Design of a five-dimensional fractional-order chaotic system and its sliding mode control

Tong, Yaonan; Cao, Zhiqi; Yang, Haojin; Li, Chunlai; Yu, Wenxin

doi:10.1007/s12648-021-02181-3

Cited by 9 publications

(2 citation statements)

References 21 publications

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“…7. At present, there are many definitions of fractional calculus, but this paper adopts Caputo's definition of fractional derivative [70,71]. Definition 1.…”

Section: Fractional Mathematical Modelmentioning

confidence: 99%

A 6D Fractional-Order Memristive Hopfield Neural Network and its Application in Image Encryption

Kong

Chen

et al. 2022

Front. Phys.

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This paper proposes a new memristor model and uses pinched hysteresis loops (PHL) to prove the memristor characteristics of the model. Then, a new 6D fractional-order memristive Hopfield neural network (6D-FMHNN) is presented by using this memristor to simulate the induced current, and the bifurcation characteristics and coexistence attractor characteristics of fractional memristor Hopfield neural network is studied. Because this 6D-FMHNN has chaotic characteristics, we also use this 6D-FMHNN to generate a random number and apply it to the field of image encryption. We make a series of analysis on the randomness of random numbers and the security of image encryption, and prove that the encryption algorithm using this 6D-FMHNN is safe and sensitive to the key.

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“…7. At present, there are many definitions of fractional calculus, but this paper adopts Caputo's definition of fractional derivative [70,71]. Definition 1.…”

Section: Fractional Mathematical Modelmentioning

confidence: 99%

A 6D Fractional-Order Memristive Hopfield Neural Network and its Application in Image Encryption

Kong

Chen

et al. 2022

Front. Phys.

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“…In 1992, A synchronous study of two different chaotic systems with the same initial values was carried out by Pecora and Carroll [5]. Later, there has been increasing researches on chaotic synchronization, and many methods have emerged, such as fuzzy [6], sliding mode [7] [8], adaptive [9] and projection methods [10].In fact, chaotic systems often contain parameter uncertainties and external disturbances, and researchers have become very interested in how to get the state trajectories of two chaotic systems to synchronize in finite or fixed time [11]. The terminal sliding mode control is not only simple to operate, but also has finite-time convergence and robustness to external disturbances, and is widely used to study finite and fixed time synchronization [12][13][14][15].…”

Section: Introducementioning

confidence: 99%

Fixed-time synchronization of fractional-order chameleon hyperchaotic systems based on hyperbolic sliding mode

Li,

Zhao,

Yang

2023

Preprint

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This paper proposes a new control method for a four-dimensional hyperchaotic system using the terminal sliding mode control. It eliminates the need for the traditional activation function by replacing it with a hyperbolic tangent function. This method effectively deals with the effects of parameter uncertainties and external disturbances in the systems, also eliminates the chattering phenomenon in the synchronous process, enables the response system and the drive system to reach the synchronization state in a fixed time. Finally, numerical simulations with MATLAB software were applied to verify the effectiveness of this fixed time convergence technique.

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Variable speed exponential control of a class of chaotic systems with external disturbances via sliding mode method

Luo²,

Fu³

et al. 2022

Pramana - J Phys

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Design of a five-dimensional fractional-order chaotic system and its sliding mode control

Cited by 9 publications

References 21 publications

A 6D Fractional-Order Memristive Hopfield Neural Network and its Application in Image Encryption

A 6D Fractional-Order Memristive Hopfield Neural Network and its Application in Image Encryption

Fixed-time synchronization of fractional-order chameleon hyperchaotic systems based on hyperbolic sliding mode

Variable speed exponential control of a class of chaotic systems with external disturbances via sliding mode method

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