scholarly journals Transformation of the generalized chaotic system into canonical form

2017 ◽  
Vol 3 (3) ◽  
pp. 117
Author(s):  
Roman Voliansky
Keyword(s):  
Canonical Form ◽  
Chaotic System ◽  
Discrete Model ◽  
Control Algorithm ◽  
Chaotic Systems ◽  
Numerical Algorithms ◽  
Chaotic Attractors ◽  
Output Variable ◽  
State Spaces ◽  
Sample Time

The paper deals with the developing of the numerical algorithms for transformation of generalized chaotic system into canonical form. Such transformation allows us to simplify control algorithm for chaotic system. These algorithms are defined by using Lie derivatives for output variable and solution of nonlinear equations. Usage of proposed algorithm is one of the ways for discovering of new chaotic attractors. These attractors can be obtained by transformation of known chaotic systems into various state spaces. Transformed attractors depend on both parameters of chaotic system and sample time of its discrete model.

Synchronization of Continuous Scalar Chaotic Signal from Uncertain Chaotic System

2013 ◽  
Vol 816-817 ◽  
pp. 843-846
Author(s):  
Jing Wang ◽  
Hui Zhong
Keyword(s):  
Canonical Form ◽  
Chaotic System ◽  
Chaotic Systems ◽  
System Simulation ◽  
Chaotic Signal ◽  
Response System ◽  
Synchronization Scheme

This paper presents the synchronizing problem of scalar chaotic signal. A class of nonlinear chaotic systems is discussed which has unknown part in model. The proposed approach is based on canonical form of the response system. Simulation result shows the effectiveness of our synchronization scheme.

scholarly journals Euler and RK4 Algorithms Based Implementation of Autonomous Chaotic Generator

2019 ◽  
Vol 8 (6) ◽  
pp. 4161-4165
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Numerical Algorithms ◽  
Vital Role ◽  
Fpga Implementation ◽  
Data Sets ◽  
Key Generation ◽  
Number Generator ◽  
Chaos Generator ◽  
Different Chaotic Systems

Chaotic systems plays a vital role in the field of security, data hiding and steganography. FPGA implementation makes more advantageous compared to analog one. Different chaotic systems like chaos generator and nondeterministic number generator used for security purpose and key generation were successfully realized in FPGA. In this paper, FPGA implementation of Pandey-Baghel-Singh chaotic system (PBSCS) using Euler and RK4 numerical algorithms is presented. Pandey-Baghel-Singh chaotic system were obtained using numerical differential solution and numerically modelled in Verilog with the environment of Xilinx Vivado 2017.3 design suite. The design is verified using experimental setup with the help of interfacing to PC and FPGA family of Artix-7 Nexys 4 DDR and Basys3. Performance of the FPGA based chaotic generator using Euler and RK4 algorithm are analyzed using 1 GB data sets with the maximum operating frequency achieved up to 359.71 MH

Hidden Chaotic Attractors and Synchronization for a New Fractional-Order Chaotic System

2019 ◽  
Vol 14 (8) ◽  
Author(s):  
Zuoxun Wang ◽  
Jiaxun Liu ◽  
Fangfang Zhang ◽  
Sen Leng
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Finite Time ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Chaotic Attractors ◽  
Finite Time Stability ◽  
Integer Order ◽  
Different Types ◽  
Synchronization Scheme

Although a large number of hidden chaotic attractors have been studied in recent years, most studies only refer to integer-order chaotic systems and neglect the relationships among chaotic attractors. In this paper, we first extend LE1 of sprott from integer-order chaotic systems to fractional-order chaotic systems, and we add two constant controllers which could produce a novel fractional-order chaotic system with hidden chaotic attractors. Second, we discuss its complicated dynamic characteristics with the help of projection pictures and bifurcation diagrams. The new fractional-order chaotic system can exhibit self-excited attractor and three different types of hidden attractors. Moreover, based on fractional-order finite time stability theory, we design finite time synchronization scheme of this new system. And combination synchronization of three fractional-order chaotic systems with hidden chaotic attractors is also derived. Finally, numerical simulations demonstrate the effectiveness of the proposed synchronization methods.

Generating the New Chaotic Attractors of the Lorenz System Family via Anti-Controlling Method

2012 ◽  
Vol 542-543 ◽  
pp. 1042-1046 ◽  
Author(s):  
Xin Deng
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Attractors ◽  
Chen System ◽  
Lü System ◽  
New Chaotic System ◽  
Dynamical Properties ◽  
The Lorenz System ◽  
Lu System

In this paper, the first new chaotic system is gained by anti-controlling Chen system,which belongs to the general Lorenz system; also, the second new chaotic system is gained by anti-controlling the first new chaotic system, which belongs to the general Lü system. Moreover,some basic dynamical properties of two new chaotic systems are studied, either numerically or analytically. The obtained results show clearly that Chen chaotic system and two new chaotic systems also can form another Lorenz system family and deserve further detailed investigation.

The Control and Synchronization of a Class of Chaotic Systems With Output Variable and External Disturbance

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
Runzi Luo ◽  
Yanhui Zeng
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
External Disturbance ◽  
Output Variable ◽  
Output State ◽  
State Variable ◽  
Unified Chaotic System ◽  
Control And Synchronization

This paper investigates the control and synchronization of a class of chaotic systems with external disturbance. The chaotic systems are assumed that only the output state variable is available. By using the output state variable, two types synchronization schemes, i.e., the chaos-based synchronization and the observer-based synchronization schemes, are discussed. Some novel criteria for the control and synchronization of a class of chaotic systems with external disturbance are proposed. The unified chaotic system is taken as an example to demonstrate the efficiency of the proposed approach.

A Novel Cubic–Equilibrium Chaotic System with Coexisting Hidden Attractors: Analysis, and Circuit Implementation

2017 ◽  
Vol 27 (04) ◽  
pp. 1850066 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Christos Volos ◽  
Sajad Jafari ◽  
Tomasz Kapitaniak
Keyword(s):  
Chaotic System ◽  
Autonomous System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Complex Dynamics ◽  
Three Dimensional ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
Hidden Attractors ◽  
Dynamical Properties

Chaotic systems with a curve of equilibria have attracted considerable interest in theoretical researches and engineering applications because they are categorized as systems with hidden attractors. In this paper, we introduce a new three-dimensional autonomous system with cubic equilibrium. Fundamental dynamical properties and complex dynamics of the system have been investigated. Of particular interest is the coexistence of chaotic attractors in the proposed system. Furthermore, we have designed and implemented an electronic circuit to verify the feasibility of such a system with cubic equilibrium.

scholarly journals Circuit Implementation Synchronization between Two Modified Fractional-Order Lorenz Chaotic Systems via a Linear Resistor and Fractional-Order Capacitor in Parallel Coupling

2021 ◽  
Vol 2021 ◽  
pp. 1-8 ◽  
Author(s):  
Juan Liu ◽  
Xuefeng Cheng ◽  
Ping Zhou
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
Lorenz Chaotic System ◽  
Simulation Results ◽  
Synchronization Scheme

In this study, a modified fractional-order Lorenz chaotic system is proposed, and the chaotic attractors are obtained. Meanwhile, we construct one electronic circuit to realize the modified fractional-order Lorenz chaotic system. Most importantly, using a linear resistor and a fractional-order capacitor in parallel coupling, we suggested one chaos synchronization scheme for this modified fractional-order Lorenz chaotic system. The electronic circuit of chaos synchronization for modified fractional-order Lorenz chaotic has been given. The simulation results verify that synchronization scheme is viable.

scholarly journals Complex Chaotic Attractor via Fractal Transformation

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1115 ◽  
Author(s):  
Shengqiu Dai ◽  
Kehui Sun ◽  
Shaobo He ◽  
Wei Ai
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Digital Circuit ◽  
Chaotic Attractors ◽  
Chaotic Sequences ◽  
Three Dimensional Space

Based on simplified Lorenz multiwing and Chua multiscroll chaotic systems, a rotation compound chaotic system is presented via transformation. Based on a binary fractal algorithm, a new ternary fractal algorithm is proposed. In the ternary fractal algorithm, the number of input sequences is extended from 2 to 3, which means the chaotic attractor with fractal transformation can be presented in the three-dimensional space. Taking Lorenz system, rotation Lorenz system and compound chaotic system as the seed chaotic systems, the dynamics of the complex chaotic attractors with fractal transformation are analyzed by means of bifurcation diagram, complexity and power spectrum, and the results show that the chaotic sequences with fractal transformation have higher complexity. As the experimental verification, one kind of complex chaotic attractors is implemented by DSP, and the result is consistent with that of the simulation, which verifies the feasibility of digital circuit implement.

scholarly journals A Chaotic System with an Infinite Number of Equilibrium Points: Dynamics, Horseshoe, and Synchronization

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Christos Volos ◽  
Sundarapandian Vaidyanathan ◽  
Xiong Wang
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Equilibrium Analysis ◽  
Chaotic Attractors ◽  
Hidden Attractors ◽  
New Chaotic System ◽  
Topological Horseshoes

Discovering systems with hidden attractors is a challenging topic which has received considerable interest of the scientific community recently. This work introduces a new chaotic system having hidden chaotic attractors with an infinite number of equilibrium points. We have studied dynamical properties of such special system via equilibrium analysis, bifurcation diagram, and maximal Lyapunov exponents. In order to confirm the system’s chaotic behavior, the findings of topological horseshoes for the system are presented. In addition, the possibility of synchronization of two new chaotic systems with infinite equilibria is investigated by using adaptive control.

scholarly journals Multivariate Multiscale Complexity Analysis of Self-Reproducing Chaotic Systems

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 556 ◽  
Author(s):  
Shaobo He ◽  
Chunbiao Li ◽  
Kehui Sun ◽  
Sajad Jafari
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Complexity Analysis ◽  
Initial Conditions ◽  
Scale Factor ◽  
The Self ◽  
Permutation Entropy ◽  
Chaotic Attractors

Designing a chaotic system with infinitely many attractors is a hot topic. In this paper, multiscale multivariate permutation entropy (MMPE) and multiscale multivariate Lempel–Ziv complexity (MMLZC) are employed to analyze the complexity of those self-reproducing chaotic systems with one-directional and two-directional infinitely many chaotic attractors. The analysis results show that complexity of this class of chaotic systems is determined by the initial conditions. Meanwhile, the values of MMPE are independent of the scale factor, which is different from the algorithm of MMLZC. The analysis proposed here is helpful as a reference for the application of the self-reproducing systems.

Sign in / Sign up

Export Citation Format

Share Document