Chaotic System

The generation of Lagrangian chaos has been studied experimentally in a twisted duct flow, a configuration representing a three-dimensional steady open flow in which various signatures of Lagrangian chaos are documented. The twisted duct consists of four 90∘ bends of square cross-section; the plane of curvature of each bend is at 90∘ to that of its neighbors. Dean roll-cells, generated

We investigate the effects of a time-correlated noise on an extended chaotic system. The chosen model is the Lorenz'96, a kind of toy model used for climate studies. The system is subjected to both temporal and spatiotemporal perturbations. Through the analysis of the system's time evolution and its time correlations, we have obtained numerical evidence for two stochastic resonance-like behaviors.

– In this paper, we will provide an overview of the mechanisms used in image protection, especially Chaos-based encryption techniques available today. We will see how previously proposed methods such as Data Encryption Standard (DES), Triple Data ...

Abstract: In this paper, we investigate the control and reduced-order synchronization in a new third-order chaotic system derived from the rigid body dynamics. A recursive backstepping control is designed based on Lyapunov stability theory to eliminate the chaotic behaviour. To ...

It has been recently investigated that the jerk dynamical systems are the simplest ever systems, which possess variety of dynamical behaviors including chaotic motion. Interestingly, the jerk dynamical systems also describe various phenomena in physics and engineering such as electrical circuits, mechanical oscillators, laser physics, solar wind driven magnetosphere ionosphere (WINDMI) model, damped harmonic oscillator driven by nonlinear memory term, biological systems etc. In many practical situations chaos is undesirable phenomenon, which may lead to irregular operations in physical systems. Thus from a practical point of view, one would like to convert chaotic solutions into periodic limit cycle or fixed point solutions. On the other hand, there has been growing interest to use chaos profitably by synchronizing chaotic systems due to its potential applications in secure communication. In this paper, we have made a thorough investigation of synchronization of identical chaotic jerk dynamical systems by implementing three well-known techniques: (i) Pecora-Carroll (PC) technique, (ii) Feedback (FB) technique and (iii) Active Passive decomposition (APD). We have given a detailed review of these techniques followed by the results of our investigations of identical synchronization of chaos in jerk dynamical systems. The stability of identical synchronization in all the aforesaid methods has also been discussed through the transversal stability analysis. Our extensive numerical calculation results reveal that in PC and FB techniques the x-drive configuration is able to produce the stable identical synchronization in all the chaotic jerk dynamical systems considered by us (except for a few cases), however y-drive and z-drive configurations do not lead to the stable identical synchronization. For the APD approach, we have suggested a generalized active passive decomposition, which leads to the stable identical synchronization without being bothered about the specific form of the jerk dynamical system. Several other active passive decompositions have also been listed with their corresponding conditional Lyapunov exponents to achieve the stable identical synchronization in various chaotic jerk dynamical systems.

The study of health behavior change, including nutrition and physical activity behaviors, has been rooted in a cognitive-rational paradigm. Change is conceptualized as a linear, deterministic process where individuals weigh pros and cons, and at the point at which the benefits outweigh the cost change occurs. Consistent with this paradigm, the associated statistical models have almost exclusively assumed a linear relationship between psychosocial predictors and behavior. Such a perspective however, fails to account for non-linear, quantum influences on human thought and action. Consider why after years of false starts and failed attempts, a person succeeds at increasing their physical activity, eating healthier or losing weight. Or, why after years of success a person relapses. This paper discusses a competing view of health behavior change that was presented at the 2006 annual ISBNPA meeting in Boston. Rather than viewing behavior change from a linear perspective it can be viewed a...

Acoustic signals of vowels preceding nasal sounds were examined for nasalization by using nonlinear time-series analysis to represent the speech signal in a multidimensional embedding space. Recurrence quantification analysis (RQA), originally developed to study the behavior of nonlinear dynamical systems, were used on the speech signals to indicate their deterministic chaotic behavior and to show the differences between nasalized and

This paper examines and contrasts the feasibility of joint state and parameter estimation of noise-driven chaotic systems using the extended Kalman filter (EKF), ensemble Kalman filter (EnKF), and particle filter (PF). In particular, we consider the chaotic vibration of a noisy Duffing oscillator perturbed by combined harmonic and random inputs ensuing a transition probability density function (pdf) of motion which displays strongly non-Gaussian features. This system offers computational simplicity while exhibiting a kaleidoscope of dynamical behavior with a slight change of input and system parameters. An extensive numerical study is undertaken to contrast the performance of various nonlinear filtering algorithms with respect to sparsity of observational data and strength of model and measurement noise. In general, the performance of EnKF is better than PF for smaller ensemble size, while for larger ensembles PF outperforms EnKF. For moderate measurement noise and frequent measurement data, EKF is able to correctly track the dynamics of the system. However, EKF performance is unsatisfactory in the presence of sparse observational data or strong measurement noise.

In this paper, we apply backstepping control method to derive new results for the adaptive controller and synchronizer design for the Arneodo chaotic system (1980), when the system parameters are unknown. First, we design an adaptive backstepping controller to stabilize the Arneodo system to its unstable equilibrium at the origin. Next, we design an adaptive backstepping controller to achieve global chaos synchronization of the identical Arneodo chaotic systems with unknown parameters. MATLAB simulations have been detailed to illustrate the proposed adaptive backstepping controller and synchronizer design for Arneodo chaotic system with unknown parameters.

It has been recently investigated that the jerk dynamical systems are the simplest ever systems, which possess variety of dynamical behaviors including chaotic motion. Interestingly, the jerk dynamical systems also describe various phenomena in physics and engineering such as electrical circuits, mechanical oscillators, laser physics, solar wind driven magnetosphere ionosphere (WINDMI) model, damped harmonic oscillator driven by nonlinear memory term,

In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two dimensional grid. Active traders are characterised by the decision to buy, (+1), or sell, (-1), a stock at a certain discrete time step. The remaining cells are inactive,(0). The trading dynamics is then determined by the stochastic interaction between traders belonging to the same cluster. Most of the stylized aspects of the financial market time series are reproduced by the model.

The control problem is discussed for a chaotic system without equilibrium in this paper. On the basis of the linear mathematical model of the two-wheeled self-balancing robot, a novel chaotic system which has no equilibrium is proposed. The basic dynamical properties of this new system are studied via Lyapunov exponents and Poincaré map. To further demonstrate the physical realizability of the presented novel chaotic system, a chaotic circuit is designed. By using fractional-order operators, a controller is designed based on the state-feedback method. According to the Gronwall inequality, Laplace transform and Mittag-Leffler function, a new control scheme is explored for the whole closed-loop system. Under the developed control scheme, the state variables of the closed-loop system are controlled to stabilize them to zero. Finally, the numerical simulation results of the chaotic system with equilibrium and without equilibrium illustrate the effectiveness of the proposed control scheme.

We predict and numerically observe strong periodic orbit effects in the properties of weakly open quantum systems with a chaotic classical limit. Antiscars lead to a large number of exponentially narrow isolated resonances when the single-channel (or tunneling) opening is located on a short unstable orbit of the closed system; the probability to remain in the system at long times is thus exponentially enhanced over the random matrix theory prediction. The distribution of resonance widths and the probability to remain are quantitatively given in terms of only the stability matrix of the orbit on which the opening is placed. The long-time remaining probability density is nontrivially distributed over the available phase space; it can be enhanced or suppressed near orbits other than the one on which the lead is located, depending on the periods and classical actions of these other orbits. These effects of the short periodic orbits on quantum decay rates have no classical counterpart, a...