Mean square function synchronization of chaotic systems with stochastic effects

2012 ◽  
Vol 70 (1) ◽  
pp. 289-294 ◽  
Author(s):  
Yuhua Xu ◽  
Bing Li ◽  
Wuneng Zhou ◽  
Jian’an Fang
Keyword(s):  
Chaotic Systems ◽  
Square Function ◽  
Mean Square ◽  
Stochastic Effects ◽  
Function Synchronization

scholarly journals Secure Communication of Fractional Complex Chaotic Systems Based on Fractional Difference Function Synchronization

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Jiaxun Liu ◽  
Zuoxun Wang ◽  
Minglei Shu ◽  
Fangfang Zhang ◽  
Sen Leng ◽  
...  
Keyword(s):  
Secure Communication ◽  
Chaotic Systems ◽  
Digital Signal ◽  
Fractional Difference ◽  
Voice Signal ◽  
Difference Function ◽  
Image Cryptosystem ◽  
Definition Of ◽  
Complex Chaotic Systems ◽  
Function Synchronization

Fractional complex chaotic systems have attracted great interest recently. However, most of scholars adopted integer real chaotic system and fractional real and integer complex chaotic systems to improve the security of communication. In this paper, the advantages of fractional complex chaotic synchronization (FCCS) in secure communication are firstly demonstrated. To begin with, we propose the definition of fractional difference function synchronization (FDFS) according to difference function synchronization (DFS) of integer complex chaotic systems. FDFS makes communication secure based on FCCS possible. Then we design corresponding controller and present a general communication scheme based on FDFS. Finally, we respectively accomplish simulations which transmit analog signal, digital signal, voice signal, and image signal. Especially for image signal, we give a novel image cryptosystem based on FDFS. The results demonstrate the superiority and good performances of FDFS in secure communication.

Function Projective Synchronization in Complex Networks with Stochastic Effects via Hybrid Feedback Control

2014 ◽  
Vol 511-512 ◽  
pp. 1008-1011
Author(s):  
Yun Guo Jin ◽  
Shou Ming Zhong
Keyword(s):  
Feedback Control ◽  
Complex Networks ◽  
Control Method ◽  
Exponential Synchronization ◽  
Projective Synchronization ◽  
Mean Square ◽  
Stochastic Effects ◽  
Function Projective Synchronization ◽  
Feedback Control Method

In this paper, the problem of function projective synchronization is investigated for complex networks with stochastic effects. A hybrid feedback control method is designed to achieve function projective synchronization for the complex networks. Using Gronwally' inequality, we obtain some conditions to guarantee that the complex networks can realize mean square synchronization and mean square exponential synchronization, respectively.

scholarly journals Delayed impulive SDEs driven by multiplicative fBm noise and additive fBm noise

2021 ◽  
Author(s):  
Xia Zhou ◽  
Dongpeng Zhou ◽  
Xiu Liu ◽  
Jinde Cao ◽  
Changfeng Xue
Keyword(s):  
Chaotic Systems ◽  
Impulsive Control ◽  
Chaotic Oscillator ◽  
Mean Square ◽  
Ultimate Boundedness ◽  
Response System ◽  
Pth Moment Exponential Stability ◽  
The Stability ◽  
Moment Exponential Stability ◽  
Lyapunov Technique

The stability and boundedness for delayed impulsive SDEs driven by fBm are studied in this paper. Two kinds of noises, i.e, additive fBm noise and mul-tiplicative fBm noise are both taken into consideration. By using stochastic Lyapunov technique and impulsive control theory, sufficient criteria for pth moment exponential stability and mean square ultimate boundedness are derived, for two kinds of fBm driven delayed impulsive SDEs, respectively. As application, the obtained results are used to do practical synchronization w.r.t. a class of chaotic systems, in which the response system is perturbed by additive fBm noises. Finally, A Chua chaotic oscillator is given to verify the validity and applicability of the derived results.

Finite-time complex function synchronization of multiple complex-variable chaotic systems with network transmission and combination mode

2018 ◽  
Vol 24 (22) ◽  
pp. 5461-5471 ◽  
Author(s):  
Xiangyong Chen ◽  
Jinde Cao ◽  
Ju H Park ◽  
Guangdeng Zong ◽  
Jianlong Qiu
Keyword(s):  
Complex Variable ◽  
Finite Time ◽  
Chaotic Systems ◽  
Simulation Analysis ◽  
Complex Function ◽  
Finite Time Stability ◽  
Detailed Simulation ◽  
Synchronization Mechanisms ◽  
Combination Mode ◽  
Function Synchronization

Two kinds of finite-time complex function synchronization for multiple complex-variable chaotic systems are investigated. Both the transmission mode and combination mode are respectively considered. By considering complex functions as the scaling factors, the definitions of the two different synchronization mechanisms are established, and the appropriate schemes are proposed to guarantee the finite-time stability of all error systems. Furthermore, two verifiable criteria are derived to synchronize multi-systems. Finally, detailed simulation analysis is provided to validate the effectiveness of all innovations.

A Fast Image Encryption by Bit-Chaotic-Shuffle Based on Chaotic Systems

2012 ◽  
Vol 424-425 ◽  
pp. 761-764
Author(s):  
Chuan Kuei Huang ◽  
Hsiau Hsian Nien ◽  
Shu Li Hsu ◽  
Siang Shang Tu
Keyword(s):  
Chaotic Systems ◽  
Computer Networking ◽  
Correction Coefficient ◽  
Mean Square ◽  
Level Spectrum ◽  
Key Space ◽  
Highly Sensitive ◽  
Technology Users ◽  
Encryption Method ◽  
Single Pixel

Due to rapid developments in computer networking and communi- cation technology, users have begun to use personal computers to transmit images through the internet. However, this activity puts users at risk of hacker attacks and theft. Although single pixel position shuffling can eliminate an image’s contour, it cannot hide the characteristics of the grey-level spectrum. Because the dynamic trajectories of a chaotic system are highly sensitive to the initial values of the system, applying chaotic-ciphering to the image will result in a good encryption effect, and significantly enhance the key space of the encrypted image. For these reasons, this paper propose a novel and simple Bit-Chaotic-Shuffle (BCS) technique for encryption on color images that is based on multi chaotic systems. This technique not only eliminates image contours, but also disorders the characteristics of the RGB-level spectrum. This encryption method also adopts three chaotic systems in which the key space reaches 10137, thoroughly preventing decryption by an exhaustive attack. This paper further applies the correction coefficient and Mean Square Error (MSE) methods to prove the encryption and the high security performance of the proposed encryption system

ANTICIPATED FUNCTION SYNCHRONIZATION WITH UNKNOWN PARAMETERS OF DISCRETE-TIME CHAOTIC SYSTEMS

2009 ◽  
Vol 20 (04) ◽  
pp. 597-608 ◽  
Author(s):  
YIN LI ◽  
BIAO LI ◽  
YONG CHEN
Keyword(s):  
Chaotic System ◽  
Discrete Time ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Law ◽  
Unknown Parameters ◽  
Synchronization Problem ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems ◽  
Function Synchronization

In this paper, firstly, the control problem for the chaos synchronization of discrete-time chaotic (hyperchaotic) systems with unknown parameters are considered. Next, backstepping control law is derived to make the error signals between drive 2D discrete-time chaotic system and response 2D discrete-time chaotic system with two uncertain parameters asymptotically synchronized. Finally, the approach is extended to the synchronization problem for 3D discrete-time chaotic system with two unknown parameters. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.

Phase Characterization in Experimental Chaotic Systems

2014 ◽  
Vol 706 ◽  
pp. 137-148
Author(s):  
R. Follmann ◽  
E. Rosa ◽  
E.E.N. Macau ◽  
J.R.C. Piqueira
Keyword(s):  
Time Series ◽  
Chaotic Systems ◽  
Mean Square ◽  
Attractor Reconstruction ◽  
Wide Range ◽  
Experimental Time Series ◽  
The Mean ◽  
Phase Characterization ◽  
Scalar Time Series ◽  
Sinusoidal Function

In this work we present and discuss a method for measuring the phase of chaotic systems. This method has as input a scalar time series and operates by estimating a fundamental frequency for short segments, or windows, along the whole extension of the signal. It minimizes the mean square error of fitting a sinusoidal function to the series segment. This approach does not require following the trajectory on the attractor, works well over a wide range of adjustable parameters, is of easy implementation, and is particularly appealing for experimental settings with single signal outputs since there is no need of attractor reconstruction. We demonstrate the applicability of this method on experimental time series obtained from two coupled Chua circuits.

scholarly journals Lyapunov-Based Controller for a Class of Stochastic Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Hossein Shokouhi-Nejad ◽  
Amir Rikhtehgar Ghiasi ◽  
Saeed Pezeshki
Keyword(s):  
Differential Equation ◽  
White Noise ◽  
Transient Response ◽  
Chaotic Systems ◽  
Direct Method ◽  
Control Law ◽  
Mean Square ◽  
Intrinsic Properties ◽  
General Control ◽  
Simulation Results

This study presents a general control law based on Lyapunov’s direct method for a group of well-known stochastic chaotic systems. Since real chaotic systems have undesired random-like behaviors which have also been deteriorated by environmental noise, chaotic systems are modeled by exciting a deterministic chaotic system with a white noise obtained from derivative of Wiener process which eventually generates an Ito differential equation. Proposed controller not only can asymptotically stabilize these systems in mean-square sense against their undesired intrinsic properties, but also exhibits good transient response. Simulation results highlight effectiveness and feasibility of proposed controller in outperforming stochastic chaotic systems.

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