to cope with nonlinearities. Some effects of transmission noise on the demodulation procedure are discussed. Numerical simulations on the Chua's circuit are provided to illustrate our findings.
DRIVING TRAJECTORIES IN CHAOTIC SYSTEMS
Authors: MACAU E. E. N. , GREBOGI C.
Published: April 2003

This work presents the main ideas and the fundamental procedures for guiding trajectories on chaotic systems and for stabilizing chaotic orbits, all with the use of small perturbations. We consider an extension of the Ott–Grebogi–Yorke method of controlling chaos and an associated procedure for guiding trajectories on chaotic sets of high dimensional systems. We argue that those techniques can be used even if the chaotic invariant set is nonattractive. As nonattractive chaotic invariant sets commonly exist embedded in high dimensional systems, we also argue that we can combine chaotic control techniques with system control strategies to generate a powerful mechanism for manipulating the dynamics. We present an example in which we change and alter system's evolution at will using only small perturbations to some accessible parameter.
A DIRECT COMPUTATION OF THE PHASE STABILITY CRITERION FOR SPATIALLY HOMOGENEOUS TIME PERIODIC SOLUTIONS CLOSE TO A HOPF BIFURCATION
Authors: RISLER EMMANUEL
Published: April 2003

We provide an elementary direct computation of the classical criterion governing the (linear) phase stability under inhomogeneous perturbations of a spatially homogeneous periodic orbit close to a spatially homogeneous supercritical Hopf bifurcation.
SPATIAL DISORDER OF CNN — WITH ASYMMETRIC OUTPUT FUNCTION
Authors: BAN JUNG-CHAO , CHIEN KAI-PING , LIN SONG-SUN , HSU CHENG-HSIUNG
Published: April 2003

This investigation will describe the spatial disorder of one-dimensional Cellular Neural Networks (CNN). The steady state solutions of the one-dimensional CNN can be replaced as an iteration map which is one dimensional under certain parameters. Then, the maps are chaotic and the spatial entropy of the steady state solutions is a three-dimensional devil-staircase like function.
CODIMENSION TWO BIFURCATIONS IN A PREDATOR–PREY SYSTEM WITH GROUP DEFENSE
Authors: XIAO DONGMEI , RUAN SHIGUI
Published: April 2003

In this paper we study the qualitative behavior of a predator–prey system with nonmonotonic functional response. The system undergoes a series of bifurcations including the saddle-node bifurcation, the supercritical Hopf bifurcation, and the homoclinic bifurcation. For different parameter values the system could have a limit cycle or a homoclinic loop, or exhibit the so-called "paradox of enrichment" phenomenon. In the generic case, the model has the bifurcation of cusp-type codimension two (i.e. the Bogdanov–Takens bifurcation) but no bifurcations of codimension three.
INTELLIGENCE AND COOPERATIVE SEARCH BY COUPLED LOCAL MINIMIZERS
Authors: SUYKENS JOHAN A. K. , VANDEWALLE JOOS , DE MOOR BART
Published: April 2003

We show how coupling of local optimization processes can lead to better solutions than multistart local optimization consisting of independent runs. This is achieved by minimizing the average energy cost of the ensemble, subject to synchronization constraints between the state vectors of the individual local minimizers. From an augmented Lagrangian which incorporates the synchronization constraints both as soft and hard constraints, a network is derived wherein the local minimizers interact and exchange information through the synchronization constraints. From the viewpoint of neural networks, the array can be considered as a Lagrange programming network for continuous optimization and as a cellular neural network (CNN). The penalty weights associated with the soft state synchronization constraints follow from the solution to a linear program. This shows that the energy cost of the ensemble should maximally decrease. In this way successful local minimizers can implicitly impose their state to the others through a mechanism of master–slave dynamics resulting in a cooperative search mechanism. Improved information spreading within the ensemble is obtained by applying the concept of small-world networks. We illustrate the new optimization method on two different problems: supervized learning of multilayer perceptrons and optimization of Lennard–Jones clusters. The initial distribution of the local minimizers plays an important role. For the training of multilayer perceptrons this is related to the choice of the prior on the interconnection weights in Bayesian learning methods. Depending on the choice of this initial distribution, coupled local minimizers (CLM) can avoid overfitting and produce good generalization, i.e. reach a state of intelligence. In potential energy surface optimization of Lennard–Jones clusters, this choice is equally important. In this case it can be related to considering a confining potential. This work suggests, in an interdisciplinary context, the importance of information exchange and state synchronization within ensembles, towards issues such as evolution, collective behavior, optimality and intelligence.
CLOSURES OF FRACTAL SETS IN NONLINEAR DYNAMICAL SYSTEMS WITH SWITCHED INPUTS
Authors: WADA RYOICHI , GOHARA KAZUTOSHI
Published: April 2003

This paper studies closures of fractal sets observed in nonlinear dynamical systems excited stochastically by switched inputs. The Duffing oscillator and the forced dumped pendulum are analyzed as examples. The dynamics of the system is characterized by a fractal set in the phase space. We can numerically construct a closure that encloses the fractal set. Furthermore, it is shown that the closure is a limit cycle attractor of a dynamical system defined by the switching manifold.
COMBINATORIAL CONTROL OF GLOBAL DYNAMICS IN A CHAOTIC DIFFERENTIAL EQUATION
Authors: BOLLT ERIK M.
Published: April 2003

Controlling chaos has been an extremely active area of research in applied dynamical systems, following the introduction of the Ott, Grebogi, Yorke (OGY) technique in 1990 [Ott et al., 1990], but most of this research based on parametric feedback control uses local techniques. Associated with a dynamical system which pushes forward initial conditions in time, transfer operators, including the Frobenius–Perron operator, are associated dynamical systems which push forward ensemble distributions of initial conditions. In [Bollt, 2000a, 2000b; Bollt & Kostelich, 1998], we have shown that such global representations of a discrete dynamical system are useful in controlling certain aspects of a chaotic dynamical system which could only be accessible through such a global representation. Such aspects include invariant measure targeting, as well as orbit targeting. In this paper, we develop techniques to show that our previously discrete time techniques are accessible also to a differential equation. We focus on the Duffing oscillator as an example. We also show that a recent extension of our techniques by Góra and Boyarsky [1999] can be further simplified and represented in a convenient and compact way by using a tensor product.
LOCAL STABILITY, HOPF AND RESONANT CODIMENSION-TWO BIFURCATION IN A HARMONIC OSCILLATOR WITH TWO TIME DELAYS
Authors: LIAO XIAOFENG , CHEN GUANRONG
Published: April 2003

A harmonic oscillator with two discrete time delays is considered. The local stability of the zero solution of this equation is investigated by analyzing the corresponding transcendental characteristic equation of its linearized equation and employing the Nyquist criterion. Some general stability criteria involving the delays and the system parameters are derived. By choosing one of the delays as a bifurcation parameter, the model is found to undergo a sequence of Hopf bifurcation. The direction and stability of the bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. Resonant codimension-two bifurcation is also found to occur in this model. A complete description is given to the location of points in the parameter space at which the transcendental characteristic equation possesses two pairs of pure imaginary roots, ±iω1, ±iω2 with ω1:ω2 = m:n, where m and n are positive integers. Some numerical examples are finally given for justifying the theoretical results.
BIFURCATION ANALYSIS IN FLEXIBLE ROTOR SUPPORTED BY ACTIVE MAGNETIC BEARING
Authors: JANG MING-JYI , CHEN CHA'O-KUANG
Published: April 2003

In this paper, bifurcation analysis of the dynamic response of active magnetic bearing (AMB) with flexible rotor is presented, which includes the coupling effect between X-Y directions caused by rotational motion. The AMB systems include many nonlinear factors, such as mass imbalance, mass ratio with disk and journal, material property of shaft, and magnetic forces, etc., and its dynamic behavior are inherently nonlinear. Bifurcation diagrams of shaft journal's center, trajectories, power spectra, and Poincaré maps are used to analyze the dynamic behavior of the AMB system under different operational conditions. The key factors affecting the dynamic characteristics of the AMB system are identified. It will be beneficial to the design of AMB system.
FORMALIZING THE FUNCTIONAL MODEL WITHIN OBJECT-ORIENTED DESIGN
Authors: WANG ENOCH Y. , CHENG BETTY H. C.
Published: April 2003

The data flow diagram (DFD), originally introduced for structured design purposes, depicts the functions that a system or a module should provide. The objective of a software system is to implement specific functionalities. The function-oriented decomposition strategy of DFDs in the conventional design process for structured design conflicts with the spirit of object-orientation. So far, there is no object-oriented method that has successfully integrated DFDs into the object-oriented development process. In this paper, we demonstrate how DFDs can be modified in order to be integrated into object-oriented development. The Object Modeling Technique (OMT) is used as the context for object-oriented development. In addition, a set of formalization rules are proposed to provide formal semantics for DFDs in order to integrate the functional model with the other two models of OMT, namely, the object and dynamic models, in terms of the underlying formal semantics.
PLANNING SUPPORT TO SOFTWARE PROCESS EVOLUTION
Authors: CONRADI REIDAR , NGUYEN MINH NGOC , WANG ALF INGE , LIU CHUNNIAN
Published: April 2003

The ability to handle changes is a characteristic feature of successful software projects. The problem addressed in this paper is what should be done in project planning and iterative replanning so that the project can react effectively to changes. Thus the work presents research results in software engineering, as well as transfer of methods in knowledge engineering to software engineering, applying the AI planning technique to software process modeling and software project management. Our method is based on inter-project experience and evolution patterns. We propose a new classification of software projects, identifying and characterizing ten software process evolution patterns and link them to different project profile. Based on the evolution patterns, we discuss the planning support for process evolution and propose several methods that are new or significantly extend existing work, e.g. cost estimation of process changes, evolution pattern analysis, and a coarse process model for the initial planning and the iterative replanning process. The preliminary results have shown that the study of evolution patterns, based on inter-project experience, can provide valuable guidance in software process understanding and improvement.
FORMAL SUPPORT FOR AN INFORMAL BUSINESS MODELLING METHOD
Authors: CHEN-BURGER YUN-HEH , ROBERTSON DAVID , STADER JUSSI
Published: April 2003

Business modelling methods are popular but, since they operate primarily in the early stages of software lifecycles, most are informal. This paper describes how we have used a conventional formal notation (first order predicate logic) in combination with automated support tools to replicate the key components of an established, informal, business modelling method: IBM's Business System Development Method (BSDM). We describe the knowledge which we represent formally at each stage in the method and explain how the move from informal to formal representation allows us to provide guidance and consistency checking during the development lifecycle of the model. It also allows us to extend the original method to a model execution phase which is not described in the original informal method. The role of the formal notation in this case is not to provide a formal semantics for BSDM but to provide a framework for sharing the information supplied at different modelling stages and which we can supplement with simple forms of automated analysis.
SPECIFICATION OF SOFTWARE ARCHITECTURE
Authors: GERKEN MARK J.
Published: April 2003

Over the past several years, software architecture representation and analysis has become an active area of research. However, most approaches to software architecture representation and analysis have been informal. We postulate that through formality, the term "architecture" can be precisely defined and important properties of systems, such as semantic compatibility between connected entities, can be investigated with precision. In this paper, we use category theory and algebraic specifications to develop a formal definition of architecture and show how architecture theory can be used in the construction of software specifications.
AN APPROACH TO QUANTITATIVE SOFTWARE ARCHITECTURE SENSITIVITY ANALYSIS
Authors: LUNG CHUNG-HORNG , KALAICHELVAN KALAI
Published: April 2003

Software architectures are often claimed to be robust. However, there is no explicit and concrete definition of software architecture robustness. This paper gives a definition of software architecture robustness and presents a set of architecture metrics that were applied to real-time telecommunications software for the evaluation of robustness. The purpose of this study is to provide a structured method to support software architecture evaluations and downstream software implementations. The study also expands the software architecture research to quantitative and measurable evaluations as opposed to qualitative assessments. In addition, this paper presents an empirical case study of applying the metrics. The approach and the metrics data provide insights into software architecture sensitivity analysis on system qualities and trade-off analysis among a set of design alternatives to support product evolution.
USING FUZZY REASONING TO SUPPORT AUTOMATED PROGRAM UNDERSTANDING
Authors: BURNSTEIN ILENE , SANER FLOYD
Published: April 2003

In this paper we describe how fuzzy reasoning can assist an automated program understanding/fault localization tool with program understanding tasks. We are developing such a tool called BUG-DOCTOR, which is based on a blackboard framework. A fuzzy reasoner is proposed as a component for one of its knowledge sources, the Plan Processor. The Plan Processor retrieves a set of program plans from a plan library using indices called signatures. These plans are candidates for matching against the code we are trying to understand. The fuzzy reasoner will support the Plan Processor with the task of ranking the retrieved plans in order of similarity to the target code. The most highly ranked plan can then be used for the complex plan/code matching required for automated program understanding. Experiments with a fuzzy reasoning prototype are promising, and we believe that this approach to plan processing may eliminate the need for exhaustive plan library searches. The success of the fuzzy reasoning approach could lead to automated program understanders that scale up for use on large software systems from a variety of problem domains.
CASE-BASED SOFTWARE QUALITY PREDICTION
Authors: GANESAN K. , KHOSHGOFTAAR TAGHI M. , ALLEN EDWARD B.
Published: April 2003

Highly reliable software is becoming an essential ingredient in many systems. However, assuring reliability often entails time-consuming costly development processes. One cost-effective strategy is to target reliability-enhancement activities to those modules that are likely to have the most problems. Software quality prediction models can predict the number of faults expected in each module early enough for reliability enhancement to be effective.

This paper introduces a case-based reasoning technique for the prediction of software quality factors. Case-based reasoning is a technique that seeks to answer new problems by identifying similar "cases" from the past. A case-based reasoning system can function as a software quality prediction model. To our knowledge, this study is the first to use case-based reasoning systems for predicting quantitative measures of software quality.

A case study applied case-based reasoning to software quality modeling of a family of full-scale industrial software systems. The case-based reasoning system's accuracy was much better than a corresponding multiple linear regression model in predicting the number of design faults. When predicting faults in code, its accuracy was significantly better than a corresponding multiple linear regression model for two of three test data sets and statistically equivalent for the third.
CREATING TOOLS IN A SOFTWARE ENVIRONMENT BASED ON GRAPH REWRITING RULES
Authors: DE LUCIA A. , TORTORA G. , TUCCI M.
Published: April 2003

This paper presents the software development workbench WSDW (Web structure-oriented Software Development Workbench) together with the tool development language TDL. WSDW is an integrated structure-oriented software environment which contains several tools for software evolution. The integration of tools is achieved by sharing a program representation which is based upon the mathematical concept of relation: the web structure is the basic high level representation of programs within the environment. The TDL language is a structure-oriented language that supports the creation of a wide variety of tools both for software development and maintenance. The elementary statements in a TDL program are web rewriting rules and manipulations of programs are expressed as web transformations. Moreover, to make program transformations more intuitive to the tool programmer, web rewriting rules are expressed graphically. Each tool in WSDW performs a sequence of web transformations and new software tools can be implemented as TDL programs and integrated into WSDW.
TEST SCENARIO GENERATION BASED ON FORMAL SPECIFICATION AND USAGE PROFILE
Authors: CHANG KAI H. , LIAO SHIH-SUNG , CHAPMAN RICHARD , CHEN CHUN-YU
Published: April 2003

This paper presents a method for test scenario generation based on formal specifications and usage profiles. It is a major component of a framework for testing object-oriented programs. In this framework, the requirements of a software system are formally specified. The anticipated application of the system is expressed in a usage profile, which is a state model that indicates the dynamic behavior of the system and execution probabilities for the behaviors. The state model is used as a guide to derive the anticipated operation scenarios. An enhanced state transition diagram is used to represent the state model, which incorporates hierarchy, usage and parameter information. Since the number of feasible scenarios can be extremely large, probability and importance criteria are used to select the most probable and important scenarios.
CONSTRUCTING FLOW-BASED TOOLS WITH GENERATIVE AND COMPOSITIONAL TECHNIQUES
Authors: YANG JI-TZAY , WANG FENG-JIAN , CHU WILLIAM C. , HU CHUNG-HUA
Published: April 2003

In this paper, a model called object-oriented attribute grammar (OOAG), which combines both compositional and generative techniques, is presented to effectively construct flow-based tools that deal with fine-grained language semantics as well as a mass of graphics-drawing activities. OOAG, which consists of two interrelated parts: a model-view-shape (MVS) class framework and an AG++, an object-oriented extension to traditional AGs, is intended to preserve both advantages introduced by respective OO and AG models, such as rapid prototyping, reusability, extensibility, incrementality, and applicability. So far, a flow-based editor associated with two flow-analyzer prototypes, DU/UD tools and a program slicer, have been implemented using OOAG on the Windows environment. Our flow-based editor can be used to construct programs by specifying the associated flow information in a visual way, while (incremental) flow analyzers incorporated into the editor can help analyze incomplete program fragments to locate and inform the user of possible errors or anomalies during programming.
FROM SOFTWARE REUSE TO DATABASE REUSE
Authors: EGYHAZY C. J.
Published: April 2003

Our principal objective in this paper is to show how we have adapted a domain analysis methodology, used previously in software reuse, to the formulation of a single query against federated databases. Currently, we query federated databases by writing queries against each of the legacy databases, merge the responses, and resolve syntactic and semantic differences manually. Such a solution places unacceptable expectations on most users, thus being impractical. In this paper, we propose an approach that requires the instantiation of a single query_class specification against federated databases, that also resolves simple syntactic and semantic differences on demand, without using a global schema for member databases. We illustrate the approach by instantiating a single query_class specification built against three legacy database schemata. In summary, domain analysis tools not only facilitate the formulation of query specifications, but they also help to resolve the database heterogeneity problem.
VERIFYING REQUIREMENTS THROUGH MATHEMATICAL MODELLING AND ANIMATION
Authors: KAZMIERCZAK EDMUND , DART PHILIP , STERLING LEON , WINIKOFF MICHAEL
Published: April 2003

Achieving confidence in the correctness, completeness and consistency of requirements specifications can be problematic and the consequences of incorrect requirements can be costly. In this paper we argue that specification and animation can provide reasonably high levels of assurance in the requirements without the overheads of using general purpose theorem proving tools. We propose a framework based on mode analysis and the operational semantics of logic programs for animating specifications. The framework allows us to combine prototyping and limited forms of automated deduction to increase our levels of confidence in specifications. Finally, we show how such a framework can be used to increase the level of confidence in the correctness of a simple dependency management system specification written in Z.