A New Class of Chaotic Circuit with Logic Elements

2015 ◽  
Vol 24 (09) ◽  
pp. 1550136 ◽  
Author(s):  
Hongtao Li ◽  
Chunbiao Li ◽  
Zeshi Yuan ◽  
Wen Hu ◽  
Xiaochen Zhen
Keyword(s):  
Numerical Simulation ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Logic Gate ◽  
Chaotic Circuit ◽  
Chaotic Flows ◽  
New Class ◽  
Piecewise Linearity

When signum operation is applied in chaotic systems to realize piecewise-linearity, the original nonlinearity turns to be a kind of Boolean calculation, and correspondingly the chaotic circuit can be implemented by an analog structure embedded with some logic-gate circuits. In this paper, as examples based on the diffusionless Lorenz system we proposed a couple of chaotic flows with signum piecewise-linearity, which experimentally resorts to digital gate circuits. The experimental chaotic circuit with logic elements was built, and the oscillation in the physical circuit agrees well with the numerical simulation.

Circuit Design Contains a Class of Squared Term Lorenz Family Chaotic System

2014 ◽  
Vol 602-605 ◽  
pp. 2684-2687
Author(s):  
Yu Zhang ◽  
Chong Lou Tong ◽  
Teng Fei Lei
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Exponent ◽  
Circuit Design ◽  
Chaotic System ◽  
Lorenz System ◽  
Three Dimensional ◽  
System Stability ◽  
Experimental Simulation ◽  
Chaotic Circuit ◽  
New Class

A new class of three-dimensional chaotic system is constructed by algebraic methods, which has a similar structure with the classic Lorenz system but contains the square term. The equilibrium point of the system stability is analyzed, and the numerical simulation is carried on the bifurcation diagram and Lyapunov exponent. The chaotic circuit of these systems is designed by using the software of EWB. The results of the experimental simulation verify the existence of the chaotic attractor, which provides theoretical reference to the application of such system.

ACTIVE TRACKING CONTROL OF THE HYPERCHAOTIC LORENZ SYSTEM

2008 ◽  
Vol 22 (19) ◽  
pp. 1859-1865 ◽  
Author(s):  
XINGYUAN WANG ◽  
DAHAI NIU ◽  
MINGJUN WANG
Keyword(s):  
Numerical Simulation ◽  
Tracking Control ◽  
Chaotic Systems ◽  
Lorenz System ◽  
The Self ◽  
Hyperchaotic System ◽  
Reference Signals ◽  
Tracking Controller ◽  
Hyperchaotic Lorenz System ◽  
Simulation Results

A nonlinear active tracking controller for the four-dimensional hyperchaotic Lorenz system is designed in the paper. The controller enables this hyperchaotic system to track all kinds of reference signals, such as the sinusoidal signal. The self-synchronization of the hyperchaotic Lorenz system and the different-structure synchronization with other chaotic systems can also be realized. Numerical simulation results show the effectiveness of the controller.

A Useful Chaotic Family with Single Linearity and Circuit Implementation Based on FPGA

2016 ◽  
Vol 26 (01) ◽  
pp. 1750017 ◽  
Author(s):  
Zeshi Yuan ◽  
Hongtao Li ◽  
Xiaohua Zhu
Keyword(s):  
Field Programmable Gate Array ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Register Transfer Level ◽  
Chaotic Circuit ◽  
Chaotic Flows ◽  
Chaotic Model ◽  
Field Programmable ◽  
Simulation Results

Recently, a series of typical three-dimensional dissipative chaotic flows where all but one of the nonlinearities are quadratic are studied. Based on this research, a novel chaotic model with only one single linearity is proposed by introducing cubic terms and four new chaotic systems with various characteristics are found. Besides, a chaotic family with a single linearity is constructed with those four chaotic systems and 12 existing systems SL1–SL[Formula: see text] of the chaotic flows. Exploiting the new systems, basic dynamic behaviors are analyzed, including the strange attractors, equilibrium points, Lyapunov exponents as well as the property of multistability. In addition, the corresponding simulation results are illustrated to show those properties expressly. In realizing the chaotic circuit, we utilize the field programmable gate array (FPGA), which is of considerable flexibility, good programmability and stability, instead of analog devices that are easily affected by surroundings. More importantly, the circuit of the proposed chaotic family is realized on a single FPGA over register transfer level (RTL) using 32-bit fixed-point operation. Finally, an experimental FPGA-based circuit is constructed, and the output results are shown on oscilloscope, which agree well with the numerical simulations.

STATISTICS OF SOME LOW-DIMENSIONAL CHAOTIC FLOWS

2001 ◽  
Vol 11 (10) ◽  
pp. 2675-2682 ◽  
Author(s):  
ELENA S. DIMITROVA ◽  
OLEG I. YORDANOV
Keyword(s):  
Chaotic Systems ◽  
Lorenz System ◽  
Slow Process ◽  
Chaotic Flows ◽  
Onset Of Chaos ◽  
Controlling Parameter ◽  
The Lorenz System ◽  
Low Dimensional ◽  
Statistical Symmetry ◽  
Statistical Functions

As a result of the recent finding that the Lorenz system exhibits blurred self-affinity for values of its controlling parameter slightly above the onset of chaos, we study other low-dimensional chaotic flows with the purpose of providing an approximate description of their second-order, two-point statistical functions. The main pool of chaotic systems on which we focus our attention is that reported by Sprott [1994], generalized however to depend on their intrinsic number of parameters. We show that their statistical properties are adequately described as processes with spectra having three segments all of power-law type. On this basis we identify quasi-periodic behavior pertaining to the relatively slow process in the attractors and approximate self-affine statistical symmetry characterizing the fast processes.

Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
Author(s):  
P. D. Kamdem Kuate ◽  
Qiang Lai ◽  
Hilaire Fotsin
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
The Novel ◽  
Algebraic Equations ◽  
The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

A New Category of Three-Dimensional Chaotic Flows with Identical Eigenvalues

2020 ◽  
Vol 30 (02) ◽  
pp. 2050026 ◽  
Author(s):  
Zahra Faghani ◽  
Fahimeh Nazarimehr ◽  
Sajad Jafari ◽  
Julien C. Sprott
Keyword(s):  
Chaotic Systems ◽  
Autonomous Systems ◽  
Three Dimensional ◽  
Special Property ◽  
Computer Search ◽  
Chaotic Flows ◽  
Stable Equilibria ◽  
Dynamical Properties ◽  
Simple Systems ◽  
First Time

In this paper, some new three-dimensional chaotic systems are proposed. The special property of these autonomous systems is their identical eigenvalues. The systems are designed based on the general form of quadratic jerk systems with 10 terms, and some systems with stable equilibria. Using a systematic computer search, 12 simple chaotic systems with identical eigenvalues were found. We believe that systems with identical eigenvalues are described here for the first time. These simple systems are listed in this paper, and their dynamical properties are investigated.

Optimal Synchronization of a Memristive Chaotic Circuit

2016 ◽  
Vol 26 (06) ◽  
pp. 1650093 ◽  
Author(s):  
Michaux Kountchou ◽  
Patrick Louodop ◽  
Samuel Bowong ◽  
Hilaire Fotsin ◽  
Jurgen Kurths
Keyword(s):  
Numerical Simulations ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Analog Circuit ◽  
Electronic Circuit ◽  
Dynamical Behavior ◽  
Circuit Implementation ◽  
Chaotic Circuit ◽  
Dynamical Properties ◽  
Analog Circuit Implementation

This paper deals with the problem of optimal synchronization of two identical memristive chaotic systems. We first study some basic dynamical properties and behaviors of a memristor oscillator with a simple topology. An electronic circuit (analog simulator) is proposed to investigate the dynamical behavior of the system. An optimal synchronization strategy based on the controllability functions method with a mixed cost functional is investigated. A finite horizon is explicitly computed such that the chaos synchronization is achieved at an established time. Numerical simulations are presented to verify the effectiveness of the proposed synchronization strategy. Pspice analog circuit implementation of the complete master-slave-controller systems is also presented to show the feasibility of the proposed scheme.

scholarly journals Numerical detection of unstable periodic orbits in continuous-time dynamical systems with chaotic behaviors

2007 ◽  
Vol 14 (5) ◽  
pp. 615-620 ◽  
Author(s):  
Y. Saiki
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
Infinite Number ◽  
Continuous Time ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Complex Phenomenon ◽  
Unstable Periodic Orbits ◽  
Newton Raphson ◽  
The Lorenz System

Abstract. An infinite number of unstable periodic orbits (UPOs) are embedded in a chaotic system which models some complex phenomenon. Several algorithms which extract UPOs numerically from continuous-time chaotic systems have been proposed. In this article the damped Newton-Raphson-Mees algorithm is reviewed, and some important techniques and remarks concerning the practical numerical computations are exemplified by employing the Lorenz system.

STABILIZATION OF CHAOTIC SYSTEMS USING LINEAR SAMPLED-DATA CONTROLLER

2007 ◽  
Vol 17 (06) ◽  
pp. 2021-2031 ◽  
Author(s):  
H. K. LAM ◽  
F. H. F. LEUNG
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Design Procedure ◽  
Sampling Period ◽  
Feedback Gain ◽  
Sampled Data ◽  
Lyapunov Approach ◽  
And Performance ◽  
Data Controller

This paper proposes a linear sampled-data controller for the stabilization of chaotic system. The system stabilization and performance issues will be investigated. Stability conditions will be derived based on the Lyapunov approach. The findings of the maximum sampling period and the feedback gain of controller, and the optimization of system performance will be formulated as a generalized eigenvalue minimization problem. Based on the analysis result, a stable linear sampled-data controller can be realized systematically to stabilize a chaotic system. An example of stabilizing a Lorenz system will be given to illustrate the design procedure and effectiveness of the proposed approach.

Jacobi Stability of Simple Chaotic Systems with One Lyapunov Stable Equilibrium

2021 ◽  
Author(s):  
Changzhi Li ◽  
Biyu Chen ◽  
Aimin Liu ◽  
Huanhuan Tian
Keyword(s):  
Chaotic Systems ◽  
Stable Equilibrium ◽  
Geometrical Structure ◽  
Chaotic Behavior ◽  
Internal Environment ◽  
Small Perturbations ◽  
Chaotic Flows ◽  
Dynamical Behaviors ◽  
Onset Of Chaos ◽  
Deviation Vector

Abstract This paper presents Jacobi stability analysis of 23 simple chaotic systems with only one Lyapunov stable equilibrium by Kosambi-Cartan-Chern (KCC) theory, and analyzes the chaotic behavior of these systems from the geometric viewpoint. Different from Lyapunov stability, the unique equilibrium for each system is always Jacobi unstable. Moreover, the dynamical behaviors of deviation vector near equilibrium are discussed to reveal the onset of chaos for these 23 systems, and show furtherly the coexistence of unique Lyapunov stable equilibrium and chaotic attractor for each system geometrically. The obtaining results show that these chaotic systems are not robust to small perturbations of the equilibrium, indicating that the systems are extremely sensitive to internal environment. This reveals that the chaotic flows generated by these systems may be related to Jacobi instability of the equilibrium. It is hoped that the study of this paper can help reveal the true geometrical structure of hidden chaotic attractors.

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