scholarly journals Study on Amplitude Modulation Principle of Chaotic System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
Jian-Rong Du ◽  
Chun-Lai Li ◽  
Kun Qian ◽  
Zhao-Yu Li ◽  
Wen Li
Keyword(s):  
Chaotic System ◽  
Amplitude Modulation ◽  
Chaotic Systems ◽  
Nonlinear Coefficient ◽  
Signal Amplitude ◽  
Chaotic Signal ◽  
Necessary Condition ◽  
Simple Method ◽  
Preliminary Study ◽  
Nonzero Equilibrium

Exploring the amplitude modulation phenomenon of chaotic signal has become a subject of great concern in recent years. This paper mainly concentrates on the preliminary study on amplitude modulation principle of a chaotic system. First, two 3D chaotic systems with quadratic product terms are introduced for studying the amplitude modulation phenomenon of chaotic signal. It is found that the signal amplitude of the first system can be controlled by partial quadratic coefficient. But for the second system, none of nonlinear coefficient can be employed to control the signal amplitude. Then, the amplitude modulation principle of chaotic system is preliminarily studied by exploring the intrinsic relationship between nonzero equilibrium point and phase space trajectory, and it is further validated by introducing unified parameter to the two 3D chaotic systems. As a necessary condition, the principle provides a feasible and simple method for constructing and analyzing an amplitude modulation chaotic system.

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.

Matrix Projective Synchronization of Chaotic Systems and the Application in Secure Communication

2014 ◽  
Vol 644-650 ◽  
pp. 4216-4220
Author(s):  
Feng Liu
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Chaotic Signal ◽  
Projective Synchronization ◽  
Information Signal ◽  
Simulation Results

First of all, we investigate adaptive matrix projective synchronization of the chaotic system. Finally, this method is applied to secure communication through improved chaotic masking. The information signal is mixed with the chaotic signal before being transmitted, and is recovered without distortion through the synchronized receiver. Simulation results show that the scheme has a good performance.

scholarly journals A novel chaotic system and its topological horseshoe

2013 ◽  
Vol 18 (1) ◽  
pp. 66-77 ◽  
Author(s):  
Chunlai Li ◽  
Lei Wu ◽  
Hongmin Li ◽  
Yaonan Tong
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Signal Amplitude ◽  
Topological Horseshoe ◽  
Lorenz Chaotic System ◽  
Construction Pattern ◽  
Lyapunov Exponent Spectrum

Based on the construction pattern of Chen, Liu and Qi chaotic systems, a new threedimensional (3D) chaotic system is proposed by developing Lorenz chaotic system. It’s found that when parameter e varies, the Lyapunov exponent spectrum keeps invariable, and the signal amplitude can be controlled by adjusting e. Moreover, the horseshoe chaos in this system is investigated based on the topological horseshoe theory.

SYNCHRONIZATION BASED SIGNAL TRANSMISSION WITH HETEROGENEOUS CHAOTIC SYSTEMS

2000 ◽  
Vol 10 (11) ◽  
pp. 2489-2497 ◽  
Author(s):  
K. MURALI
Keyword(s):  
Chaotic System ◽  
Small Amplitude ◽  
Feedback Loop ◽  
Chaotic Systems ◽  
Signal Transmission ◽  
Chaotic Signal ◽  
Digital Information ◽  
Information Signal ◽  
New Information

By considering cascaded heterogeneous chaotic systems with drive-response configurations, information signal is encoded in the first chaotic system of the drive-module. A small amplitude chaotic signal from this first system is used as new information signal to the second different chaotic system within the drive-module. The chaotic signal from the second system of the drive-module is now transmitted to the response-module. An appropriate feedback loop is constructed in the response-module to achieve synchronization among the variables of the drive- and response-modules. We apply this approach to transmit analog and digital information signals in which the quality of the recovered signal is higher and the encoding is potentially secure.

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.

Soft Computing Simulations of Chaotic Systems

2019 ◽  
Vol 29 (08) ◽  
pp. 1950112 ◽  
Author(s):  
Erivelton G. Nepomuceno ◽  
Priscila F. S. Guedes ◽  
Alípio M. Barbosa ◽  
Matjaž Perc ◽  
Robert Repnik
Keyword(s):  
Lower Bound ◽  
Soft Computing ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Logistic Map ◽  
Largest Lyapunov Exponent ◽  
Lower And Upper Bounds ◽  
Finite Precision ◽  
Chua Circuit ◽  
Widespread Interest

Soft computing strategies are drawing widespread interest in engineering and science fields, particularly so because of their capacity to reason and learn in a domain of inherent uncertainty, approximation, and unpredictability. However, soft computing research devoted to finite precision effects in chaotic system simulations is still in a nascent stage, and there are ample opportunities for new discoveries. In this paper, we consider the error that is due to finite precision in the simulation of chaotic systems. We present a generalized version of the lower bound error using an arbitrary number of natural interval extensions. The lower bound error has been used to simulate a chaotic system with lower and upper bounds. The width of this interval does not diverge, which is an advantage compared to other techniques. We illustrate our approach on three systems, namely the logistic map, the Singer map and the Chua circuit. Moreover, we validate the method by calculating the largest Lyapunov exponent.

MUTUAL AND SELF-COMPOUNDING OF CHAOTIC SYSTEMS

1996 ◽  
Vol 06 (04) ◽  
pp. 759-767
Author(s):  
R. SINGH ◽  
P.S. MOHARIR ◽  
V.M. MARU
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Dynamic Systems ◽  
Mantle Convection ◽  
Chaotic Systems ◽  
Compound System ◽  
Two Systems

The notion of compounding a chaotic system was introduced earlier. It consisted of varying the parameters of the compoundee system in proportion to the variables of the compounder system, resulting in a compound system which has in general higher Lyapunov exponents. Here, the notion is extended to self-compounding of a system with a real-earth example, and mutual compounding of dynamic systems. In the former, the variables in a system perturb its parameters. In the latter, two systems affect the parameters of each other in proportion to their variables. Examples of systems in such compounding relationships are studied. The existence of self-compounding is indicated in the geodynamics of mantle convection. The effect of mutual compounding is studied in terms of Lyapunov exponent variations.

scholarly journals Hybrid Passivity Based and Fuzzy Type-2 Controller for Chaotic and Hyper-Chaotic Systems

2017 ◽  
Vol 11 (2) ◽  
pp. 96-103 ◽  
Author(s):  
Fernando Serrano ◽  
Josep M. Rossell
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic System ◽  
Control Strategy ◽  
Chaotic Systems ◽  
Control Law ◽  
Four Dimensions ◽  
Design Requirements ◽  
The Stability ◽  
Theoretical Results

AbstractIn this paper a hybrid passivity based and fuzzy type-2 controller for chaotic and hyper-chaotic systems is presented. The proposed control strategy is an appropriate choice to be implemented for the stabilization of chaotic and hyper-chaotic systems due to the energy considerations of the passivity based controller and the flexibility and capability of the fuzzy type-2 controller to deal with uncertainties. As it is known, chaotic systems are those kinds of systems in which one of their Lyapunov exponents is real positive, and hyper-chaotic systems are those kinds of systems in which more than one Lyapunov exponents are real positive. In this article one chaotic Lorentz attractor and one four dimensions hyper-chaotic system are considered to be stabilized with the proposed control strategy. It is proved that both systems are stabilized by the passivity based and fuzzy type-2 controller, in which a control law is designed according to the energy considerations selecting an appropriate storage function to meet the passivity conditions. The fuzzy type-2 controller part is designed in order to behave as a state feedback controller, exploiting the flexibility and the capability to deal with uncertainties. This work begins with the stability analysis of the chaotic Lorentz attractor and a four dimensions hyper-chaotic system. The rest of the paper deals with the design of the proposed control strategy for both systems in order to design an appropriate controller that meets the design requirements. Finally, numerical simulations are done to corroborate the obtained theoretical results.

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.

DCSK performance analysis of a chaos-based communication using a newly designed chaotic system

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Namrata Biswas ◽  
Raja Mohamed I
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Signal ◽  
Coherent Detection ◽  
Phase Portraits ◽  
Modulation Scheme ◽  
Threshold Control ◽  
New Chaotic System ◽  
Shift Keying ◽  
Chaos Shift Keying

Abstract In this paper, a new chaotic system has been introduced and the fundamental properties of the system were investigated and presented using a bifurcation diagram, max Lyapunov exponent (LE) and phase portraits. The synchronization of the drive and response system has been done using the threshold control parameter. Later the differential chaos shift keying (DCSK) modulation scheme has been carried out for the system as it is the most efficient modulation scheme. The demodulator detects the data without the use of chaotic signal phase recovery, as it uses the non-coherent detection technique. The results were compared with other modulation schemes using the bit error rate (BER) graph. It reveals that the proposed chaos-based system could be used for secure communication. The system has been implemented using the MATLAB Simulink technique.

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