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Perpetual points represent a new interesting topic in the literature of nonlinear dynamics. This paper introduces some chaotic flows with four different structural features from the viewpoint of fixed points and perpetual points. [ABSTRACT FROM AUTHOR]

This Letter analyzes the hyperchaotic dynamics of the fractional-order Rössler system from a time-domain point of view. The approach exploits the Adomian decomposition method (ADM), which generates series solution of the fractional differential equations. A remarkable finding of the Letter is that hyperchaos occurs in the fractional Rössler system with order as low as 3.12. This represents the lowest order reported in literature for any hyperchaotic system studied so far. [ABSTRACT FROM AUTHOR]

Nonlinear dynamics of a real plane and periodically forced triple pendulum is investigated experimentally and numerically. Mathematical modeling includes details, taking into account some characteristic features (for example, real characteristics of joints built by the use of roller bearings) as well as some imperfections (asymmetry of the forcing) of the real system. Parameters of the model are obtained by a combination of the estimation from experimental data and direct measurements of the system's geometric and physical parameters. A few versions of the model of resistance in the joints are tested in the identification process. Good agreement between both numerical simulation results and experimental measurements have been obtained and presented. Some novel features of our real system chaotic dynamics have also been reported, and a novel approach of the rolling bearings friction modeling is proposed, among other. [ABSTRACT FROM AUTHOR]

Ten years ago, Dixon et al. [1993] studied the behavior of a continuous-time system displaying erratic, apparently chaotic, dynamics. This is a paradoxical case since the system is two-dimensional, which is seemingly a violation of the Poincare–Bendixon theorem. Using numerical studies, Dixon et al. explained such a behavior from the presence of an attracting singularity, which induces arbitrarily large sensitivity to initial conditions. The aim of this letter is to use singularity regularization techniques to study the dynamics around the system singularity. The results obtained in this way explain the paradoxical situation of having continuous "chaotic" dynamics in a two-dimensional system. [ABSTRACT FROM AUTHOR]

Complex vibrations of an Euler–Bernoulli beam with different types of nonlinearities are considered. An arbitrary beam clamping is considered, and deflection constraints (point barriers) are introduced in some beam points along its length. The influence of a constraint, as well as of the amplitude and frequency of excitation on the vibrations is analyzed. Scenarios of transition to chaos owing to the introduced nonlinearities are reported. [ABSTRACT FROM AUTHOR]

A new neighborhood selection method is presented for both deterministic and probabilistic cellular automata models. The detection criteria are built explicitly on the corresponding contribution which is made to the value of each updated cell from each detected cell in the evolution. Theoretical analysis and numerical simulations demonstrate the effectiveness of this new method. [ABSTRACT FROM AUTHOR]

Modern Science is finding new methods of looking at biological, physical or social phenomena. Traditional methods of quantification are no longer sufficient and new approaches are emerging. These approaches make it apparent that the phenomena the observer is looking at are not classifiable by conventional methods. These phenomena are complex. A complex system, as Chua's oscillator, is a nonlinear configuration whose dynamical behavior is chaotic. Chua's oscillator equations allow to define the basic behavior of a dynamical system and to detect the changes in the qualitative behavior of a system when bifurcation occurs, as parameters are varied. The typical set of behavior of a dynamical system can be detailed as equilibrium points, limit cycles, strange attractors. The concepts, methods and paradigms of Dynamical Systems Theory can be applied to understand human behavior. Human behavior is emergent and behavior patterns emerge thanks to the way the parts or the processes are coordinated among themselves. In fact, the listening process in humans is complex and it develops over time as well. Sound and music can be both inside and outside humans. This tutorial concerns the translation of Chua's oscillators into music, in order to find a new way of understanding complexity by using music. By building up many computational models which allow the translation of some quantitative features of Chua's oscillator into sound and music, we have created many acoustical and musical compositions, which in turn present the characteristics of dynamical systems from a perceptual point of view. We have found interesting relationships between dynamical systems behavior and their musical translation since, in the process of listening, human subjects perceive many of the structures as possible to perceive in the behavior of Chua's oscillator. In other words, human cognitive abilities can analyze the large and complicated patterns produced by Chua's systems translated into music, achieving the cognitive economy and the coordination and synthesis of countless data at our disposal that occur in the perception of dynamic events in the real world. Music can be considered the semantics of dynamical systems, which gives us a powerful method for interpreting complexity. [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]

We consider the nonlinear bistable dynamic system that is the archetypal system giving way to the phenomenon of stochastic resonance for noise-improved signal processing. Independently of a strict stochastic resonance effect, we use this bistable system as a nonlinear filter for a detection task on a binary signal. We expose a methodology to tune the nonlinear filter at its best performance that minimizes its probability of detection error. The optimally tuned nonlinear filter is then compared to the ideal matched filter, which is the optimal filter for the detection with Gaussian noise. We show that the performance of the nonlinear filter, although (expectedly) not as good, comes close to that of the ideal matched filter operating in its strict nominal conditions. We next examine several possible departures, quite plausible in practical operation, from the nominal conditions of the ideal matched filter. We demonstrate that in such degraded conditions, the nonlinear filter can catch up and surpass the performance of the matched filter. This reveals a robustness superiority of the nonlinear filter, compared to the matched filter operating outside its strict nominal conditions. [ABSTRACT FROM AUTHOR]

Illuminative deformation patterns of a honeycomb structure are presented. A representative volume element of a honeycomb structure consisting of 2 × 2 hexagonal cells is modeled to be a ${\rm D}_6\dot{+}({\rm C}_2\times\tilde{\rm C}_2)$-equivariant system. The bifurcation mechanism and an exhaustive list of possible bifurcated patterns are obtained by group-theoretic bifurcation theory. A flower mode of the honeycomb is shown to have the same symmetry as the so-called anti-hexagon in the Rayleigh–Bénard convection. A numerical bifurcation analysis is conducted on an elastic in-plane honeycomb structure consisting of 2×2 cells to produce beautiful wallpapers of bifurcating deformation patterns and, in turn, to highlight the achievement of the paper. New deformation patterns of a honeycomb structure have been found and classified in a systematic manner. Knowledge of the symmetries of the bifurcating solutions has turned out to be vital in the successful numerical tracing of the bifurcated paths. This paper paves the way for the introduction of the results hitherto obtained for flow patterns in fluid dynamics into the study of patterns on materials. [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]

A special numerical technique has been developed for identification of solitary wave solutions of Boussinesq and Korteweg–de Vries equations. Stationary localized waves are considered in the frame moving to the right. The original ill-posed problem is transferred into a problem of the unknown coefficient from over-posed boundary data in which the trivial solution is excluded. The Method of Variational Imbedding is used for solving the inverse problem. The generalized sixth-order Boussinesq equation is considered for illustrations. [ABSTRACT FROM AUTHOR]

A method for controlling onto saddle-type fixed points developed by Yagasaki and Uozumi is extended so as to make the capture region many times larger than that of the original method. [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]

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]

We show that transmitter and receiver systems consisting of cascaded chaotic optical rings can synchronize when they are coupled by using direct light injection from the transmitter into the receiver. Binary messages can be transmitted by the chaotic switching scheme. The proposed chaos secure communication system can satisfy some requirements to enhance security. [ABSTRACT FROM AUTHOR]

A new NARMA based smoothing algorithm is introduced for chaotic and nonchaotic time series. The new algorithm employs a cross-validation method to determine the smoother structure, requires very little user interaction, and can be combined with wavelet thresholding to further enhance the noise reduction. Numerical examples are included to illustrate the application of the new algorithm. [ABSTRACT FROM AUTHOR]

Based on analytic and numerical investigations of chaotic vibrations and quasiperiodic rotations of the Froude pendulum, we present a sufficient condition for controlling chaos by means of a weak resonant excitation as the initial phase difference Ψ varies. It is shown via the Melnikov function method that the initial phase difference Ψ plays a vital role in suppressing or inducing chaotic motions or quasiperiodic rotations. [ABSTRACT FROM AUTHOR]

We consider the dynamics of the first vibrational mode of a suspension bridge, resulting from the coupling between its roadbed (elastic beam) and the hangers, supposed to be one-sided springs which respond only to stretching. The external forcing is due to time-periodic vortices produced by impinging wind on the bridge structure. We have studied some relevant dynamical phenomena in such a system, like periodic and quasiperiodic responses, chaotic motion, and boundary crises. In the weak dissipative limit the dynamics is mainly multistable, presenting a variety of coexisting attractors, both periodic and chaotic, with a highly involved basin of attraction structure. [ABSTRACT FROM AUTHOR]

Dynamical behaviors of a three-dimensional autonomous chaotic system with two double-scroll attractors are studied. Some basic properties such as bifurcation, routes to chaos, periodic windows and compound structure are demonstrated with various numerical examples. System equilibria and their stabilities are discussed, and chaotic features of the attractors are justified numerically. [ABSTRACT FROM AUTHOR]