Search results for "chaotic system"
showing 10 items of 10 documents
Approximating hidden chaotic attractors via parameter switching.
2018
In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The parameter switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustration. In Refs. 1–3, it is proved that the attractors of a chaotic system, considered as the unique numerical …
Scattering lengths and universality in superdiffusive L\'evy materials
2012
We study the effects of scattering lengths on L\'evy walks in quenched one-dimensional random and fractal quasi-lattices, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling properties of the random-walk probability distribution, we show that the effect of the varying scattering length can be reabsorbed in the multiplicative coefficient of the scaling length. This leads to a superscaling behavior, where the dynamical exponents and also the scaling functions do not depend on the value of the scattering length. Within the scaling framework, we obtain an exact expression for the multiplicative coefficient as a function of the scattering length both in the a…
Feigenbaum graphs: a complex network perspective of chaos
2011
The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map…
A Novel Method of Distance Measurement Based on Pulse Position Modulation and Synchronization of Chaotic Signals Using Ultrasonic Radar Systems
2009
This paper deals with a novel method of transmission and receipt of a signal based on both the property of two chaotic systems generating the same chaotic signal when they are synchronized and the property of pulse position modulation (PPM) to be insensitive to the distortions of the transmission channel. The method is discussed in the context of ultrasonic radar systems, in which the transmitter and receiver, which consist of ultrasonic sensors, are near each other, and the received signal consists of the transmitted signal reflected by an obstacle. A reference sinusoidal signal is superimposed to a chaotic signal generated by a master chaotic system, and the whole signal is modulated acco…
On differences and similarities in the analysis of Lorenz, Chen, and Lu systems
2015
Currently it is being actively discussed the question of the equivalence of various Lorenz-like systems and the possibility of universal consideration of their behavior (Algaba et al., 2013a,b, 2014b,c; Chen, 2013; Chen and Yang, 2013; Leonov, 2013a), in view of the possibility of reduction of such systems to the same form with the help of various transformations. In the present paper the differences and similarities in the analysis of the Lorenz, the Chen and the Lu systems are discussed. It is shown that the Chen and the Lu systems stimulate the development of new methods for the analysis of chaotic systems. Open problems are discussed.
Génétique des textes et système chaotique
2016
Textual genetics and chaotic system Although we share Louis Hay's idea that it is impossible to homologate and systematize the operations which can be observed in manuscripts, it is however possible to interpret whatever creation process in terms of the passage from entropy to order. The possibility of an analogy between text and chaotic system had been advanced by Noëlle Batt according to whom each work actually satisfies the principles of the chaotic system. It is starting from such principles that we will try to show the analogy between chaotic system and textual genetics: 1. The fact that we are dealing with an evolving system (with variables and permanent features) endowed with a tempo…
-Infinity robust controller design for the synchronization of master-slave chaotic systems with disturbance input
2012
Published version of an article from the journal: Modeling, Identification and Control. Also available from the publisher: http://dx.doi.org/10.4173/mic.2012.1.3 This paper is concerned with the robust control problems for the synchronization of master-slave chaotic systems with disturbance input. By constructing a series of Lyapunov functions, novel H1 robust syn- chronization controllers are designed, whose control regulation possess the characteristic of simpleness and explicitness. Finally, numerical simulations are provided to demonstrate the e ectiveness of the proposed techniques.
The chaotic Dadras–Momeni system: control and hyperchaotification
2015
In this paper a novel three-dimensional autonomous chaotic system, the so called Dadras-Momeni system, is considered and two different control techniques are employed to realize chaos control and chaos synchronization. Firstly, the optimal control of the chaotic system is discussed and an open loop feedback controller is proposed to stabilize the system states to one of the system equilibria, minimizing the cost function by virtue of the Pontryagin’s minimum principle. Then, an adaptive control law and an update rule for uncertain parameters, based on Lyapunov stability theory, are designed both to drive the system trajectories to an equilibrium or to realize a complete synchronization of t…
Intermittent and passivity based control strategies for a hyperchaotic system
2013
In this paper a four-dimensional hyperchaotic system with only one equilibrium is consid- ered and it is shown how the control and the synchronization of this system can be realized via two different control techniques. Firstly, we propose a periodically intermittent con- troller to stabilize the system states to the equilibrium and to achieve the projective syn- chronization of the system both in its periodic and hyperchaotic regime. Then, based on the stability properties of a passive system, we design a linear passive controller, which only requires the knowledge of the system output, to drive the system trajectories asymptoti- cally to the origin. Using the same passivity-based method, …
Complex behavior of ray in gaussian index profile periodicaly segmented waveguide
2006
International audience; In this article, we present a numerical analysis concerning ray propagation in a multimode periodic segmented waveguide with a gaussian index segment profile. We show that this simple waveguide configuration exhibits a complex ray dynamics that can be regular or chaotic depending on the initial conditions.