Approximating hidden chaotic attractors via parameter switching

Marius-F. Danca; Nikolay V. Kuznetsov; Guanrong Chen

doi:10.1063/1.5007925

Approximations of chaotic attractors and its circuit design based on the parameter switching algorithm

Acta Physica Sinica ◽

10.7498/aps.64.200508 ◽

2015 ◽

Vol 64 (20) ◽

pp. 200508

Author(s):

Luo Shao-Xuan ◽

He Bo-Xia ◽

Qiao Ai-Min ◽

Wang Yan-Chun

Keyword(s):

Circuit Design ◽

Chaotic Attractors ◽

Switching Algorithm ◽

Parameter Switching

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Generating Multiple Spherical Attractors via Parameter Switching Control

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127421502412 ◽

2021 ◽

Vol 31 (16) ◽

Author(s):

Changchun Sun ◽

Qicheng Xu

Keyword(s):

Continuous Time ◽

Three Dimensional ◽

Switching Control ◽

Control Technique ◽

Chaotic Attractors ◽

Time System ◽

Offset Boosting ◽

State Dependent ◽

Parameter Switching ◽

Continuous Time System

A three-dimensional smooth continuous-time system with a parameter and two quadratic terms is constructed and a spherical attractor is generated. There exist multiple coexisting spherical attractors based on offset boosting. Two classes of switching signals that depend on the time and the state are designed respectively. By employing a parameter switching control technique, multiple spherical attractors can be generated. Simultaneously, complex chaotic attractors can also be generated by designing a state-dependent switching signal. Numerical examples and corresponding simulations show the effectiveness of the switching control technique.

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

IEICE Proceeding Series ◽

10.15248/proc.1.443 ◽

2014 ◽

Vol 1 ◽

pp. 443-446

Author(s):

Yutaka Shimada ◽

Takuya Kobayashi ◽

Tohru Ikeguchi ◽

Kazuyuki Aihara

Keyword(s):

Chaotic Attractors ◽

Visualization Analysis

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A MODIFIED GENERALIZED LORENZ-TYPE SYSTEM AND ITS CANONICAL FORM

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127409023834 ◽

2009 ◽

Vol 19 (06) ◽

pp. 1931-1949 ◽

Cited By ~ 7

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.

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

Inventions ◽

10.3390/inventions6030049 ◽

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.

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