SYNCHRONIZATION THEOREM FOR A CHAOTIC SYSTEM

1995 ◽  
Vol 05 (01) ◽  
pp. 297-302 ◽  
Author(s):  
JÖRG SCHWEIZER ◽  
MICHAEL PETER KENNEDY ◽  
MARTIN HASLER ◽  
HERVÉ DEDIEU
Keyword(s):  
Lyapunov Function ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Secure Communication ◽  
Communication Systems ◽  
Chaotic Systems ◽  
Secure Communications ◽  
Error Feedback ◽  
Response System ◽  
Synchronization Method

Since Pecora & Carroll [Pecora & Carroll, 1991; Carroll & Pecora, 1991] have shown that it is possible to synchronize chaotic systems by means of a drive-response partition of the systems, various authors have proposed synchronization schemes and possible secure communications applications [Dedieu et al., 1993, Oppenheim et al., 1992]. In most cases synchronization is proven by numerically computing the conditional Lyapunov exponents of the response system. In this work a new synchronization method using error-feedback is developed, where synchronization is provable using a global Lyapunov function. Furthermore, it is shown how this scheme can be applied to secure communication systems.

A SIMPLE WAY TO SYNCHRONIZE CHAOTIC SYSTEMS WITH APPLICATIONS TO SECURE COMMUNICATION SYSTEMS

1993 ◽  
Vol 03 (06) ◽  
pp. 1619-1627 ◽  
Author(s):  
CHAI WAH WU ◽  
LEON O. CHUA
Keyword(s):  
Lyapunov Exponents ◽  
Secure Communication ◽  
Communication Systems ◽  
Chaotic Systems ◽  
Functional Form ◽  
Response System ◽  
Definition Of

In this paper, we provide a scheme for synthesizing synchronized circuits and systems. Synchronization of the drive and response system is proved trivially without the need for computing numerically the conditional Lyapunov exponents. We give a definition of the driving and response system having the same functional form, which is more general than the concept of homogeneous driving by Pecora & Carroll [1991]. Finally, we show how synchronization coupled with chaos can be used to implement secure communication systems. This is illustrated with examples of secure communication systems which are inherently error-free in contrast to the signal-masking schemes proposed in Cuomo & Oppenheim [1993a,b] and Kocarev et al. [1992].

scholarly journals A Torus-Chaotic System and Its Pseudorandom Properties

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Jizhao Liu ◽  
Xiangzi Zhang ◽  
Qingchun Zhao ◽  
Jing Lian ◽  
Fangjun Huang ◽  
...  
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic System ◽  
Cyber Security ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Random Number ◽  
Current Knowledge ◽  
Random Number Generator ◽  
Qr Code ◽  
Security Systems

Exploring and investigating new chaotic systems is a popular topic in nonlinear science. Although numerous chaotic systems have been introduced in the literature, few of them focus on torus-chaotic system. The aim of our short work is to widen the current knowledge of torus chaos. In this paper, a new torus-chaotic system is proposed, which has one positive Lyapunov exponent, two zero Lyapunov exponents, and two negative Lyapunov exponents. The dynamic behavior is investigated by Lyapunov exponents, bifurcations, and stability. The analysis shows that this system has an interesting route leading to chaos. Furthermore, the pseudorandom properties of output sequence are well studied and a random number generator algorithm is proposed, which has the potential of being used in several cyber security systems such as the verification code, secure QR code, and some secure communication protocols.

APPLICATION OF ICA–EEMD TO SECURE COMMUNICATIONS IN CHAOTIC SYSTEMS

2012 ◽  
Vol 23 (04) ◽  
pp. 1250028 ◽  
Author(s):  
SHIH-LIN LIN ◽  
PI-CHENG TUNG ◽  
NORDEN E. HUANG
Keyword(s):  
White Noise ◽  
Secure Communication ◽  
Communication Systems ◽  
Chaotic Systems ◽  
Gaussian White Noise ◽  
Secure Communications ◽  
Original Message ◽  
Mixture Of Gaussian

We propose the application of ICA–EEMD to secure communication systems. ICA–EEMD is employed to retrieve the message data encrypted by a mixture of Gaussian white noise and chaotic noise. The results showed that ICA–EEMD can effectively extract the two original message data.

scholarly journals Constructing Discrete Chaotic Systems with Positive Lyapunov Exponents

2018 ◽  
Vol 28 (07) ◽  
pp. 1850084 ◽  
Author(s):  
Chuanfu Wang ◽  
Chunlei Fan ◽  
Qun Ding
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic System ◽  
Secure Communication ◽  
Discrete System ◽  
Chaotic Systems ◽  
Hyperchaotic System ◽  
Universal Method ◽  
Periodic Attractors ◽  
Chaotic Secure Communication ◽  
Hyperchaotic Systems

The chaotic system is widely used in chaotic cryptosystem and chaotic secure communication. In this paper, a universal method for designing the discrete chaotic system with any desired number of positive Lyapunov exponents is proposed to meet the needs of hyperchaotic systems in chaotic cryptosystem and chaotic secure communication, and three examples of eight-dimensional discrete system with chaotic attractors, eight-dimensional discrete system with fixed point attractors and eight-dimensional discrete system with periodic attractors are given to illustrate how the proposed methods control the Lyapunov exponents. Compared to the previous methods, the positive Lyapunov exponents are used to reconstruct a hyperchaotic system.

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.

scholarly journals A Novel Fast Convergence Control Scheme for a Class of 3D Chaotic Systems with Uncertain Parameters and External Disturbances

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Haipeng Su ◽  
Runzi Luo ◽  
Ling Xu ◽  
Meichun Huang ◽  
Jiaojiao Fu
Keyword(s):  
Lyapunov Function ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Fast Convergence ◽  
Uncertain Parameters ◽  
External Disturbances ◽  
Solution Approach ◽  
New Chaotic System ◽  
Convergence Control ◽  
The Stability

This paper studies the control of a class of 3D chaotic systems with uncertain parameters and external disturbances. A new method which is referred as the analytical solution approach is firstly proposed for constructing Lyapunov function. Then, for suppressing the trajectories of the 3D chaotic system to its equilibrium point 00,0,0, a novel fast convergence controller containing parameter λ which determines the convergence rate of the system is presented. By using the designed Lyapunov function, the stability of the closed-loop system is proved via the Lyapunov stability theorem. Computer simulations are employed to a new chaotic system to illustrate the effectiveness of the theoretical results.

LAG PROJECTIVE STOCHASTIC PERTURBED SYNCHRONIZATION FOR CHAOTIC SYSTEMS AND ITS APPLICATION IN SECURE COMMUNICATION

2008 ◽  
Vol 22 (24) ◽  
pp. 4175-4188 ◽  
Author(s):  
YANG TANG ◽  
JIAN-AN FANG ◽  
LIANG CHEN
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Stochastic Perturbation ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Adaptive Feedback ◽  
Communication Scheme ◽  
Simulation Results ◽  
Feedback Method

In this paper, a simple and systematic adaptive feedback method for achieving lag projective stochastic perturbed synchronization of a new four-wing chaotic system with unknown parameters is presented. Moreover, a secure communication scheme based on the adaptive feedback lag projective synchronization of the new chaotic systems with stochastic perturbation and unknown parameters is presented. The simulation results show the feasibility of the proposed method.

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.

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