Identification of fractional chaotic system parameters

2004 ◽  
Vol 22 (4) ◽  
pp. 897-905 ◽  
Author(s):  
Yousef Al-Assaf ◽  
Reyad El-Khazali ◽  
Wajdi Ahmad
Keyword(s):  
Chaotic System ◽  
System Parameters ◽  
Fractional Chaotic System

scholarly journals An Efficient Method of Image Encryption Using Rossler Chaotic System

2021 ◽  
Vol 10 (2) ◽  
pp. 11
Author(s):  
Yasir Ahmed Hamza ◽  
Marwan Dahar Omer
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Initial Conditions ◽  
Computation Time ◽  
Encryption Algorithm ◽  
Brute Force ◽  
Symmetric Encryption ◽  
New Approach ◽  
System Parameters ◽  
Plain Image

In this study, a new approach of image encryption has been proposed. This method is depends on the symmetric encryption algorithm RC4 and Rossler chaotic system. Firstly, the encryption key is employed to ciphering a plain image using RC4 and obtains a ciphered-image. Then, the same key is used to generate the initial conditions of the Rossler system. The system parameters and the initial conditions are used as the inputs for Rossler chaotic system to generate the 2-dimensional array of random values. The resulted array is XORed with the ciphered-image to obtain the final encrypted-image. Based on the experimental results, the proposed method has achieved high security and less computation time. Also, the proposed method can be resisted attacks like (statistical, brute-force, and differential).

scholarly journals A Hidden Chaotic System with Multiple Attractors

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1341
Author(s):  
Xiefu Zhang ◽  
Zean Tian ◽  
Jian Li ◽  
Xianming Wu ◽  
Zhongwei Cui
Keyword(s):  
Phase Diagram ◽  
Lyapunov Exponent ◽  
Numerical Methods ◽  
Chaotic System ◽  
Time Domain ◽  
Chaotic Attractor ◽  
Largest Lyapunov Exponent ◽  
Spectral Entropy ◽  
Multiple Attractors ◽  
System Parameters

This paper reports a hidden chaotic system without equilibrium point. The proposed system is studied by the software of MATLAB R2018 through several numerical methods, including Largest Lyapunov exponent, bifurcation diagram, phase diagram, Poincaré map, time-domain waveform, attractive basin and Spectral Entropy. Seven types of attractors are found through altering the system parameters and some interesting characteristics such as coexistence attractors, controllability of chaotic attractor, hyperchaotic behavior and transition behavior are observed. Particularly, the Spectral Entropy algorithm is used to analyze the system and based on the normalized values of Spectral Entropy, the state of the studied system can be identified. Furthermore, the system has been implemented physically to verify the realizability.

scholarly journals Generation of Multi-Scroll Chaotic Attractors from a Jerk Circuit with a Special Form of a Sine Function

Electronics ◽  
2020 ◽  
Vol 9 (5) ◽  
pp. 842
Author(s):  
Pengfei Ding ◽  
Xiaoyi Feng
Keyword(s):  
Chaotic System ◽  
Special Form ◽  
Electronic Circuit ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Sine Function ◽  
Sign Function ◽  
System Parameters ◽  
Left And Right

A novel chaotic system for generating multi-scroll attractors based on a Jerk circuit using a special form of a sine function (SFSF) is proposed in this paper, and the SFSF is the product of a sine function and a sign function. Although there are infinite equilibrium points in this system, the scroll number of the generated chaotic attractors is certain under appropriate system parameters. The dynamical properties of the proposed chaotic system are studied through Lyapunov exponents, phase portraits, and bifurcation diagrams. It is found that the scroll number of the chaotic system in the left and right part of the x-y plane can be determined arbitrarily by adjusting the values of the parameters in the SFSF, and the size of attractors is dominated by the frequency of the SFSF. Finally, an electronic circuit of the proposed chaotic system is implemented on Pspice, and the simulation results of electronic circuit are in agreement with the numerical ones.

scholarly journals Finite-Time Synchronizing Fractional-Order Chaotic Volta System with Nonidentical Orders

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Jian-Bing Hu ◽  
Ling-Dong Zhao
Keyword(s):  
Fractional Calculus ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic System ◽  
Finite Time ◽  
Chaotic Systems ◽  
Fractional Differentiation ◽  
Fractional Chaotic System

We investigate synchronizing fractional-order Volta chaotic systems with nonidentical orders in finite time. Firstly, the fractional chaotic system with the same structure and different orders is changed to the chaotic systems with identical orders and different structure according to the property of fractional differentiation. Secondly, based on the lemmas of fractional calculus, a controller is designed according to the changed fractional chaotic system to synchronize fractional chaotic with nonidentical order in finite time. Numerical simulations are performed to demonstrate the effectiveness of the method.

ON THE BOUNDNESS OF SOME SOLUTIONS OF THE LÜ SYSTEM

2012 ◽  
Vol 22 (01) ◽  
pp. 1250015 ◽  
Author(s):  
FUCHEN ZHANG ◽  
CHUNLAI MU ◽  
XIAOWU LI
Keyword(s):  
Lyapunov Function ◽  
Chaotic System ◽  
System Parameters ◽  
Lü System ◽  
Lu System

By constructing a suitable Lyapunov function, we show that for the Lü chaotic system parameters in some specified regions, the solutions of the system are globally bounded.

scholarly journals Chaos Synchronization between Fractional-Order Unified Chaotic System and Rossler Chaotic System

2012 ◽  
Vol 562-564 ◽  
pp. 2088-2091
Author(s):  
Xian Yong Wu ◽  
Yi Long Cheng ◽  
Kai Liu ◽  
Xin Liang Yu ◽  
Xian Qian Wu
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Dynamics ◽  
Chaotic Attractors ◽  
System Parameters ◽  
Unified Chaotic System ◽  
Simulation Results ◽  
Drive Systems ◽  
Asymptotic Synchronization

The chaotic dynamics of the unified chaotic system and the Rossler system with different fractional-order are studied in this paper. The research shows that the chaotic attractors can be found in the two systems while the orders of the systems are less than three. Asymptotic synchronization of response and drive systems is realized by active control through designing proper controller when system parameters are known. Theoretical analysis and simulation results demonstrate the effective of this method.

scholarly journals Pseudo-Random Number Generator Based on Logistic Chaotic System

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 960 ◽  
Author(s):  
Luyao Wang ◽  
Hai Cheng
Keyword(s):  
Chaotic System ◽  
Random Number ◽  
Chaotic Behavior ◽  
Statistical Tests ◽  
Random Sequence ◽  
Random Number Generator ◽  
Statistical Characteristics ◽  
Random Number Generators ◽  
System Parameters ◽  
Pseudo Random Number

In recent years, a chaotic system is considered as an important pseudo-random source to pseudo-random number generators (PRNGs). This paper proposes a PRNG based on a modified logistic chaotic system. This chaotic system with fixed system parameters is convergent and its chaotic behavior is analyzed and proved. In order to improve the complexity and randomness of modified PRNGs, the chaotic system parameter denoted by floating point numbers generated by the chaotic system is confused and rearranged to increase its key space and reduce the possibility of an exhaustive attack. It is hard to speculate on the pseudo-random number by chaotic behavior because there is no statistical characteristics and infer the pseudo-random number generated by chaotic behavior. The system parameters of the next chaotic system are related to the chaotic values generated by the previous ones, which makes the PRNG generate enough results. By confusing and rearranging the output sequence, the system parameters of the previous time cannot be gotten from the next time which ensures the security. The analysis shows that the pseudo-random sequence generated by this method has perfect randomness, cryptographic properties and can pass the statistical tests.

Stability and Hopf bifurcation analysis of a new four-dimensional hyper-chaotic system

2020 ◽  
Vol 34 (29) ◽  
pp. 2050327
Author(s):  
Liangqiang Zhou ◽  
Ziman Zhao ◽  
Fangqi Chen
Keyword(s):  
Hopf Bifurcation ◽  
Chaotic System ◽  
Bifurcation Theory ◽  
Center Manifold ◽  
Equilibrium Points ◽  
Chaotic Attractors ◽  
Local Dynamic ◽  
Chaotic Motions ◽  
System Parameters ◽  
Lyapunov Coefficient

With both analytical and numerical methods, local dynamic behaviors including stability and Hopf bifurcation of a new four-dimensional hyper-chaotic system are studied in this paper. All the equilibrium points and their stability conditions are obtained with the Routh–Hurwitz criterion. It is shown that there may exist one, two, or three equilibrium points for different system parameters. Via Hopf bifurcation theory, parameter conditions leading to Hopf bifurcation is presented. With the aid of center manifold and the first Lyapunov coefficient, it is also presented that the Hopf bifurcation is supercritical for some certain parameters. Finally, numerical simulations are given to confirm the analytical results and demonstrate the chaotic attractors of this system. It is also shown that the system may evolve chaotic motions through periodic bifurcations or intermittence chaos while the system parameters vary.

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