scholarly journals A fractional-order multistable locally active memristor and its chaotic system with transient transition, state jump

2021 ◽  
Author(s):  
Wenli Xie ◽  
Chunhua Wang ◽  
Hairong Lin
Keyword(s):  
Transition State ◽  
Fractional Order ◽  
Chaotic System

scholarly journals A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation

Inventions ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 49
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Basil H. Jasim ◽  
Yasir I. A. Al-Yasir ◽  
Raed A. Abd-Alhameed ◽  
Bilal Naji Alhasnawi
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Real World ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
State Variables ◽  
Digital Implementation ◽  
Dynamical Behaviors ◽  
Real World Applications

In this paper, a new fractional order chaotic system without equilibrium is proposed, analytically and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigations were used to describe the system’s dynamical behaviors including the system equilibria, the chaotic attractors, the bifurcation diagrams, and the Lyapunov exponents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attractors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive control theory was developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state variables for the master and slave. Consequently, the update laws of the slave parameters are obtained, where the slave parameters are assumed to be uncertain and are estimated corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results were obtained by MATLAB and the Arduino Due boards, respectively, with a good consistency between the simulation results and the experimental results, indicating that the new fractional order chaotic system is capable of being employed in real-world applications.

scholarly journals A new image encryption algorithm based on the OF-LSTMS and chaotic sequences

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yi He ◽  
Ying-Qian Zhang ◽  
Xin He ◽  
Xing-Yuan Wang
Keyword(s):  
Image Encryption ◽  
Fractional Order ◽  
Chaotic System ◽  
Short Term Memory ◽  
Encryption Algorithm ◽  
Chaotic Sequences ◽  
Long Short Term Memory ◽  
Input Gate ◽  
And Diffusion ◽  
Image Encryption Algorithm

AbstractIn this paper, a novel image encryption algorithm based on the Once Forward Long Short Term Memory Structure (OF-LSTMS) and the Two-Dimensional Coupled Map Lattice (2DCML) fractional-order chaotic system is proposed. The original image is divided into several image blocks, each of which is input into the OF-LSTMS as a pixel sub-sequence. According to the chaotic sequences generated by the 2DCML fractional-order chaotic system, the parameters of the input gate, output gate and memory unit of the OF-LSTMS are initialized, and the pixel positions are changed at the same time of changing the pixel values, achieving the synchronization of permutation and diffusion operations, which greatly improves the efficiency of image encryption and reduces the time consumption. In addition the 2DCML fractional-order chaotic system has better chaotic ergodicity and the values of chaotic sequences are larger than the traditional chaotic system. Therefore, it is very suitable to image encryption. Many simulation results show that the proposed scheme has higher security and efficiency comparing with previous schemes.

scholarly journals The dynamics of a new chaotic system through the Caputo–Fabrizio and Atanagan–Baleanu fractional operators

2019 ◽  
Vol 11 (7) ◽  
pp. 168781401986654 ◽  
Author(s):  
Muhammad Altaf Khan
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Order Parameter ◽  
Numerical Procedure ◽  
Numerical Approach ◽  
Fractional Operators ◽  
Fundamental Properties ◽  
Chaotic Model ◽  
New Chaotic System ◽  
Model Apply

The aim of this article is to analyze the dynamics of the new chaotic system in the sense of two fractional operators, that is, the Caputo–Fabrizio and the Atangana–Baleanu derivatives. Initially, we consider a new chaotic model and present some of the fundamental properties of the model. Then, we apply the Caputo–Fabrizio derivative and implement a numerical procedure to obtain their graphical results. Further, we consider the same model, apply the Atangana–Baleanu operator, and present their analysis. The Atangana–Baleanu model is used further to present a numerical approach for their solutions. We obtain and discuss the graphical results to each operator in details. Furthermore, we give a comparison of both the operators applied on the new chaotic model in the form of various graphical results by considering many values of the fractional-order parameter [Formula: see text]. We show that at the integer case, both the models (in Caputo–Fabrizio sense and the Atangana–Baleanu sense) give the same results.

scholarly journals Sliding Mode Control and Modified Generalized Projective Synchronization of a New Fractional-Order Chaotic System

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Junbiao Guan ◽  
Kaihua Wang
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Secure Communication ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Control Technique ◽  
Order System ◽  
Mode Control ◽  
The Stability

A new fractional-order chaotic system is addressed in this paper. By applying the continuous frequency distribution theory, the indirect Lyapunov stability of this system is investigated based on sliding mode control technique. The adaptive laws are designed to guarantee the stability of the system with the uncertainty and external disturbance. Moreover, the modified generalized projection synchronization (MGPS) of the fractional-order chaotic systems is discussed based on the stability theory of fractional-order system, which may provide potential applications in secure communication. Finally, some numerical simulations are presented to show the effectiveness of the theoretical results.

The feedback control of fractional order unified chaotic system

2010 ◽  
Vol 19 (2) ◽  
pp. 020508 ◽  
Author(s):  
Yang Jie ◽  
Qi Dong-Lian
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Unified Chaotic System

HYPERCHAOS IN THE FRACTIONAL-ORDER NONAUTONOMOUS CHEN'S SYSTEM AND ITS SYNCHRONIZATION

2005 ◽  
Vol 16 (05) ◽  
pp. 815-826 ◽  
Author(s):  
HONGBIN ZHANG ◽  
CHUNGUANG LI ◽  
GUANRONG CHEN ◽  
XING GAO
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic System ◽  
Three Dimensional ◽  
Synchronization Problem ◽  
Driving Signal

Recently, a new hyperchaos generator, obtained by controlling a three-dimensional autonomous chaotic system — Chen's system — with a periodic driving signal, has been found. In this letter, we formulate and study the hyperchaotic behaviors in the corresponding fractional-order hyperchaotic Chen's system. Through numerical simulations, we found that hyperchaos exists in the fractional-order hyperchaotic Chen's system with order less than 4. The lowest order we found to have hyperchaos in this system is 3.4. Finally, we study the synchronization problem of two fractional-order hyperchaotic Chen's systems.

A simple fractional-order chaotic system based on memristor and memcapacitor and its synchronization application

2021 ◽  
Vol 152 ◽  
pp. 111306
Author(s):  
Akif Akgül ◽  
Karthikeyan Rajagopal ◽  
Ali Durdu ◽  
Muhammed Ali Pala ◽  
Ömer Faruk Boyraz ◽  
...  
Keyword(s):  
Fractional Order ◽  
Chaotic System
Sign in / Sign up

Export Citation Format

Share Document