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.

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.

scholarly journals Realization of a Novel Chaotic System Using Coupling Dual Chaotic System

2021 ◽  
Author(s):  
Salam K. Mousa ◽  
Raied K. Jamal
Keyword(s):  
Time Series ◽  
Chaotic System ◽  
Optical Communications ◽  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Fourier Transforms ◽  
Optical Coupling ◽  
Before And After ◽  
The Lorenz System

Abstract This paper establishes coupling between two various chaotic systems for Lorenz and Rössler circuits. The x-dynamics of Lorenz circuit was coupled numerically with the x dynamics of Rössler circuit. As a result of the optical coupling between these two chaotic systems, it has been observed an exceptional variation in the time series and attractors, which exhibits a novel behavior, leading to a promises method for controlling the chaotic systems. However, performing fast Fourier transforms (FFT) of chaotic dynamics before and after coupling showed an increase in the bandwidth of the Rössler system after its coupling with the Lorenz system, which, in turn increases the possibility of using this system for secure and confidential optical communications.

Determination of Unstable Limit Cycles in Chaotic Systems by the Method of Unrestricted Harmonic Balance

1991 ◽  
Vol 46 (6) ◽  
pp. 499-502 ◽  
Author(s):  
Klaus Neymeyr ◽  
Friedrich Franz Seelig
Keyword(s):  
Chaotic System ◽  
Limit Cycles ◽  
Harmonic Balance ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Method Of Harmonic Balance ◽  
The Lorenz System

AbstractThe method of unrestricted harmonic balance (UHB) which is a generalization of the old method of harmonic balance and that was developed in preceding papers, is mathematically refined and applied to the evaluation of unstable limit cycles. The method is demonstrated for the case of the best investigated chaotic system, namely the Lorenz system. Some representative results are given

Adaptive Synchronization of Time-Delay Chaotic Systems with Intermittent Control

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Yuangan Wang ◽  
Dong Li
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Adaptive Synchronization ◽  
Intermittent Control ◽  
Periodically Intermittent Control ◽  
Control Scheme ◽  
The Lorenz System

AbstractTime delay is a common but not negligible phenomenon in nonlinear systems, which affects the performance of synchronization. Based on principles of intermittent control and Lyapunov stability theories, we establish the synchronization criteria of the time-delay chaotic systems via adaptive intermittent control. The proposed control scheme is under aperiodically intermittent control, which is also extended to periodically intermittent control to better realization. Finally, to verify the effectiveness of our results, we choose the Lorenz system to do simulation.

Chaos in the Periodically Parametrically Excited Lorenz System

2021 ◽  
Vol 31 (08) ◽  
pp. 2130024
Author(s):  
Weisheng Huang ◽  
Xiao-Song Yang
Keyword(s):  
Chaotic Dynamics ◽  
Lorenz System ◽  
Stable Equilibrium ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Parametrically Excited ◽  
The Lorenz System

We demonstrate in this paper a new chaotic behavior in the Lorenz system with periodically excited parameters. We focus on the parameters with which the Lorenz system has only two asymptotically stable equilibrium points, a saddle and no chaotic dynamics. A new mechanism of generating chaos in the periodically excited Lorenz system is demonstrated by showing that some trajectories can visit different attractor basins due to the periodic variations of the attractor basins of the time-varying stable equilibrium points when a parameter of the Lorenz system is varying periodically.

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.

scholarly journals S-Box Based Image Encryption Application Using a Chaotic System without Equilibrium

2019 ◽  
Vol 9 (4) ◽  
pp. 781 ◽  
Author(s):  
Xiong Wang ◽  
Ünal Çavuşoğlu ◽  
Sezgin Kacar ◽  
Akif Akgul ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Chaotic Behavior ◽  
Encryption Algorithm ◽  
Phase Portraits ◽  
Hidden Attractors ◽  
New Chaotic System ◽  
Image Encryption Algorithm

Chaotic systems without equilibrium are of interest because they are the systems with hidden attractors. A nonequilibrium system with chaos is introduced in this work. Chaotic behavior of the system is verified by phase portraits, Lyapunov exponents, and entropy. We have implemented a real electronic circuit of the system and reported experimental results. By using this new chaotic system, we have constructed S-boxes which are applied to propose a novel image encryption algorithm. In the designed encryption algorithm, three S-boxes with strong cryptographic properties are used for the sub-byte operation. Particularly, the S-box for the sub-byte process is selected randomly. In addition, performance analyses of S-boxes and security analyses of the encryption processes have been presented.

Locally Active Memristor with Three Coexisting Pinched Hysteresis Loops and Its Emulator Circuit

2020 ◽  
Vol 30 (13) ◽  
pp. 2050184
Author(s):  
Minghao Zhu ◽  
Chunhua Wang ◽  
Quanli Deng ◽  
Qinghui Hong
Keyword(s):  
Active Region ◽  
Chaotic System ◽  
Piecewise Linear ◽  
Chaotic Oscillation ◽  
Hysteresis Loops ◽  
State Equation ◽  
The Novel ◽  
Oscillation System ◽  
Memristor Emulator ◽  
Pinched Hysteresis

Locally active memristors with multiple coexisting pinched hysteresis loops have attracted the attention of researchers. However, the currently reported multiple coexisting pinched hysteresis loops memristors are obtained by adding additional piecewise-linear terms into the original Chua corsage memristor. This paper proposes a novel locally active memristor by introducing a polynomial characteristic function into the state equation. The novel memristor has three coexisting pinched hysteresis loops, large relative range of active region and simple emulator circuit. The characteristics of the novel memristor such as power-off plot, coexisting pinched hysteresis loops and DC [Formula: see text]–[Formula: see text] plot are studied. The memristor is used in a Chua chaotic system to investigate the effects of locally active characteristic on the chaotic oscillation system. Furthermore, the memristor emulator and chaotic system are designed and implemented by commercial circuit elements. The hardware experiments are consistent with numerical simulations.

T–S FUZZY ADAPTIVE DELAYED FEEDBACK SYNCHRONIZATION FOR TIME-DELAYED CHAOTIC SYSTEMS WITH UNCERTAIN PARAMETERS

2011 ◽  
Vol 25 (23n24) ◽  
pp. 3253-3267 ◽  
Author(s):  
CHOON KI AHN ◽  
PYUNG SOO KIM
Keyword(s):  
Chaotic Systems ◽  
Lorenz System ◽  
Fuzzy Model ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Adaptive Synchronization ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Takagi Sugeno ◽  
Fuzzy Adaptive

In this paper, we propose a new adaptive synchronization method, called a fuzzy adaptive delayed feedback synchronization (FADFS) method, for time-delayed chaotic systems with uncertain parameters. An FADFS controller that is based on the Lyapunov–Krasovskii theory, Takagi–Sugeno (T–S) fuzzy model, and delayed feedback control is developed to guarantee adaptive synchronization. The proposed controller can be obtained by solving the linear matrix inequality (LMI) problem. A numerical example using a time-delayed Lorenz system is discussed to assess the validity of the proposed FADFS method.

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