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A complex model for evolving the update strategy of a Particle Swarm Optimisation (PSO) algorithm is described in this paper. The model is a hybrid technique that combines a Genetic Algorithm (GA) and a PSO algorithm. Each GA chromosome is an array encoding a meaning for updating the particles of the PSO algorithm. The Evolved PSO algorithm is compared to several human-designed PSO algorithms by using ten artificially constructed functions and one real-world problem. Numerical experiments show that the Evolved PSO algorithm performs similarly and sometimes even better than the Standard approaches for the considered problems. The Evolved PSO is highly scalable (regarding the size of the problem's input), being able to solve problems having different dimensions. [ABSTRACT FROM AUTHOR]

A new multi-class classifier, decision tree SVM (DTSVM) which is a binary decision tree with a very simple structure is presented in this paper. In DTSVM, a problem of multi-class classification is decomposed into a series of ones of binary classification. Here, the binary decision tree is generated by using kernel clustering algorithm, and each non-leaf node represents one binary classification problem. By compared with the other multi-class classification methods based on the binary classification SVMs, the scale and the complexity of DTSVM are less, smaller number of support vectors are needed, and has faster test speed. The final simulation results confirm the feasibility and the validity of DTSVM. [ABSTRACT FROM AUTHOR]

A temporal flexible planning problem that involves contingent and requirement events can be formulated as a simple temporal network with uncertainty (STNU). An STNU is controllable when there is a strategy for executing the requirement events (or actions) in such a way that all the conditions involving contingent events can be satisfied in all situations. The most interesting and useful controllability property is dynamic controllability in which the remaining actions in an STNU can always be scheduled under all possible feasible durations of future contingent events when all the past contingent events are known. In this paper, we propose and study a novel problem of assigning bounds on the duration of each requirement link in order for the resulting STNU to be dynamically controllable and to minimize the total cost over the allowed durations of all requirement links. We first prove the NP hardness of the problem with a linear cost function. We then formulate the dynamic controllability of an STNU as the constraints in a nonlinear optimization problem. Finally, we present methods for reducing the number of constraints in order to make the problem tractable and to demonstrate the computational performance of our methods. [ABSTRACT FROM AUTHOR]

This paper addresses a novel sentence reduction algorithm based on a decision tree model in which semantic information is used to enhance the accuracy of sentence reduction. The proposed algorithm is able to deal with the changeable order problem in sentence reduction. Furthermore, the use of decision list to solve the fragment problem in sentence reduction based decision tree model is also discussed. Our experimental results show an improvement when compared with earlier methods. [ABSTRACT FROM AUTHOR]

Propositional satisfiability (SAT) problem is fundamental to the theory of NP-completeness. Indeed, using the concept of "polynomial-time reducibility" all NP-complete problems can be polynomially reduced to SAT. Thus, any new technique for satisfiability problems will lead to general approaches for thousands of hard combinatorial problems. In this paper, we introduce the incremental propositional satisfiability problem that consists of maintaining the satisfiability of a propositional formula anytime a conjunction of new clauses is added. More precisely, the goal here is to check whether a solution to a SAT problem continues to be a solution anytime a new set of clauses is added and if not, whether the solution can be modified efficiently to satisfy the old formula and the new clauses. We will study the applicability of systematic and approximation methods for solving incremental SAT problems. The systematic method is based on the branch and bound technique while the approximation methods rely on stochastic local search and genetic algorithms. Experimental tests, conducted on randomly generated SAT instances, demonstrate the efficiency in time of the approximation methods over the branch and bound algorithm. However these approximation methods do not always guarantee the completeness of the solution returned. We show that a method we propose that uses non systematic search in a limited form together with branch and bound has the best compromise, in practice, between time and quality of the solution returned (success ratio). [ABSTRACT FROM AUTHOR]

In this paper, we study limit cycles in the Liénard equation: ẍ + f(x)ẋ + g(x) = 0 where f(x) is an even polynomial function with degree 2m, while g(x) is a third-degree, odd polynomial function. In phase space, the system has three fixed points, one saddle point at the origin and two linear centers which are symmetric about the origin. It is shown that the system can have 2m small (local) limit cycles in the vicinity of two focus points and several large (global) limit cycles enclosing all the small limit cycles. The method of normal forms is employed to prove the existence of the small limit cycles and numerical simulation is used to show the existence of large limit cycles. [ABSTRACT FROM AUTHOR]

In mobile systems, some nodes link dynamically through different channels at different times. The π-calculus is a popular process algebra for specification and verification of systems with dynamic linking and synchronous, rendezvous message passing communication of component processes. Dynamic linking can be elegantly specified in it by sending channels to be used for further communication as messages. However, in order to be able to use the π-calculus, one has to learn its process-algebraic concepts and laws. On the other hand, specification and verification in the Temporal Logic of Actions (TLA) is almost entirely based on ordinary mathematics (i.e., first-order predicate logic, set theory, etc.). Therefore, this paper proposes a TLA approach to the specification and verification of systems with synchronous communication and dynamic linking similar to the π-calculus one. It is presented with help of a TLA specification and verification of a parametric mobile network handover procedure which has previously been specified with the π-calculus. In fact, TLA+ is used as the specification language, thus achieving completely formal specifications. [ABSTRACT FROM AUTHOR]

Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers were written on these systems, a complete understanding of this class is still missing. Classical problems, and in particular, Hilbert's 16th problem [Hilbert, 1900, 1902], are still open for this class. In this article we make an interdisciplinary global study of the subclass $\overline{QW2}$ which is the closure within real quadratic differential systems, of the family QW2 of all such systems which have a weak focus of second order. This class $\overline{QW2}$ also includes the family of all quadratic differential systems possessing a weak focus of third order and topological equivalents of all quadratic systems with a center. The bifurcation diagram for this class, done in the adequate parameter space which is the three-dimensional real projective space, is quite rich in its complexity and yields 373 subsets with 126 phase portraits for $\overline{QW2}$, 95 for QW2, 20 having limit cycles but only three with the maximum number of limit cycles (two) within this class. The phase portraits are always represented in the Poincaré disc. The bifurcation set is formed by an algebraic set of bifurcations of singularities, finite or infinite and by a set of points which we suspect to be analytic corresponding to global separatrices which have connections. Algebraic invariants were needed to construct the algebraic part of the bifurcation set, symbolic computations to deal with some quite complex invariants and numerical calculations to determine the position of the analytic bifurcation set of connections. The global geometry of this class $\overline{QW2}$ reveals interesting bifurcations phenomena; for example, all phase portraits with limit cycles in this class can be produced by perturbations of symmetric (reversible) quadratic systems with a center. Many other nonlinear phenomena displayed here form material for further studies. [ABSTRACT FROM AUTHOR]

This paper is to compute a Nash equilibrium in a fuzzy environment, which is represented by a fuzzy approximate Nash equilibrium in a space of discrete mixed strategies. For discrete mixed strategies, the relationship between the discrete degree and the approximate degree is discussed. Based on the fuzzy regret degree, a genetic algorithm for computing a fuzzy Nash equilibrium is given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of interval-valued nested set on the universal set X, propose two representation theorems and equivalent classification theorem of interval-valued fuzzy set. These works can be used in setting up the basic theory of interval-valued fuzzy set. [ABSTRACT FROM AUTHOR]

In this paper, the reasons for the shortcoming of Zadeh's fuzzy set theory — it cannot correctly reflect different kinds of fuzzy phenomenon in the natural world — are discussed. In addition, the proof of the error of Zadeh's fuzzy set theory — it incorrectly defined the set complement that cannot exist in Zadeh's fuzzy set theory — is proposed. This error of Zadeh's fuzzy set theory causes confusion in thinking, logic and conception. It causes the seriously mistaken belief that logics of fuzzy sets necessarily go against classical and normal thinking, logic and conception. Two new fuzzy set theories, C-fuzzy set theory and probability-like fuzzy set theory, the N-fuzzy set theory, are proposed. The two are equivalent, and both overcome the error and shortcoming of Zadeh's fuzzy set theory, and they are consistent with normal, natural and classical thinking, logic and concepts. The similarities of N-fuzzy set theory with probability theory are also examined. [ABSTRACT FROM AUTHOR]

Recently Saul and Lee proposed a mixture model for discriminative classification of non-negative data via non-negative matrix factorization for feature extraction. In order to improve the generalization, this paper considers a sparse version of the model. The basic idea is to minimize the sum of the weights of un-normalized mixture models for posterior distributions according to regularization method. Experiments on CBCL face database and USPS digit data set assess the validity of the proposed approach. [ABSTRACT FROM AUTHOR]

In Global Positioning System (GPS), receivers use FFT-based convolvers to acquire the signals. This paper shows a robust substitute algorithm for calculating the convolution that is less sensitive to additive noise. [ABSTRACT FROM AUTHOR]

In this paper, a procedure for comparing the patterns of time series using wavelets is developed. Randomization tests based on the ratio of the sum of squared wavelet coefficients of pairs of time series at different scales are used. A simulation study using pairs of different types of time series using the Haar and Daubechies wavelets is carried out. The results reveal that the tests perform fairly well at scales where there are a sufficient number of wavelet coefficients. The tests are applied to a set of financial time series. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a multiscale technique for the analysis of deformation phenomena of the Earth. Classically, the basis functions under use are globally defined and show polynomial character. In consequence, only a global analysis of deformations is possible such that, for example, the water load of an artificial reservoir is hardly to model in that way. Up till now, the alternative to realize a local analysis can only be established by assuming the investigated region to be flat. In what follows, we propose a local analysis based on tools (Navier scaling functions and wavelets) taking the (spherical) surface of the Earth into account. Our approach, in particular, enables us to perform a zooming-in procedure. In fact, the concept of Navier wavelets is formulated in such a way that subregions with larger or smaller data density can accordingly be modelled with a higher or lower resolution of the model, respectively. [ABSTRACT FROM AUTHOR]

Inference problems are one of the main research topics in the artificial intellect field. So far there have been various inference systems, some of them have been applied in fuzzy control according to their feature. In 1989, the concept of truth-valued flow inference was introduced by Wang1, and its mathematical theory of truth-valued flow inference was set up by Wang2 in 1995. In this paper, aimed at the real meaning of the truth-valued in the truth-valued flow inference, we introduce the concepts of the inner product truth-valued and inner product truth-valued flow inference, and analyze some inference algorithms of fuzzy control at present in detail. We reveal that the fuzzy inference algorithms in fuzzy control at present are all regarded as inner product truth-valued flow inference algorithm. Finally, inner product truth-valued flow inference approach is generalized in the multiple inputs and single output. [ABSTRACT FROM AUTHOR]

This paper explores Heilpern's notions of fuzzy mapping and the fixed point theorem for fuzzy mappings. The fixed point theorem for fuzzy mappings as introduced by Heilpern has been generalized and some characterizations are done in this context. [ABSTRACT FROM AUTHOR]

In this paper, by using Sengupta and Pal's method of comparison of interval numbers and a new set of arithmetic operations for interval numbers, we propose a theory for the study of arithmetic operations on interval numbers. [ABSTRACT FROM AUTHOR]

In this paper we construct a one-parameter family of interpolating multigenerators which generalize the scalar generators constructed in Ref. 4 in a natural way. Furthermore we extend this approach to design a family of interpolating orthonormal multigenerators. The construction is based on the factorization techniques introduced in Ref. 27. [ABSTRACT FROM AUTHOR]

We consider a discrete-time multi-server queue for which the moments of the stationary queue length can be expressed in terms of series over the zeros in the closed unit disk of a queue-specific characteristic function. In many important cases these zeros can be considered to be located on a queue-specific curve, called generalized Szegö curve. By adopting a special parametrization of these Szegö curves, the relevant zeros occur as equidistant samples of a 2π-periodic function whose Fourier coefficients can be determined analytically. Thus the series occurring in the expressions for the moments can be written as Fourier aliasing series with terms given in analytic form. This gives rise to formulas for e.g. the mean and variance of the queue length that are reminiscent of Spitzer's identity for the moment generating function of the steady-state waiting time for a G/G/1 queue. Indeed, by considering the queue under investigation as a G/G/1 queue, the new formulas for the mean and variance also follow from Spitzer's identity. The approach in this paper can also be used to compute the probability distribution function of the queue length in analytic form. [ABSTRACT FROM AUTHOR]

Tandem queueing models play an important role in many real world systems such as computer systems, production lines, and service systems. This paper proposes a procedure to construct the membership functions of the performance measures in tandem queueing systems, in that the arrival rate and service rates are fuzzy numbers. The basic idea is to transform a fuzzy tandem queue to a family of crisp tandem queues by applying the α -cut approach. Then on the basis of α -cut representation and the extension principle, a pair of mathematical programs is formulated to describe this family of crisp tandem queues, via which the membership functions of the performance measures are derived. Two numerical examples are solved successfully to demonstrate the validity of the proposed approach. Since the performance measures are expressed by membership functions rather than by crisp values, the fuzziness of input information is completely conserved. Thus the proposed approach for fuzzy systems can represent the system more accurately, and more information is provided for designing queueing systems. The successful extension of tandem queues to fuzzy environments permits tandem queueing models to have wider applications. [ABSTRACT FROM AUTHOR]

Traditionally the beta distribution has been used due to its ease for computing the mean of tasks, times, cash-flows, etc. because, in this case, the expected value is a weighted average of optimistic, most likely and pessimistic values. One of the critiques of PERT has been the difficulty of introducing the level of confidence that the expert has in his own estimate of the modal value. The Belief in Fuzzy Probability Estimations of Time (BIFPET) model uses human judgement instead of stochastic assumptions to determine the duration of a project. Thus, each supervisor responsible of an activity specifies the three values with their respective probabilities. The manager accepts these probabilities or may extend them within a certain range, according to his belief in these likelihoods or the degree of control exercised by himself in achieving the lower bound of the expected value. However, this approach can be implemented in the PERT methodology. Thus, in this paper, we introduce the confidence that the manager has in the most likely value supplied by the supervisor in order to determine the specific beta distribution to model the variable, showing the advantages of this intuitive procedure which moreover can be easily implemented. [ABSTRACT FROM AUTHOR]

Interval-valued fuzzy sets constitute an extension of fuzzy sets which give an interval approximating the "real" (but unknown) membership degree. Interval-valued fuzzy sets are equivalent to intuitionistic fuzzy sets in the sense of Atanassov which give both a membership degree and a non-membership degree, whose sum must be smaller than or equal to 1. Both are equivalent to L-fuzzy sets w.r.t. a special lattice L*. In fuzzy set theory, an important class of triangular norms is the class of those that satisfy the residuation principle. In a previous paper5 we gave a construction for t-norms on L* satisfying the residuation principle which are not t-representable. In this paper we investigate the Smets-Magrez axioms and some other properties for the residual implicator generated by such t-norms. [ABSTRACT FROM AUTHOR]

The period-1 motion of a piecewise-linear system under a periodic excitation is predicted analytically through the Poincaré mapping and the corresponding mapping sections formed by the switch planes pertaining to the two constraints. The mapping relationship generates a set of nonlinear algebraic equations from which the period-1 motion is determined analytically. The stability and bifurcation of the period-1 motion are determined, and numerical simulations are carried out for confirmation of the analytical prediction of period-1 motion. An unsymmetrical stable period-1 motion is observed. This investigation helps us understand the dynamical behavior of period-1 motion in the piecewise-linear system and more efficiently obtain other periodic motions and chaos through numerical simulations. The similar methodology presented in this paper can be used for other nonsmooth dynamical systems. [ABSTRACT FROM AUTHOR]

The Multi-Tier (M-Tier) algorithm proposed in [1], has enabled an enhanced correlation between dynamic resource utilization and QoS guarantees. The algorithm favored the delay sensitive applications. Indirectly, this infers that the assignment of priorities practiced in the algorithm is static. In redesigning the algorithm, priority assignments should be able to be implemented dynamically. Thus, enabling an embedded element to provide implementation mobility. This would depend upon the current status of the classified buffers and the tolerance level of the delay sensitive traffic. Integrating control parameters to enable alternation in scheduling priorities is an option to resolve the element of partiality present in the M-Tier algorithm. Thereafter, the proposed algorithm will be denoted as the M-Tier(T) algorithm [2]. The paper proposes a detailed mathematical model for the analysis of dynamic resource reservation algorithms implemented in IP switches. The semi-markov process (SMP) approach utilized provides an accurate performance prediction and representation of resource reservation mechanisms. The algorithm correlates the average packet delay and packet loss ratio parameters to activate the dynamic resource reservation mechanism in a hierarchical manner. The developed models are validated through discrete-event simulation. The performance of the algorithm is studied in terms of average packet delay and network throughput. [ABSTRACT FROM AUTHOR]

This paper presents a fast algorithm for solving the n-queens problem. The basic idea of this algorithm is to use pre-computed solutions in 75% of the cases, while the remaining cases are solved by calling the Sosic's algorithm. The novelty of this algorithm is in the observation that these pre-computable cases exhibit a modular nature. In addition, the pre-computed solutions run 100 times faster than Sosic's algorithm in most cases. [ABSTRACT FROM AUTHOR]

This paper presents a study on the problem of Hopf bifurcation control of time delayed systems with weak nonlinearity via delayed feedback control. It focusses on two control objectives: one is to annihilate the periodic solution, namely to perform a linear delayed feedback control so that the trivial equilibrium is asymptotically stable, and the other is to obtain an asymptotically stable periodic solution with given amplitude via linear or nonlinear delayed feedback control. On the basis of the averaging method and the center manifold reduction for delayed differential equations, an effective method is developed for this problem. It has been shown that a linear delayed feedback can always stabilize the unstable trivial equilibrium of the system, and a linear or nonlinear delayed feedback control can always achieve an asymptotically stable periodic solution with desired amplitude. The illustrative example shows that the theoretical prediction is in very good agreement with the simulation results, and that the method is valid with high accuracy not only for delayed systems with weak nonlinearity and via weak feedback control, but also for those when the nonlinearity and feedback control are not small. [ABSTRACT FROM AUTHOR]

This paper is an attempt to give new results, by a computer-assisted study, on some global bifurcations that change the structure of the domain of feasible trajectories (bounded discrete trajectories having an ecological sense) which can be obtained by the union of all rank preimages of axes. Three two-dimensional recurrence equations (or maps) are analyzed. The two first maps are degenerated invertible maps (i.e. the inverses of them are well defined except a set of zero lebergue measure) for which the basins of attractor are obtained by the backward iteration of a stable manifold of a saddle fixed point belonging to the basin boundary, and the interior domains of feasible trajectories are given by the intersection between the basin of attractor and the first quadrant. The other is a noninvertible map which is investigated by the use of critical curves, a powerful tool for the analysis of global properties of two-dimensional maps. [ABSTRACT FROM AUTHOR]

A new hierarchical uncertainty model for combining different evidence about a system of statistically independent random variable is studied in the paper. It is assumed that the first-order level of the model is represented by sets of lower and upper previsions (expectations) of random variables and the second-order level is represented by sets of lower and upper probabilities which can be viewed as confidence weights for interval-valued expectations of the first-order level. The model is rather general and allows us to compute probability bounds and "average" bounds for previsions of a function of random variables. A numerical example illustrates this model. [ABSTRACT FROM AUTHOR]

This paper describes an efficient and adaptive method of threshold estimation for removing impulse noise from images, based on Double Density Wavelet Transform (DDWT). The performance of image de-noising algorithms using wavelet transforms can be improved significantly by fixing an optimum threshold value, based on the analysis of the statistical parameters of subband coefficients. In this proposed method, the choice of the threshold estimation is carried out by analyzing the statistical parameters of the wavelet subband coefficients like standard deviation, arithmetic mean and geometrical mean. Here the noisy image is first decomposed into many levels to obtain different frequency bands using DDWT. Then soft thresholding method is used to remove the noisy coefficients, by fixing the optimum threshold value by the proposed method. Experimental results on several test images by using the proposed method show that, the proposed method yields significantly superior image quality and better Peak Signal-to-Noise Ratio (PSNR). Some comparisons with the best available results will be given in order to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper we develop a theory for analysing the "radius" of the Lie algebra of a matrix Lie group, which is a measure of the size of its commutators. Complete details are given for the Lie algebra 픰픬(n) of skew symmetric matrices where we prove $\| [X,Y] \| \leq \sqrt{2} \|X\| \cdot \|Y\|$, X, Y ∈ 픰픬(n), for the Frobenius norm. We indicate how these ideas might be extended to other matrix Lie algebras. We discuss why these ideas are of interest in applications such as geometric integration and optimal control. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method to research lag synchronization of the identical master-slave chaotic Lur'e systems via replacing variables control with time delay. By means of absolute stability theory, we prove two types of sufficient conditions for the lag synchronization: Lur'e criterion and frequency domain criterion. Based on the criteria, we suggest an optimization scheme to design the control variables. Applying the scheme to general Chua's circuits, we obtain the parameter ranges in which the master-slave Chua's circuits laggingly synchronize or not by varied single-variable control. Finally, we cite the examples by illustration of the results. [ABSTRACT FROM AUTHOR]

In this paper, we develop a simple linear feedback controller, which employs only one of the states of the system, to stabilize the modified Chua's circuit to an invariant set which consists of its nontrivial equilibria. Moreover, we show for the first time that the closed loop modified Chua's circuit satisfies set stability which can be considered as a generalization of common Lyapunov stability of an equilibrium point. Simulation results are presented to verify our method. [ABSTRACT FROM AUTHOR]

By analyzing the dynamic behaviors of the transiently chaotic neural network and greedy heuristic for the maximum independent set (MIS) problem, we present an improved transiently chaotic neural network for the MIS problem in this paper. Extensive simulations are performed and the results show that this proposed transiently chaotic neural network can yield better solutions to p-random graphs than other existing algorithms. The efficiency of the new model is also confirmed by the results on the complement graphs of some DIMACS clique instances in the second DIMACS challenge. Moreover, the improved model uses fewer steps to converge to stable state in comparison with the original transiently chaotic neural network. [ABSTRACT FROM AUTHOR]

This paper describes a method for separating online handwritten patterns into Japanese text, figures and mathematical formulas. Today, Tablet PCs and electronic whiteboards provide much larger writing area for pen interfaces unlike PDAs (Personal Digital Assistants), through which users can easily input text, write mathematical formulas and draw figures on the screen. The fact that these objects can be written by a single pen (marker) without switching the device, mode, software or whatever else, and without any writing restrictions such as grids or boxes is one of the most important benefits of the pen interfaces. However, the task of segmenting these objects is challenging. To address this issue, we have applied a probabilistic model employing stroke features, stroke crossings and stroke densities. Further, we partially apply the approach of segmentation by recognition. Although the current recognizer for formulas is not a true recognizer, we have achieved about 81% correct segmentation for all the strokes when applied to our newly prepared database of mixed patterns. This method has been compared with a neural-network. The results show that our method is generally better but less effective in distinguishing figures from other components. [ABSTRACT FROM AUTHOR]

In this paper, we study the number of limit cycles in a family of polynomial systems. Using bifurcation methods, we obtain the maximal number of limit cycles in global bifurcation. [ABSTRACT FROM AUTHOR]

This paper investigates limit cycling behavior of observer-based controlled mechanical systems with friction compensation. The limit cycling is induced by the interaction between friction and friction compensation, which is based on the estimated velocity. The limit cycling phenomenon, which is experimentally observed in a rotating arm manipulator, is analyzed through computational bifurcation analysis. The computed bifurcation diagram confirms that the limit cycles can be eliminated by enlarging observer gains and controller gains at the cost of a steady state error. The numerical results match well with laboratory experiments. [ABSTRACT FROM AUTHOR]

In this paper, a class of MIMO nonlinear systems are studied. Some frequency domain conditions are established for the property of dichotomy. These kinds of systems can also be viewed as a class of interconnected systems composed of SISO systems through some linear and nonlinear interconnections. A class of nonlinear input and output interconnections are presented. The corresponding condition for testing dichotomy is given. Furthermore, Chua's circuit and interconnected Chua's circuit are studied to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper illustrates the recent phenomenon of chaotic beats in a modified version of Chua's circuit, driven by two sinusoidal inputs with slightly different frequencies. In order to satisfy the constraints imposed by the beats dynamics, a novel implementation of the voltage-controlled characteristic of the Chua diode is proposed. By using Pspice simulator, the behavior of the designed circuit is analyzed both in time-domain and state-space, confirming the chaotic nature of the phenomenon and the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

The fold-flip bifurcation occurs if a map has a fixed point with multipliers +1 and -1 simultaneously. In this paper the normal form of this singularity is calculated explicitly. Both local and global bifurcations of the unfolding are analyzed by exploring a close relationship between the derived normal form and the truncated amplitude system for the fold-Hopf bifurcation of ODEs. Two examples are presented, the generalized Hénon map and an extension of the Lorenz-84 model. In the latter example the first-, second- and third-order derivatives of the Poincaré map are computed using variational equations to find the normal form coefficients. [ABSTRACT FROM AUTHOR]

Of concern is a two-dimensional map T of the form T(x,y)=(y,F(y)-bx). Here F is a three-piece linear map. In this paper, we first prove a theorem which states that a semiconjugate condition for T implies the existence of Smale horseshoe. Second, the theorem is applied to show the spatial chaos of one-dimensional Cellular Neural Networks. We improve a result of Hsu [2000]. [ABSTRACT FROM AUTHOR]

A fuzzy variable is a function from a possibility space to the set of real numbers, while a bifuzzy variable is a function from a possibility space to the set of fuzzy variables. In this paper, a concept of chance distribution is originally presented for bifuzzy variable, and the linearity of expected value operator of bifuzzy variable is proved. Furthermore, bifuzzy simulations are designed and illustrated by some numerical experiments. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy sets are a generalization of ordinary fuzzy sets which are characterized by a membership function and a non-membership function. In this paper we consider the problem of ranking a set of intuitionistic fuzzy numbers. We adopt a statistical viewpoint and interpret each intuitionistic fuzzy number as an ensemble of ordinary fuzzy numbers. This enables us to define a fuzzy rank and a characteristic vagueness factor for each intuitionistic fuzzy number. We show the reasonablesness of the results obtained by examining several test cases. [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]

In this paper, boundary anticontrol of spatiotemporal chaos for 1D hyperbolic equations is studied. Firstly, a new definition of chaotic vibrations for PDEs is given in terms of the growth rate of the total variations of the solutions with respect to the spatial variable as t→∞. Then, a boundary feedback controller is designed as composing with a sawtooth function, which can drive the originally nonchaotic linear or nonlinear dynamical system chaotic. Finally, as applications, anticontrol of chaos for 1D linear wave equations with linear or nonlinear boundary conditions is discussed. [ABSTRACT FROM AUTHOR]

In this paper we show that a system containing any knot or link can be directly constructed in a simple way. The system is not chaotic and can even contain wild knots. [ABSTRACT FROM AUTHOR]

This is the first of two papers introducing a new dynamical phenomenon, strongly related to the problems of synchronization and control of chaotic dynamical systems, and presenting the corresponding mathematical analysis, conducted both experimentally and theoretically. In particular, it is shown that different dynamical models (ordinary differential equations) admitting chaotic behavior organized by a homoclinic bifurcation to a saddle-focus (Shil'nikov-like chaos) tend to have a particular selective property when externally perturbed. Namely, these systems settle on a very narrow chaotic behavior, which is strongly correlated to the forcing signal, when they are slightly perturbed with an external signal which is similar to their corresponding generating cycle. Here, the "generating cycle" is understood to be the saddle cycle colliding with the equilibrium at the homoclinic bifurcation. On the other hand, when they are slightly perturbed with a generic signal, which has no particular correlation with their generating cycle, their chaotic behavior is reinforced. This peculiar behavior has been called qualitative resonance underlining the fact that such chaotic systems tend to resonate with signals that are qualitatively similar to an observable of their corresponding generating cycle. Here, the results of an experimental analysis are presented together with an intuitive geometrical qualitative model of the phenomenon. [ABSTRACT FROM AUTHOR]

In this paper, we present a flatness based control approach for the stabilization and tracking problem, for the well-known Chua chaotic circuit, that includes an additional input. We introduce two feedback controller design options for the set-point stabilization and the trajectory tracking problem: a direct pole placement approach, and Generalized Proportional Integral (GPI) approach based only on measured inputs and outputs. [ABSTRACT FROM AUTHOR]

This paper presents a time-delayed impulsive feedback approach to the problem of stabilization of periodic orbits in chaotic hybrid systems. The rigorous stability analysis of the proposed method is given. Using the time-delayed impulsive feedback method, we analyze the problem of detecting various periodic orbits in a special class of hybrid system, a switched arrival system, which is a prototype model of many manufacturing systems and computer systems where a large amount of work is processed in a unit time. We also consider the problem of stabilization of periodic orbits of chaotic piecewise affine systems, especially Chua's circuit, which is another important special class of hybrid systems. [ABSTRACT FROM AUTHOR]

Constructing models of nonlinear time series is typically NP-hard. One of the difficulties is the local minima, and it is difficult to find a global best model. Some methods have already been proposed that attempt to find good models with reasonable computation time. In this paper we propose new methods that can compensate for a drawback of a method previously proposed by Judd and Mees. A standard approach to NP-hard problems is simulated annealing. We apply these methods to build models of annual sunspot numbers and a laser time series, and compare the results. The results indicate that the performance of the proposed method is comparable to that of simulated annealing in both time series. The performance of Judd and Mees method is almost the same as that of the other methods for the annual sunspot data, but not as good for laser time series. The Judd and Mees method is computationally the fastest of all the methods, and the proposed method is faster than simulated annealing. [ABSTRACT FROM AUTHOR]