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This paper re-evaluates the security of a chaotic image encryption algorithm called MCKBA/ HCKBA and finds that it can be broken efficiently with two known plain-images and the corresponding cipher-images. In addition, it is reported that a previously proposed breaking on MCKBA/HCKBA can be further improved by reducing the number of chosen plain-images from four to two. The two attacks are both based on the properties of solving a composite function involving the carry bit, which is composed of the modulo addition and the bitwise OR operations. Both rigorous theoretical analysis and detailed experimental results are provided. [ABSTRACT FROM AUTHOR]

Escape time algorithm is a classical algorithm to calculate the Julia sets, but it has the disadvantage of dull color and cannot record the iterative process of the points. In this paper, we present the equipotential point algorithm to calculate the Julia sets by recording the strike frequency of the points in the iterative process. We calculate and analyze the Julia sets in the complex plane by using this algorithm. Finally, we discuss the iteration trajectory of a single point. [ABSTRACT FROM AUTHOR]

In this paper, the problem of pinning impulsive synchronization for complex dynamical networks with directed or undirected but a strongly connected topology is investigated. To remedy this problem, we propose an efficient algorithm to find certain suitable nodes to be controlled via pinning and these selected nodes, in general, could be different at distinct impulsive time instants. The proposed algorithm guarantees the efficiency of the designed pinning impulsive strategy for the global exponential synchronization of state-coupled dynamical networks under an easily-verified condition. In other words, impulsive controllers and an efficient algorithm are designed to control a small fraction of the nodes, which successfully controls the whole dynamical network. Furthermore, we also estimate the upper bound of the number of pinning nodes, which is shown to be closely related to the impulsive intervals. The relationship implies that the required number of pinning nodes, which should be controlled for the successful control of the whole dynamical network, can be greatly reduced by reducing the impulses interval. Finally, simulations of scale-free and small-world networks are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we present a simple and accessible way to enhance the stable behaviors of a chaotic dynamical system which models a cancer growth, as presented in [Itik & Banks, 2010]. The algorithm presented in [Danca et al., 2012], approximates numerically any attractor of a system belonging to a defined class of dynamical systems, by alternating the control parameter in relatively short periods of time. When switching the control parameter within a set of values corresponding to some chaotic behaviors, the result may be a stable evolution or, reversely a chaotic behavior may be obtained by switching the parameter within a set of values corresponding to stable evolutions. This apparently surprising phenomenon is, in fact, a generalization of the known Parrondo's paradox. [ABSTRACT FROM AUTHOR]

Applying gear shifting algorithms to the implementation of Phase Locked Loops (PLLs) can significantly improve their performances. However, the behaviors of gear shifting digital PLLs (GSDPLLs) have not been fully studied due to the existence of newly adaptive control parameters. These parameters play a very important role in the design of GSDPLLs. In this paper, various nonlinear behaviors of GSDPLLs including the steady state periodic behaviors, divergent behaviors and chaotic behaviors, are studied. In particular, the effects of the initial conditions of GSDPLLs on their dynamical behaviors are investigated. The obtained results are useful for the design of GSDPLLs. Numerical simulation results are presented for illustrations. [ABSTRACT FROM AUTHOR]

The past few years have witnessed the great success of a new family of paradigms, social tagging networks, which allows users to freely associate social tags to items and efficiently manage them. Thus it provides us a promising way to effectively find useful and interesting information. In this paper, we consider two typical roles of social tags: (i) an accessorial tool helping users organize items; (ii) a bridge that connects users and items. We then propose a hybrid algorithm to integrate the two different roles to obtain better recommendation performance. Experimental results on a real-world data set, Del.icio.us, shows that it can significantly enhance both the algorithmic accuracy and diversity. [ABSTRACT FROM AUTHOR]

A complete characterization of the stability boundary of a class of nonlinear dynamical systems that admit energy functions is developed in this paper. This characterization generalizes the existing results by allowing the type-zero saddle-node nonhyperbolic equilibrium points on the stability boundary. Conceptual algorithms to obtain optimal estimates of the stability region (basin of attraction) in the form of level sets of a given family of energy functions are derived. The behavior of the stability region and the corresponding estimates are investigated for parameter variation in the neighborhood of a type-zero saddle-node bifurcation value. [ABSTRACT FROM AUTHOR]

In this paper, we examine the localization problem of compact invariant sets of discrete-time nonlinear systems. The localization procedure consists in applying the iterative algorithm based on the extremum condition. An analysis of a location of compact invariant sets of the Henon system is realized for all values of its parameters. [ABSTRACT FROM AUTHOR]

In this paper, a symbolic dynamical model of the average queue size of the random early detection (RED) algorithm is proposed. The conditions for both the system parameters and the initial conditions that the average queue size of the RED algorithm would converge to a fixed point are derived. These results are useful for network engineers to design both the system parameters and the initial conditions so that internet networks can achieve a good performance. [ABSTRACT FROM AUTHOR]

In this paper, we consider bifurcation of limit cycles in near-Hamiltonian systems. A new method is developed to study the analytical property of the Melnikov function near the origin for such systems. Based on the new method, a computationally efficient algorithm is established to systematically compute the coefficients of Melnikov function. Moreover, we consider the case that the Hamiltonian function of the system depends on parameters, in addition to the coefficients involved in perturbations, which generates more limit cycles in the neighborhood of the origin. The results are applied to a quadratic system with cubic perturbations to show that the system can have five limit cycles in the vicinity of the origin. [ABSTRACT FROM AUTHOR]

In this paper, we design a cellular automaton and a discrete-time cellular neural network (DTCNN) using nonlinear passive memristors. They can perform a number of applications, such as logical operations, image processing operations, complex behaviors, higher brain functions, RSA algorithm, etc. By modifying the characteristics of nonlinear memristors, the memristor DTCNN can perform almost all functions of memristor cellular automaton. Furthermore, it can perform more than one function at the same time, that is, it allows multitasking. [ABSTRACT FROM AUTHOR]

Chaos based encryption may offer new quality in secure data transmission. A recently proposed Chaotic-Key Based Algorithm (CKBA) has been shown to be unavoidably susceptible to chosen/known-plaintext attacks and ciphertext-only attacks. In this paper, Hyper Chaotic-Key Based Algorithm (HCKBA) using hyper chaos is proposed to enhance the security of CKBA. The enhanced security of the proposed algorithm is analyzed through cryptanalysis. Further, VLSI architecture of the proposed algorithm is designed. The VLSI architecture is implemented on an image using XILINX's ModelSim to demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

A short review is given of recent papers on the relaxation to (incompressible) absolute equilibrium. A new algorithm to construct absolute equilibrium of spectrally truncated compressible flows is described. The algorithm uses stochastic processes based on the Clebsch representation of the velocity field to generate density and velocity fields that follow by construction the absolute equilibrium stationary probability. The new method is shown to reproduce the well-known Gaussian results in the incompressible limit. The irrotational compressible absolute equilibrium case is characterized and the distribution is shown to be non-Gaussian. The high-temperature compressible spectra are found not to obey k2 scaling. Finally, oscillating behavior in constant-pressure variable-temperature relaxation is obtained, suggesting the presence of second sound. [ABSTRACT FROM AUTHOR]

This paper addresses the cryptanalysis of three chaos-based secure communication schemes recently proposed by Yu et al. [2007]. Attacks with adaptive observers designed by the dynamical minimization algorithm are assumed. Considering Kerckhoff's principle, i.e. assuming that the basic structure of a cryptosystem is known but some user-specified parameters remain in secret, it is demonstrated that the covered messages in all these schemes can be estimated and hence their securities are challenged. [ABSTRACT FROM AUTHOR]

This stage of our journey through the universe of one-dimensional binary Cellular Automata is devoted to period-1 rules, constituting the first of the six groups in which we systematized the 88 globally-independent CA rules. The first part of this article is mainly dedicated to reviewing the terminology and the empirical results found in the previous papers of our quest. We also introduce the concept of the ω-limit orbit with the purpose of linking our work to the classical theory of nonlinear dynamical systems. Moreover, we present the basin tree diagrams of all period-1 rules — except for rule $\kern.5pt{\fboxsep2pt\fbox{0}}\kern.5pt\xspace$, which is trivial — along with their Boolean cubes and time-1 characteristic functions. In the second part, we prove a theorem demonstrating that all rules belonging to group 1 have robust period-1 rules for any finite, and infinite, bit-string length L. This is the first time we give analytical results on the behavior of CA local rules for large values of L and, consequently, for bi-infinite bit strings. The theoretical treatment is complemented by two remarkable practical results: an explicit formula for generating isomorphic basin trees, and an algorithm for creating new periodic orbits by concatenation. We also provide several examples of both of them, showing how they help to avoid tedious simulations. [ABSTRACT FROM AUTHOR]

The study of the local behavior of nonlinear systems in the neighborhood of a periodic orbit is a classical problem in nonlinear dynamics. Most of our knowledge stems from simulations or the numerical integration of the variational equation. Only in the case of planar oscillators, the solution of the variational equation can be found analytically, provided that an explicit expression for the periodic trajectory is available. The aim of this paper is to extend a classical theorem due to S. P. Diliberto to higher dimensional systems. In doing so, we show how the fundamental matrix solution to the variational equation of higher order differential equations can be obtained in a closed analytical form. To obtain this result, the knowledge of the periodic trajectory is not sufficient anymore, and a specific set of orthogonal vectors has to be determined. The analysis of some examples reveals that finding these vectors may be easier than solving the variational equations. [ABSTRACT FROM AUTHOR]

In this paper, we first establish a rational iteration method which can be used as a root-finding algorithm for almost every polynomial. It has no nonrepelling extraneous fixed point in the complex plane and is generally convergent for both quadratic and cubic polynomials. Then some properties of this algorithm are given. By the aid of computer, we produce pictures of the Julia sets for the iterations of some polynomials. Numerical results show that it is a root-finding method with convergence order the same as Halley's method. [ABSTRACT FROM AUTHOR]

The localization of critical parameter sets called bifurcations is often a central task of the analysis of a nonlinear dynamical system. Bifurcations of codimension 1 that can be directly observed in nature and experiments form surfaces in three-dimensional parameter spaces. In this paper, we propose an algorithm that combines adaptive triangulation with the theory of complex systems to compute and visualize such bifurcation surfaces in a very efficient way. The visualization can enhance the qualitative understanding of a system. Moreover, it can help to quickly locate more complex bifurcation situations corresponding to bifurcations of higher codimension at the intersections of bifurcation surfaces. Together with the approach of generalized models the proposed algorithm enables us to gain extensive insights in the local and global dynamics not only in one special system but in whole classes of systems. To illustrate this ability we analyze three examples from different fields of science. [ABSTRACT FROM AUTHOR]

This paper studies the bifurcation and chaos phenomena in average queue length in a developed Transmission Control Protocol (TCP) model with Random Early Detection (RED) mechanism. Bifurcation and chaos phenomena are nonlinear behavior in network systems that lead to degradation of the network performance. The TCP/RED model used is a model validated previously. In our study, only the average queue size $\bar{q}_k$ is considered, and the results are based on analytical model rather than actual measurements. The instabilities in the model are studied numerically using the conventional nonlinear bifurcation analysis. Extending from this bifurcation analysis, a modified RED algorithm is derived to prevent the observed bifurcation and chaos regardless of the selected parameters. Our modification is for the simple scenario of a single RED router carrying only TCP traffic. The algorithm neither compromises the throughput nor the average queuing delay of the system. [ABSTRACT FROM AUTHOR]

This paper introduces the notion of chaos synthesis by means of evolutionary algorithms and develops a new method for chaotic systems synthesis. This method is similar to genetic programming and grammatical evolution and is being applied along with three evolutionary algorithms: differential evolution, self-organizing migration and genetic algorithm. The aim of this investigation is to synthesize new and "simple" chaotic systems based on some elements contained in a prechosen existing chaotic system and a properly defined cost function. The investigation consists of eleven case studies: the aforementioned three evolutionary algorithms in eleven versions. For all algorithms, 100 simulations of chaos synthesis were repeated and then averaged to guarantee the reliability and robustness of the proposed method. The most significant results were carefully selected, visualized and commented in this report. [ABSTRACT FROM AUTHOR]

Random number generators are widely used in different applications. However, it is difficult to obtain a good random number generator in low precision and resource constrained system, such as an eight-bit micro-controller system which is still commonly used in industrial and consumer markets. This paper provides a practical solution for this problem based on chaotic systems. By the use of a modified Chua's circuit, it is demonstrated that the sampled state, after post-processing by a high-dimensional chaotic map, can be used as a random source even in an eight-bit environment. The randomness of the generated sequence is testified and confirmed by different statistical tests and the up-to-date statistical suite. [ABSTRACT FROM AUTHOR]

In recent years, a growing number of cryptosystems based on chaos have been proposed. But most of them have encountered many problems such as small key space and weak security. In the present paper, a new kind of chaotic cryptosystem based on Composition of Trigonometric Chaotic Maps is proposed. These maps which are defined as ratios of polynomials of degree N, have interesting properties such as invariant measure, ergodicity, variable chaotic region with respect to the control parameters and ability to construct composition form of maps. We have used a composition of chaotic map to shuffle the position of image pixels. Another composition of chaotic map is used in diffusion process. According to the performed analysis, the introduced algorithm can satisfy the required performances such as high level security, large key space and the acceptable encryption speed. [ABSTRACT FROM AUTHOR]

In this paper, we study fingerprint feature extraction via CNN with Von Neumann neighborhood. The extraction was implemented by using CNN with nine input variables, and we find that the process could also be implemented with only five variables, and an easier algorithm without compromising the effectiveness. According to the CNN model with five input variables and the corresponding CNN gene bank done by Chen et al. [2006, Http1], we can determine the CNN gene easily. Simultaneously, we also find some results in one of the references are incorrect. [ABSTRACT FROM AUTHOR]

In this paper we present some new tearing techniques to systematically formulate the state equations in symbolic normal-form for linear and/or nonlinear time-invariant large-scale analog circuits. The excess elements of the first and of the second kind are unitarily treated in order to allow a symbolic representation of the circuit with a minimum number of state variables. A procedure to reduce the state equation number of each subcircuit is also presented. The reduced-order is based on an implicit integration algorithm and on the successive elimination of the selected state variables. Examples are given to illustrate the decomposition procedure, the assignment of the connection sources and the reduced-order technique. [ABSTRACT FROM AUTHOR]

An algorithm that can decide, prior to performing the circuit analysis, if a procedure for the fast computation of the periodic steady state is necessary, is presented in this paper. The analysis of a switching supply illustrates how this algorithm works. [ABSTRACT FROM AUTHOR]

During the past decade a large number of chaos-based encryption systems have been suggested and investigated. Cryptographical analysis of these systems shows that some of them are cryptographically weak. In this paper, some general design rules for chaos-based encryption systems are derived based on strengths and weaknesses of already suggested systems. [ABSTRACT FROM AUTHOR]

We present a computer-assisted analysis of the phase space features and bifurcations of a noninvertible, discrete-time system. Our focus is on the role played by noninvertibility in generating disconnected basins of attraction and the breakup of invariant circle solutions. Transitions between basin of attraction structures are identified and organized according to "levels of complexity," a term we define in this paper. In particular, we present an algorithm that provides a computational approximation to the boundary (in phase space) separating points with different preimage behavior. The interplay between this boundary and other phase space features is shown to be crucial in understanding global bifurcations and transitions in the structure of the basin of attraction. [ABSTRACT FROM AUTHOR]

In this paper, we examine the localization problem of compact invariant sets of systems with the differentiable right-side. The localization procedure consists in applying the iterative algorithm based on the first order extremum condition originally proposed by one of authors for periodic orbits. Analysis of a location of compact invariant sets of the Lanford system is realized for all values of its bifurcational parameter. [ABSTRACT FROM AUTHOR]

Networks of neurons can perform computations that even modern computers find very difficult to simulate. Most of the existing artificial neurons and artificial neural networks are considered biologically unrealistic, nevertheless the practical success of the backpropagation algorithm and the powerful capabilities of feedforward neural networks have made neural computing very popular in several application areas. A challenging issue in this context is learning internal representations by adjusting the weights of the network connections. To this end, several first-order and second-order algorithms have been proposed in the literature. This paper provides an overview of approaches to backpropagation training, emphazing on first-order adaptive learning algorithms that build on the theory of nonlinear optimization, and proposes a framework for their analysis in the context of deterministic optimization. [ABSTRACT FROM AUTHOR]

In this paper, the combination of unsupervised clustering algorithms with feedforward neural networks in exchange rate time series forecasting is studied. Unsupervised clustering algorithms have the desirable property of deciding on the number of partitions required to accurately segment the input space during the clustering process, thus relieving the user from making this ad hoc choice. Combining this input space partitioning methodology with feedforward neural networks acting as local predictors for each identified cluster helps alleviate the problem of nonstationarity frequently encountered in real-life applications. An improvement in the one-step-ahead forecasting accuracy was achieved compared to a global feedforward neural network model for the time series of the exchange rate of the German Mark to the US Dollar. [ABSTRACT FROM AUTHOR]

Clustering can be defined as the process of "grouping" a collection of objects into subsets or clusters. The clustering problem has been addressed in numerous contexts and by researchers in different disciplines. This reflects its broad appeal and usefulness as an exploratory data analysis approach. Unsupervised clustering algorithms have been developed to address real world problems in which the number of clusters present in the dataset is unknown. These algorithms approximate the number of clusters while performing the clustering procedure. This paper is a first step towards the development of unsupervised clustering algorithms capable of identifying clusters within clusters. To this end, an unsupervised clustering algorithm is modified so as to take into consideration the fractal dimension of the data. The experimental results indicate that this approach can provide further qualitative information compared to the unsupervised clustering algorithm. [ABSTRACT FROM AUTHOR]

This paper explores the use of the nonextensive q-distribution in the context of adaptive stochastic searching. The proposed approach consists of generating the "probability" of moving from one point of the search space to another through a probability distribution characterized by the q entropic index of the nonextensive entropy. The potential benefits of this technique are investigated by incorporating it in two different adaptive search algorithmic models to create new modifications of the diffusion method and the particle swarm optimizer. The performance of the modified search algorithms is evaluated in a number of nonlinear optimization and neural network training benchmark problems. [ABSTRACT FROM AUTHOR]

This paper presents an iterative method for locating invariant tori of maps. Specifically, through the introduction of a shift function on the torus corresponding to the projection of the dynamics on the torus onto toral parameters, a discrete system of equations may be formulated whose solution approximates the spatial location of the torus. As invariant tori of continuous flows may be considered invariant under the application of the flow for a fixed time, or may correspond to invariant tori (of one less dimension) of suitably introduced Poincaré maps, the methodology applies to discrete and continuous dynamical systems alike. Moreover, the insensitivity of the method to the local stability characteristics of the invariant torus as well as to the precise nature of the flow on the torus imply, for example, that the method can be employed for the continuation of unstable invariant tori on which the dynamics are attracted to a periodic trajectory as long as the torus is sufficiently smooth. The proposed methodology as well as reduced formulations that result from a priori knowledge about the invariant torus are illustrated through some sample dynamical systems. [ABSTRACT FROM AUTHOR]

In this paper, we report on pattern formation occurring on the ACE16k CNN chip. The CNN chip can be programmed with a cloning template in order to generate spiral waves and autowaves. The waves diffract from internal sources which cannot be relocated on the network. However, by using initial and/or input images, sources (external sources) can be located at any place on the network. Furthermore a competition between autowaves generated by external and internal sources is observed. Propagation of autowaves on the inhomogeneous CNN array, formed by the fixed-state map, is presented. [ABSTRACT FROM AUTHOR]

A comparison between polynomial and wavelet expansions for the identification of coupled map lattice (CML) models for deterministic spatiotemporal dynamical systems is presented in this paper. The pattern dynamics generated by smooth and nonsmooth nonlinear maps in a well-known two-dimensional CML structure are analyzed. By using an orthogonal feedforward regression algorithm (OFR), polynomial and wavelet models are identified for the CML's in chaotic regimes. The quantitative dynamical invariants such as the largest Lyapunov exponents and correlation dimensions are estimated and used to evaluate the performance of the identified models. [ABSTRACT FROM AUTHOR]

This paper introduces a new application of the Field Programmable Analog Array. Ease of design and reprogrammability are the advantages offered by this class of analog circuits, making them an ideal environment for the implementation of chaotic circuits and their experimental characterization. Chua's circuit, a well-known paradigm of nonlinear circuits, has been used as an example of application. Experimental results show the suitability of the approach, highlighting the features of the new implementation: a fully on the fly programmable Chua's circuit has been obtained. [ABSTRACT FROM AUTHOR]

In this paper, a two-neuron network with different time delays is investigated. By analyzing the associated characteristic equation, we obtain the conditions for delay-dependent and delay-independent asymptotic stability, respectively. Furthermore, we find that if the delay is used as a bifurcation parameter, Hopf bifurcation would occur. The direction and stability of the bifurcating periodic solutions are determined by using the Nyquist criterion and the graphical Hopf bifurcation theorem. Some examples are included to illustrate our results. [ABSTRACT FROM AUTHOR]

We investigate mechanical spatial equilibria of slender elastic rods with intristic curvature. Our work is, to some extent, motivated by papers [Goriely & Tabor, 1998; Goriely & McMillen 2002]. There such rods of infinite length were recently studied to quantify the behavior of botanical filaments. In particular, an adequate explanation for the existence of helical perversions (the transition between helical segments of opposite handedness) is provided in [Goriely & Tabor, 1998]. However, this theory fails to describe multiple perversions, which can be observed in Nature. In contrast we formulate a two-point boundary-value problem describing rods of finite length with initial curvature and clamped ends. We identify trivial solutions as straight configurations and also k-covered circles, rigorously establish the existence of local bifurcations, and then compute global solutions via the Parallel Hybrid Algorithm [Domokos & Szeberényi, 2004] to find spatially complex equilibria characterized by multiple perversions. Based on computational results and the White–Fuller theorem [White, 1969; Fuller, 1971; Calugareanu, 1961] we describe a heuristic global picture of the bifurcation diagram, which can serve as an explanation for the evolution of physically observable tendril shapes. [ABSTRACT FROM AUTHOR]

We combine the techniques of almost invariant sets (using tree structured box elimination and graph partitioning algorithms) with invariant manifold and lobe dynamics techniques. The result is a new computational technique for computing key dynamical features, including almost invariant sets, resonance regions as well as transport rates and bottlenecks between regions in dynamical systems. This methodology can be applied to a variety of multibody problems, including those in molecular modeling, chemical reaction rates and dynamical astronomy. In this paper we focus on problems in dynamical astronomy to illustrate the power of the combination of these different numerical tools and their applicability. In particular, we compute transport rates between two resonance regions for the three-body system consisting of the Sun, Jupiter and a third body (such as an asteroid). These resonance regions are appropriate for certain comets and asteroids. [ABSTRACT FROM AUTHOR]

In this paper, bifurcations of limit cycles close to certain singularities of the vector fields are explored using an algorithm based on the harmonic balance method, the theory of nonlinear feedback systems and the monodromy matrix. Period-doubling, pitchfork and Neimark–Sacker bifurcations of cycles are detected close to a Gavrilov–Guckenheimer singularity in two modified Rössler systems. This special singularity has a zero eigenvalue and a pair of pure imaginary eigenvalues in the linearization of the flow around its equilibrium. The presented results suggest that the proposed technique can be promising in analyzing limit cycle bifurcations arising in the unfoldings of other complex singularities. [ABSTRACT FROM AUTHOR]

Symmetric block encryption schemes, designed on invertible two-dimensional chaotic maps on a torus or a square, prove feasible and secure for real-time image encryption according to the commonly used criteria given in the literature. In this paper, a typical map of this kind, namely, the baker map, is further extended to be three-dimensional and then used to speed up image encryption while retaining its high degree of security. The proposed algorithm is described in detail, along with its security analysis and implementation. Experimental results show that this three-dimensional baker map is 2–3 times faster than the two-dimensional one, showing its great potential in real-time image encryption applications. [ABSTRACT FROM AUTHOR]

There is an important interest in compensating thermally induced errors of modular tool systems to improve the manufacturing accuracy. In this paper, we test the hypothesis whether we can predict such thermal displacements by using a nonlinear regression analysis, namely the alternating conditional expectation algorithm (ACE [Breiman & Friedman, 1985]), reliably. The data analyzed were generated by two different finite element spindle models of modular tool systems. As the main result, we find that the ACE-algorithm is a powerful tool to model the relation between temperatures and displacements. The maximal correlation is larger than 0.999 in both cases, which demonstrates the suitability of the ACE algorithm. Furthermore, preconditions for the applicability of this approach, such as the length and the support of measured data sets, are studied. Hence, this approach seems to be promising for the application to real modular tool systems. [ABSTRACT FROM AUTHOR]

In this paper, we apply OPCL control to discrete system, and based on relative nonlinear measure, give an algorithm for estimating the radius of stable basin. We rigorously prove that this basin is bound to be of existence for nonlinear discrete system, whose goal dynamics is either periodic orbits or fixed point. We also, in particular, investigate the stable basin in a quadratic polynomial map system, and present that the stable basin is irrelevant to the goal orbits with a negative Jacobian gain matrix. Furthermore, we take the well-known Hénon system and Ikeda system as examples to illustrate the implementation of our theory, and give the corresponding simulations to reinforce our method. [ABSTRACT FROM AUTHOR]

We consider equilibrium configurations of inextensible, unshearable, isotropic, uniform and naturally straight and prismatic rods when subject to end loads and clamped boundary conditions. In a first paper [Neukirch & Henderson, 2002], we discussed symmetry properties of the equilibrium configurations of the center line of the rod. Here, we are interested in the set of all parameter values that yield equilibrium configurations that fulfill clamped boundary conditions. We call this set the solution manifold and we compute it using a recently introduced continuation algorithm. We then describe the topology of this manifold and how it comprises different interconnected layers. We show that the border set of the different layers is the well-known solution set of buckled rings. [ABSTRACT FROM AUTHOR]

This paper treats a problem of reconstructing ordinary differential equation from a single analytic time series with observational noise. We suppose that the noise is Gaussian (white). The investigation is presented in terms of classical theory of dynamical systems and modern time series analysis. We restrict our considerations on time series obtained as a numerical analytic solution of autonomous ordinary differential equation, solved with respect to the highest derivative and with polynomial right-hand side. In case of an approximate numerical solution with a rather small error, we propose a geometrical basis and a mathematical algorithm to reconstruct a low-order and low-power polynomial differential equation. To reduce the noise the given time series is smoothed at every point by moving polynomial averages using the least-squares method. Then a specific form of the least-squares method is applied to reconstruct the polynomial right-hand side of the unknown equation. We demonstrate for monotonous, periodic and chaotic solutions that this technique is very efficient. [ABSTRACT FROM AUTHOR]

In this paper, we perform our algorithm developed: in [Yu , Lee, 2001] to present the entire branches of quasiperiodic solutions starting from the bifurcation points in the branches of periodic solutions in an intervaI of parameters for the 2-mode damped, driven sine-Gordon ODE. [ABSTRACT FROM AUTHOR]

Iterated function systems (IFS) have been used since the mid 1980s in generating fractal forms and in image compression. They have the property of encoding complex structures as relatively simple and concise algorithms and data sets. The complete information for generation of an IFS structure, known as an "attractor", is held in the definition of a few transformation functions, typically affine transformations described by simple linear equations. These transform 2D or 3D objects by combinations of translation, scaling and rotation, preserving parallel lines. The process of generating an attractor using either of the two standard methods is straightforward, but the inverse problem of identifying the IFS for a particular attractor is more difficult. The paper introduces and reviews the uses of Iterated Function Systems, particularly for 2D image and 3D object generation. As well as a general exposition of the method, results developed by the author for creation of fractal objects are shown. Some are based on regular geometric structures, others mimic a number of naturally occurring forms. These deviate from normal practice in using nonaffine transformations in the IFS definition. A new method for synthesising images of smooth objects using IFS is developed and illustrated as an alternative to standard 3D rendering methods (see the cover picture), which are briefly described. [ABSTRACT FROM AUTHOR]

This paper describes a simple method for calculating unstable periodic orbits (UPOs) and their control in piecewise-linear autonomous systems. The algorithm can be used to obtain any desired UPO embedded in a chaotic attractor, and the UPO can be stabilized by a simple state feedback control. A brief stability analysis of the controlled system is also given. [ABSTRACT FROM AUTHOR]

In this paper the application of chaotic algorithms in sending computer messages is described. The communication is achieved through email. Other transmission media can also be used. The algorithm has a degree of security many orders of magnitude higher than systems based on physical electronic circuitry. Both text, image or recorded voice messages can be transmitted. The algorithm can be used for computer communication and for secure databases. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]