Article
Acoustics
Abdullah Gokyildirim, Haris Calgan, Metin Demirtas
Summary: In this study, the chaotic behavior of a 4D memristive Chen system is investigated by taking the order of the system as fractional. The nonlinear behavior of the system is observed numerically by comparing the fractional-order bifurcation diagrams and Lyapunov Exponents Spectra with 2D phase portraits. Two different fractional orders are determined where the system shows chaotic behavior. Furthermore, a single state fractional-order sliding mode controller (FOSMC) is designed to maintain the states of the system on the equilibrium points.
JOURNAL OF VIBRATION AND CONTROL
(2023)
Article
Engineering, Electrical & Electronic
Yi-Fei Pu, Bo Yu, Qiu-Yan He, Xiao Yuan
Summary: This paper proposes a chaotic circuit FMCC using fractional-order memristors. By replacing the diode in Chua's chaotic circuit with a fractional-order memristor and a negative resistor in parallel, the FMCC provides two extra degrees of freedom. Numerical simulations and hardware experiments demonstrate that the FMCC exhibits multistability, transient chaos, state transition phenomena, and has a fractional-order-sensitivity characteristic.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
(2022)
Article
Mathematics, Applied
Wei Pan, Liping Chen, Weidong Zhang
Summary: In this paper, a novel complex fractional-order hyperchaotic multi-scroll attractor is constructed by combining nonlinearities with different forming mechanism from a simple structure. The dynamics of the designed system are analyzed, and the existence of hyperchaos is verified using numerical simulations and circuit simulation results. The feasibility of the design is demonstrated through the observation of multi-scroll hyperchaotic attractors.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Interdisciplinary Applications
Lei Ren, Ming-Hung Lin, Abdulkareem Abdulwahab, Jun Ma, Hassan Saberi-Nik
Summary: In this paper, the dynamical behavior of the integer and fractional 4D hyperchaotic Rabinovich system is investigated. An optimization problem is solved analytically using the Lagrange coefficient method to find an accurate ultimate bound set (UBS) for the system. The bifurcation diagrams, Lyapunov exponents, global attractive sets, and positive invariant sets of the fractional-order system are also studied. Furthermore, the Mittag-Leffler GAS and Mittag-Leffler PIS of the proposed system are estimated using the Mittag-Leffler function and Lyapunov function method.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Computer Science, Information Systems
N. Ramesh Babu, P. Balasubramaniam, Er. Meng Joo
Summary: In this paper, a mathematical modeling of a fractional-order memristor circuit is developed by using fractional elements instead of classical circuit elements. The main contributions of this research include remodelation of a fractional order non-linear memristive hyper-chaotic system, synchronization of sender and receiver system with video cryptosystem applications, design of a fuzzy feedback controller for synchronization of the hyperchaotic system, development of video encryption and decryption algorithms, analysis of various metrics for high-level security, and demonstration of the effectiveness of the proposed algorithms through numerical simulations and experimental results.
MULTIMEDIA TOOLS AND APPLICATIONS
(2023)
Article
Multidisciplinary Sciences
Haiyan Fu, Tengfei Lei
Summary: In this paper, a class of fractional-order symmetric hyperchaotic systems is studied using the Adomian decomposition method. The nonlinear term of a fractional-order chaotic system is decomposed, and the dynamic behavior of a fractional-order hyperchaotic system is analyzed. The results show that the complexity of the system increases with the decrease of the fractional order. A circuit diagram of the system is designed based on the fractional-order circuit design principle and the simulation results are consistent with the numerical simulation, providing a foundation for the engineering applications of fractional-order hyperchaotic systems.
Article
Mathematics, Interdisciplinary Applications
Huaigu Tian, Jindong Liu, Zhen Wang, Fei Xie, Zelin Cao
Summary: The ideal magnetic flux-controlled memristor was introduced into a four-dimensional chaotic system and combined with fractional calculus theory, proposing a novel four-dimensional commensurate fractional-order system solved using the Adomian decomposition method. The system's orders, parameters, and initial values were studied as independent variables, revealing that changing these variables can lead to more complex and rich dynamical behaviors. The system exhibited an offset boosting by adding a constant term after the decoupled linear term. Numerical simulation results were validated through analog circuits and FPGA designs, and a control scheme for the system circuit was suggested.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Xiaozhong Liao, Donghui Yu, Da Lin, Manjie Ran, Jinhui Xia
Summary: This paper proposes a C-F definition-based fractional-order RLC circuit model and analyzes its basic characteristics. The results show that the proposed model can improve the consistency with the actual circuit, and has higher accuracy and flexibility.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Interdisciplinary Applications
Chunbo Xiu, Jingyao Fang, Yuxia Liu
Summary: A novel five-dimension memristive cellular neural network hyperchaotic system is designed to enrich the dynamic characteristics of CNN and reveal the influence of memristor nonlinearity. The effects of system parameters, initial values, and noise on the dynamic behavior are studied, providing criteria for parameter selection and verifying the physical realizability of chaotic characteristics. Additionally, a secure communication application example based on the hyperchaotic system is presented.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Computer Science, Hardware & Architecture
Feifei Yang, Peng Li
Summary: This paper introduces a new fractional-order memristive circuit and analyzes the complexity of the fractional-order chaotic system, showing that the SampEn algorithm effectively reflects the system's complexity. Numerical simulations demonstrate that the variability of system parameters effectively reflects the randomness of the chaotic system, and the system exhibits rich dynamical performances.
MOBILE NETWORKS & APPLICATIONS
(2021)
Article
Engineering, Multidisciplinary
Chaojun Wu, Qi Zhang, Zhang Liu, Ningning Yang
Summary: This paper presents a novel fractional-order Chua's memristive circuit and conducts theoretical analysis and numerical simulation on its dynamic characteristics, revealing that the chaotic circuit exhibits periods, bifurcations, and chaos, with a narrow period window within the chaotic region.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2021)
Article
Mathematics, Interdisciplinary Applications
Chaojun Wu, Qi Zhang, Ningning Yang, Rong Jia, Chongxin Liu
Summary: In this paper, a boost converter emulator with a memristive load instead of a resistive load is proposed, and a fractional-order model of the memristive boost converter is created. Based on different switching states, the circuit equations of the fractional-order memristive boost converter operating in continuous conduction mode are derived. Numerical simulations and comparisons with the integer-order memristive boost converter reveal the rich dynamic behavior of the fractional-order system and its expansion of stable working regions. The addition of the memristive load significantly widens the normal working regions of the system.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Mathematics, Applied
Mengjiao Wang, Mingyu An, Shaobo He, Xinan Zhang, Herbert Ho-Ching Lu, Zhijun Li
Summary: This paper first proposes a discrete memristor model and analyzes the voltage-current characteristics of the memristor. Then, the discrete memristor is coupled with a one-dimensional sine chaotic map through different coupling frameworks, and two different two-dimensional chaotic map models are generated. The dynamic behavior of the chaotic map under different coupled map frameworks is investigated by using various analytical methods, and the results show that different coupling frameworks can produce different complex dynamical behaviors for memristor chaotic maps.
Article
Engineering, Multidisciplinary
A. Lassoued, F. Nazarimehr, O. Boubaker
Summary: This paper investigates a hyperchaotic system with fractional terms and fractional-order derivatives. Simulations demonstrate that the system can generate different attractors, including equilibrium point, limit cycle, and hyperchaotic attractor. A circuit of fractional-order integrator is designed and utilized to implement the circuit of the studied system. The feasibility of the circuit implementation for the studied system is proven.
Article
Mathematics
Gayathri Vivekanandan, Mahtab Mehrabbeik, Hayder Natiq, Karthikeyan Rajagopal, Esteban Tlelo-Cuautle
Summary: This paper introduces the significance and application of fractional nonlinear systems, and proposes a neuronal model based on fractional derivatives. The dynamics of individual neurons and the collective behavior of neurons in a ring topology are investigated.
Article
Computer Science, Software Engineering
Ji Xu, Jun Mou, Jian Liu, Jin Hao
Summary: This paper proposes a novel image encryption algorithm based on the fractional-order chaotic system and compression sensing algorithm, which is implemented on DSP hardware circuit and utilizes block feedback diffusion algorithm with simultaneous scrambling calculation and diffusion operation. The simulation results demonstrate the effective encryption of digital images, while the security analysis confirms the security and effectiveness of the proposed encryption algorithm.
Article
Computer Science, Information Systems
Jin Hao, Jun Mou, Li Xiong, Yingqian Zhang, Xinyu Gao, Yuwen Sha
Summary: This paper proposes a novel color image encryption algorithm based on the fractional order laser chaotic system and DNA mutation principle, analyzing the dynamic characteristics of the system and designing an encryption scheme. By scrambling the image values using chaotic sequences and Arnold matrices, and introducing DNA diffusion algorithm and DNA mutation theory for increased randomness, the algorithm demonstrates strong encryption capabilities and resistance to multiple decryption methods, enabling secure communication of digital images.
MULTIMEDIA TOOLS AND APPLICATIONS
(2022)
Article
Multidisciplinary Sciences
Xinyu Gao, Jiawu Yu, Santo Banerjee, Huizhen Yan, Jun Mou
Summary: A multi-image encryption scheme based on the fractional-order hyperchaotic system is proposed in this paper, where multiple grayscale images are fused into a color image and then scrambled and diffused for increased security. The use of fractional hyperchaotic system assists in pixel confusion and diffusion operations, resulting in an effective encryption scheme with improved efficiency and security performance.
SCIENTIFIC REPORTS
(2021)
Article
Engineering, Mechanical
Li Xiong, Feifei Yang, Jun Mou, Xinlei An, Xinguo Zhang
Summary: This paper proposes a memristive circuit system and analyzes its dynamical characteristics. The results show that the system is suitable for image encryption application, and a new method using red-blue 3D glasses to observe chaotic attractors is proposed. Additionally, an image encryption algorithm based on DNA variation is designed and security performance analysis experiments are performed. Finally, a hardware circuit based on the memristive system is implemented.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Mechanical
Xinyu Gao, Jun Mou, Li Xiong, Yuwen Sha, Huizhen Yan, Yinghong Cao
Summary: This paper proposes a multiple-image encryption algorithm based on single-channel scrambling, diffusion, and chaotic system. The algorithm encrypts the image set by fusing and converting from the RGB channel to the HSV channel. For single-channel encryption, scrambling and diffusion operations are performed. The algorithm shows excellent encryption speed and security performance based on performance analysis.
NONLINEAR DYNAMICS
(2022)
Article
Computer Science, Information Systems
Xinyu Gao, Jun Mou, Santo Banerjee, Yinghong Cao, Li Xiong, Xiaoyang Chen
Summary: A multiple-image encryption scheme based on hyperchaotic map and 3D cube is designed in this paper. The scheme constructs a cube graph by superimposing planes and performs DNA encoding, rotation, and swapping operations on the images, achieving effective and secure image encryption.
JOURNAL OF KING SAUD UNIVERSITY-COMPUTER AND INFORMATION SCIENCES
(2022)
Article
Mathematics, Interdisciplinary Applications
Xuejun Li, Jun Mou, Yinghong Cao, Santo Banerjee
Summary: This paper studies an optical image encryption scheme based on fractional Fourier transform and five-dimensional host-induced nonlinearity fractional-order laser hyperchaotic system. By analyzing the dynamic characteristics of the proposed system and combining BP neural network, GF(17) domain diffusion and hyperchaotic random point scrambling algorithm, a novel image encryption scheme is proposed. The research provides an experimental basis and theoretical guidance for image secure communication combining fractional-order laser hyperchaotic systems and optical methods, and offers a new research perspective for optical image encryption.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Physics, Multidisciplinary
Stelios Bekiros, Samaneh Soradi-Zeid, Jun Mou, Amin Yousefpour, Ernesto Zambrano-Serrano, Hadi Jahanshahi
Summary: This article focuses on determining numerical solutions for the two-dimensional time-space fractional Schrodinger equation using the Laguerre wavelet approach. The problem is discretized and solved using a collocation method, which has been proven to provide accurate results. The numerical examples provided in the article support this claim.
Article
Mathematics
Zhenggang Guo, Junjie Wen, Jun Mou
Summary: In this paper, a new six-dimensional memristor chaotic system is designed by combining a chaotic system with a memristor. By analyzing the phase diagram, eleven different attractors are found, including a multi-wing attractor and symmetric attractors. The system is proven to have the property of a hidden chaotic attractor. The dynamic behavior of the system under parameter changes and various phenomena, such as chaos degradation and coexistence of multiple attractors, are analyzed.
Article
Mathematics
Naif D. Alotaibi, Hadi Jahanshahi, Qijia Yao, Jun Mou, Stelios Bekiros
Summary: This study introduces a novel ensemble neural network approach for accurately classifying upper limb electromyography (EMG) signals. The proposed technique integrates long short-term memory networks (LSTM) and attention mechanisms, achieving high accuracy through preprocessing and feature extraction of the signals.
Article
Mathematics
Naif D. Alotaibi, Hadi Jahanshahi, Qijia Yao, Jun Mou, Stelios Bekiros
Summary: The control of rehabilitation robots faces challenges in dealing with unknown disturbances, and many advanced techniques for controlling and identifying such systems have yet to be implemented. In this study, a novel algorithm is proposed that uses a finite estimator and Gaussian process to identify and forecast the unknown dynamics of a 2-DoF knee rehabilitation robot. The algorithm makes use of the probabilistic nature of Gaussian processes and guarantees finite-time convergence through the Lyapunov theorem.
Article
Mathematics, Interdisciplinary Applications
Xingce Liu, Jun Mou, Jue Wang, Santo Banerjee, Peng Li
Summary: In this paper, a chaotic circuit based on a memcapacitor and meminductor is constructed and its dynamic behavior is studied. The equilibrium stability and dynamic characteristics of the system are analyzed using mathematical modeling and decomposition methods, revealing some special phenomena. The circuit implementation of the system is achieved on a DSP platform, and the numerical simulation results validate the abundant dynamical characteristics of the system.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Tao Ma, Jun Mou, Bo Li, Santo Banerjee, Huizhen Yan
Summary: This paper investigates the complex dynamics of fractional-order neural networks by proposing a fractional-order Hopfield neural network (FOHNN) system and solving it using the Adomian decomposition method. The dynamics of the system are analyzed through phase diagrams, bifurcation diagrams, Lyapunov exponential spectra, and Lyapunov dimensions.
FRACTAL AND FRACTIONAL
(2022)
Article
Computer Science, Information Systems
Jieyang Wang, Hongjie Li, Zhisen Wang, Jun Mou
Summary: A new chaotic system is proposed in this paper by adding a magnetron memristor to an erbium-doped fiber laser circuit and analyzing its dynamical characteristics. A special periodic coexistence attractor phenomenon is discovered during the analysis, which can affect the system's dynamical characteristics by changing the time parameters of the AC power supply and is controllable. The chaotic system is finally implemented by constructing an equivalent analog circuit.
Article
Computer Science, Information Systems
Jin Hao, Hongjie Li, Huizhen Yan, Jun Mou
Summary: This paper proposes a color image encryption algorithm based on a chaotic system and DNA principles, which demonstrates strong encryption capabilities and resilience against various decryption methods, enabling secure communication of digital images.
