451 research outputs found

    Constructing multiwing attractors from a robust chaotic system with non-hyperbolic equilibrium points

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    We investigate a three-dimensional (3D) robust chaotic system which only holds two nonhyperbolic equilibrium points, and finds the complex dynamical behaviour of position modulation beyond amplitude modulation. To extend the application of this chaotic system, we initiate a novel methodology to construct multiwing chaotic attractors by modifying the position and amplitude parameters. Moreover, the signal amplitude, range and distance of the generated multiwings can be easily adjusted by using the control parameters, which enable us to enhance the potential application in chaotic cryptography and secure communication. The effectiveness of the theoretical analyses is confirmed by numerical simulations. Particularly, the multiwing attractor is physically realized by using DSP (digital signal processor) chip

    Un attracteur étrange 3D versatile à six ailes

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    To create additional wings to a given strange attractor, several methods based on the heteroclinic loop or switching controls for example are applied, but complicate the approach and require the extension of the system to one or more other dimensions of the phase space. This deflects us from the objectives of research on low-dimensional chaotic systems. Remaining in this narrow area of 3D phase spaces to invent multi-wing attractors constitutes the main scope of the present paper. Indeed, we present a rapid investigation of a very simple autonomous 3D system of firts-order differential equations with a rich variety of phase portraits. This new intentionally constructed model exhibits double, four-or even six-wing strange attractors. We point out that under the influence of the scalar parameters, such versatile chaotic attractors are obtained. A similar sequence was likewise observed for the periodic behaviors. Besides, both chaotic or regular featured trajectories are found to be in bilateral agreement even when the morphology of the portrait changes. Obviously, we present the basic attributes of the system and its bifurcation diagram. Eventually, we emphasize that the study of the relationship between the written differential equations and the observed characteristics of attractors remains undervalued.En vue de susciter l"apparition d"ailes supplémentaires pour un attracteur étrange donné, plusieurs méthodes basées sur la boucle hétéroclinique ou une commande de commutation, par exemple, sont appliquées. Toutefois, elles compliquent l'approche et nécessitent l'extension du système vers une ou plusieurs autres dimensions de l'espace des phases. Cela nous détourne des objectifs même de la recherche sur les systèmes chaotiques à faible dimension. C'est ainsi que rester dans cette zone étroite d'espaces de phase 3D pour inventer des attracteurs à ailes multiples constitue le principal sujet du présent article. En effet, nous présentons une étude rapide d’un système 3D très simple et autonome d’équations différentielles du premier ordre avec une grande variété de portraits de phase. Ce nouveau modèle construit intentionnellement présente des attracteurs étranges à deux, quatre voire même six ailes. Nous soulignons que sous l’influence des seuls paramètres scalaires, de tels attracteurs chaotiques versatiles sont obtenus. Une séquence similaire a également été observée pour les comportements périodiques. En outre, les trajectoires chaotiques ou régulières sont en accord bilatéral même lorsque la morphologie du portrait de phase change. Nous présentons évidemment les attributs de base du système et son diagramme de bifurcation. Finalement, nous soulignons que l’étude de la relation entre la formulation des équations différentielles et les caractéristiques observées des attracteurs demeure marginale dans la littérature scientifique

    On new chaotic and hyperchaotic systems: A literature survey

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    This paper provides a thorough survey of new chaotic and hyperchaotic systems. An analysis of the dynamic behavior of these complex systems is presented by pointing out their originality and elementary characteristics. Recently, such systems have been increasingly used in various fields such as secure communication, encryption and finance and so on. In practice, each field requires specific performances with peculiar complexity. A particular classification is then proposed in this paper based on the Lyapunov exponent, the equilibriums points and the attractor forms

    A universal variable extension method for designing multi-scroll/wing chaotic systems

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    © 2023 IEEE. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1109/TIE.2023.3299020Developing a universal design method to construct different multiscroll/wing chaotic systems (MS/WCSs) has been challenging. This article proposes a general design method for MS // WCSs called the universal variable extension method (UVEM). It is a simple but effective approach that generates one-direction (1-D) and 2-D multiscroll/wing chaotic attractors. Using any double-scroll/wing chaotic system as the basic system, the UVEM is able to construct different MS/WCSs. Employing Chua's chaotic system and Lorenz chaotic system as two examples, we construct two MSCSs (including 1-D and 2-D) and two MWCSs (including 1-D and 2-D), respectively. Theoretical analysis and numerical simulation show that the constructed MS/WCSs not only can generate 1-D and 2-D multiscroll/wing chaotic attractors but also have 1-D and 2-D initial boosting behaviors. This means that the MS/WCSs designed by the UVEM are very sensitive to their initial states, and have better unpredictability and more complex chaotic behaviors. To show the simplicity of UVEM in hardware implementation, we develop a field-programmable gate array-based digital hardware platform to implement the designed MS // WCSs. Finally, a new pseudorandom number generator is proposed to investigate the application of the MS/WCSs. All P-values obtained by the NIST SP800-22 test are larger than 0.01, which indicates that the MS/WCSs designed by UVEM have high randomness.Peer reviewe

    A 3-D four-wing attractor and its analysis

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    Abstract: In this paper, several three dimensional (3-D) four-wing smooth quadratic autonomous chaotic systems are analyzed. It is shown that these systems have a number of similar features. A new 3-D continuous autonomous system is proposed based on these features. The new system can generate a four-wing chaotic attractor with less terms in the system equations. Several basic properties of the new system is analyzed by means of Lyapunov exponents, bifurcation diagrams and Poincare maps. Phase diagrams show that the equilibria are related to the existence of multiple wings

    Simulation studies on the design of optimum PID controllers to suppress chaotic oscillations in a family of Lorenz-like multi-wing attractors

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    This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Multi-wing chaotic attractors are highly complex nonlinear dynamical systems with higher number of index-2 equilibrium points. Due to the presence of several equilibrium points, randomness and hence the complexity of the state time series for these multi-wing chaotic systems is much higher than that of the conventional double-wing chaotic attractors. A real-coded Genetic Algorithm (GA) based global optimization framework has been adopted in this paper as a common template for designing optimum Proportional-Integral-Derivative (PID) controllers in order to control the state trajectories of four different multi-wing chaotic systems among the Lorenz family viz. Lu system, Chen system, Rucklidge (or Shimizu Morioka) system and Sprott-1 system. Robustness of the control scheme for different initial conditions of the multi-wing chaotic systems has also been shown

    A new type of four-wing chaotic attractors in 3-D quadratic autonomous systems.

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    Abstract: In this paper, several smooth canonical 3-D continuous autonomous systems are proposed in terms of the coefficients of nonlinear terms. These systems are derived from the existing 3-D four-wing smooth continuous autonomous chaotic systems. These new systems are the simplest chaotic attractor systems which can exhibit four wings. They have the basic structure of the existing 3-D four-wing systems, which means they can be extended to the existing 3-D fourwing chaotic systems by adding some linear and/or quadratic terms. Two of these systems are analyzed. Although the two systems are similar to each other in structure, they are different in dynamics. One is sensitive to the initializations and sampling time, but another is not, which is shown by comparing Lyapunov exponents, bifurcation diagrams, and Poincaré maps

    Analog electronic circuit design of the Cao 4D hyperchaotic finance system

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    Chaotic and hyperchaotic systems have been used in different fields of science in recent years. Many chaotic and hyperchaotic systems with different behaviors have been introduced in the literature. Especially in chaotic system based encryption, random number generator and communication applications, hyperchaotic systems are more preferred because of their more complex characteristics. The chaotic and hyperchaotic systems introduced in the literature are generally presented only as numerical simulation. However, it is necessary to design the electronic circuit for the use of the systems in real applications. In this study, numerical simulation results of four-dimensional (4D) hyperchaotic finance system introduced by Cao in 2018 were obtained and then analog electronic circuit design was realized. Numerical simulation results and designed electronic circuit outputs have confirmed each other. As a result, it is ensured that Cao 4D hyperchaotic finance system can be used in real engineering applications
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