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

Akgül, Akif; Rajagopal, Karthikeyan; Durdu, Ali̇; Pala, Muhammed Ali; Boyraz, Ömer Faruk; Yıldız, Mustafa Zahid

doi:10.1016/j.chaos.2021.111306

Cited by 50 publications

(15 citation statements)

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“…We used the fractional order (q = 0.98); the approximation of 1/s 0.98 can be calculated as in Equation ( 9) [37]. In Figure 3, the transfer function between terminals 1 and 2 can be calculated as shown in Equation (10) [38].…”

Section: Circuit Realization Of the Fractional-order Memristormentioning

confidence: 99%

“…Figure 6 depicts the fractional-order memristor symbolic diagram. In Figure 3, the transfer function between terminals 1 and 2 can be calculated as shown in Equation (10) [38].…”

Section: Circuit Realization Of the Fractional-order Memristormentioning

confidence: 99%

“…In Equation (10), C 0 represents a unit parameter, selecting C 0 = 1 µF and H 0.98 (s). C 0 = 1/s 0.98 , that reached the resistor (R f1 and R f2 ) and capacitor values (C 1 and C 2 ) in Figure 3.…”

Section: Circuit Realization Of the Fractional-order Memristormentioning

confidence: 99%

“…Memristor-based chaotic systems are one of these application areas. Because of its nonlinearity, the memristor can be employed in chaotic circuits, and the design of memristor-based chaotic circuits with various nonlinear equations has received a lot of attention [10]. Many different memristive chaotic systems have been designed/developed and investigated as mentioned in [11].…”

Section: Introductionmentioning

confidence: 99%

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High-Security Image Encryption Based on a Novel Simple Fractional-Order Memristive Chaotic System with a Single Unstable Equilibrium Point

et al. 2021

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Fractional-order chaotic systems have more complex dynamics than integer-order chaotic systems. Thus, investigating fractional chaotic systems for the creation of image cryptosystems has been popular recently. In this article, a fractional-order memristor has been developed, tested, numerically analyzed, electronically realized, and digitally implemented. Consequently, a novel simple three-dimensional (3D) fractional-order memristive chaotic system with a single unstable equilibrium point is proposed based on this memristor. This fractional-order memristor is connected in parallel with a parallel capacitor and inductor for constructing the novel fractional-order memristive chaotic system. The system’s nonlinear dynamic characteristics have been studied both analytically and numerically. To demonstrate the chaos behavior in this new system, various methods such as equilibrium points, phase portraits of chaotic attractor, bifurcation diagrams, and Lyapunov exponent are investigated. Furthermore, the proposed fractional-order memristive chaotic system was implemented using a microcontroller (Arduino Due) to demonstrate its digital applicability in real-world applications. Then, in the application field of these systems, based on the chaotic behavior of the memristive model, an encryption approach is applied for grayscale original image encryption. To increase the encryption algorithm pirate anti-attack robustness, every pixel value is included in the secret key. The state variable’s initial conditions, the parameters, and the fractional-order derivative values of the memristive chaotic system are used for contracting the keyspace of that applied cryptosystem. In order to prove the security strength of the employed encryption approach, the cryptanalysis metric tests are shown in detail through histogram analysis, keyspace analysis, key sensitivity, correlation coefficients, entropy analysis, time efficiency analysis, and comparisons with the same fieldwork. Finally, images with different sizes have been encrypted and decrypted, in order to verify the capability of the employed encryption approach for encrypting different sizes of images. The common cryptanalysis metrics values are obtained as keyspace = 2648, NPCR = 0.99866, UACI = 0.49963, H(s) = 7.9993, and time efficiency = 0.3 s. The obtained numerical simulation results and the security metrics investigations demonstrate the accuracy, high-level security, and time efficiency of the used cryptosystem which exhibits high robustness against different types of pirate attacks.

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Section: Circuit Realization Of the Fractional-order Memristormentioning

confidence: 99%

“…Figure 6 depicts the fractional-order memristor symbolic diagram. In Figure 3, the transfer function between terminals 1 and 2 can be calculated as shown in Equation (10) [38].…”

Section: Circuit Realization Of the Fractional-order Memristormentioning

confidence: 99%

Section: Circuit Realization Of the Fractional-order Memristormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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High-Security Image Encryption Based on a Novel Simple Fractional-Order Memristive Chaotic System with a Single Unstable Equilibrium Point

et al. 2021

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“…[20] designed a new fractional nonautonomous chaotic circuit model by introducing a fractional element memristor circuit; Akgul A. [21] proposed a new fractional-order chaotic circuit with memristor and linear inductor. To show the application advantages of the proposed chaotic system, it also realized the synchronization of fractional-order chaotic system and applied it to secure communication system for the first time.…”

Section: Introductionmentioning

confidence: 99%

Audio Encryption Algorithm Based on Chen Memristor Chaotic System

Dai

Song

et al. 2021

Symmetry

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The data space for audio signals is large, the correlation is strong, and the traditional encryption algorithm cannot meet the needs of efficiency and safety. To solve this problem, an audio encryption algorithm based on Chen memristor chaotic system is proposed. The core idea of the algorithm is to encrypt the audio signal into the color image information. Most of the traditional audio encryption algorithms are transmitted in the form of noise, which makes it easy to attract the attention of attackers. In this paper, a special encryption method is used to obtain higher security. Firstly, the Fast Walsh–Hadamar Transform (FWHT) is used to compress and denoise the signal. Different from the Fast Fourier Transform (FFT) and the Discrete Cosine Transform (DCT), FWHT has good energy compression characteristics. In addition, compared with that of the triangular basis function of the Fast Fourier Transform, the rectangular basis function of the FWHT can be more effectively implemented in the digital circuit to transform the reconstructed dual-channel audio signal into the R and B layers of the digital image matrix, respectively. Furthermore, a new Chen memristor chaotic system solves the periodic window problems, such as the limited chaos range and nonuniform distribution. It can generate a mask block with high complexity and fill it into the G layer of the color image matrix to obtain a color audio image. In the next place, combining plaintext information with color audio images, interactive channel shuffling can not only weaken the correlation between adjacent samples, but also effectively resist selective plaintext attacks. Finally, the cryptographic block is used for overlapping diffusion encryption to fill the silence period of the speech signal, so as to obtain the ciphertext audio. Experimental results and comparative analysis show that the algorithm is suitable for different types of audio signals, and can resist many common cryptographic analysis attacks. Compared with that of similar audio encryption algorithms, the security index of the algorithm is better, and the efficiency of the algorithm is greatly improved.

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