scholarly journals Some criteria for chaos and no chaos in the quadratic map of the plane

2009 ◽  
Vol 22 (1) ◽  
pp. 105-117 ◽  
Author(s):  
Zeraoulia Elhadj ◽  
Clinton Sprott
Keyword(s):  
Chaotic Attractors ◽  
Quadratic Map

This paper gives some criteria for the existence and the non-existence of chaotic attractors in the general 2-D quadratic map. .

Visualization analysis on stretch-and-fold mechanism of chaotic attractors

2014 ◽  
Vol 1 ◽  
pp. 443-446
Author(s):  
Yutaka Shimada ◽  
Takuya Kobayashi ◽  
Tohru Ikeguchi ◽  
Kazuyuki Aihara
Keyword(s):  
Chaotic Attractors ◽  
Visualization Analysis

A MODIFIED GENERALIZED LORENZ-TYPE SYSTEM AND ITS CANONICAL FORM

2009 ◽  
Vol 19 (06) ◽  
pp. 1931-1949 ◽  
Author(s):  
QIGUI YANG ◽  
KANGMING ZHANG ◽  
GUANRONG CHEN
Keyword(s):  
Special Form ◽  
Topological Structure ◽  
Complex Dynamics ◽  
Type System ◽  
Chaotic Attractors ◽  
Hopf Bifurcations ◽  
Compound Structure ◽  
Two Parameters ◽  
First Time ◽  
New System

In this paper, a modified generalized Lorenz-type system is introduced, which is state-equivalent to a simple and special form, and is parameterized by two parameters useful for chaos turning and system classification. More importantly, based on the parameterized form, two classes of new chaotic attractors are found for the first time in the literature, which are similar but nonequivalent in topological structure. To further understand the complex dynamics of the new system, some basic properties such as Lyapunov exponents, Hopf bifurcations and compound structure of the attractors are analyzed and demonstrated with careful numerical simulations.

scholarly journals A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation

Inventions ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 49
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Basil H. Jasim ◽  
Yasir I. A. Al-Yasir ◽  
Raed A. Abd-Alhameed ◽  
Bilal Naji Alhasnawi
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Real World ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
State Variables ◽  
Digital Implementation ◽  
Dynamical Behaviors ◽  
Real World Applications

In this paper, a new fractional order chaotic system without equilibrium is proposed, analytically and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigations were used to describe the system’s dynamical behaviors including the system equilibria, the chaotic attractors, the bifurcation diagrams, and the Lyapunov exponents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attractors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive control theory was developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state variables for the master and slave. Consequently, the update laws of the slave parameters are obtained, where the slave parameters are assumed to be uncertain and are estimated corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results were obtained by MATLAB and the Arduino Due boards, respectively, with a good consistency between the simulation results and the experimental results, indicating that the new fractional order chaotic system is capable of being employed in real-world applications.

Chaotic Attractors Generated by a Memristor-Based Chaotic System and Julia Fractal

2021 ◽  
Vol 146 ◽  
pp. 110773
Author(s):  
Dengwei Yan ◽  
Lidan Wang ◽  
Shukai Duan ◽  
Jiaojiao Chen ◽  
Jiahao Chen
Keyword(s):  
Chaotic System ◽  
Chaotic Attractors

FROM SYMBOLIC DYNAMICS TO A DIGITAL APPROACH

2001 ◽  
Vol 11 (06) ◽  
pp. 1683-1694 ◽  
Author(s):  
K. KARAMANOS
Keyword(s):  
Symbolic Dynamics ◽  
Chaotic Attractors ◽  
Unimodal Maps ◽  
Quantitative Manner ◽  
The Asymmetry

We show that the numbers generated by the symbolic dynamics of Feigenbaum attractors are transcendental. Due to the asymmetry of the chaotic attractors of unimodal maps around the maximum in the general case, a standard conjecture, that the occurrence of chaos is related to the transcendence of the number defined by the corresponding symbolic dynamics is reassessed and formulated in a quantitative manner. It is concluded that transcendence may provide an appropriate measure of complexity.

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