Coexistence of infinite attractors in a fractional-order chaotic system with two nonlinear functions and its DSP implementation

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.

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

Nonlinear Dynamics ◽

10.1007/s11071-021-06476-2 ◽

2021 ◽

Author(s):

Wenli Xie ◽

Chunhua Wang ◽

Hairong Lin

Keyword(s):

Transition State ◽

Fractional Order ◽

Chaotic System

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

Scientific Reports ◽

10.1038/s41598-021-85377-1 ◽

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.

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

Advances in Mechanical Engineering ◽

10.1177/1687814019866540 ◽

2019 ◽

Vol 11 (7) ◽

pp. 168781401986654 ◽

Cited By ~ 6

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.

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

Mathematical Problems in Engineering ◽

10.1155/2015/941654 ◽

2015 ◽

Vol 2015 ◽

pp. 1-9 ◽

Cited By ~ 4

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.

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