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Article
Mathematics, Interdisciplinary Applications
Gang Dou et al.
Summary: This paper presents a complete design of memristive LSTM network system using memristor circuit for hardware acceleration. The proposed scheme effectively reduces power consumption and improves network calculation accuracy, achieving a hardware training accuracy as high as 88.58% in text classification task on the IMDB dataset.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Physics, Multidisciplinary
Yixin Chen et al.
Summary: In this paper, a new mix chaotic circuit with a pi-shaped structure is proposed, which consists of two memristors, a memcapacitor, an inductor, and a capacitor. The equilibrium point and dynamical behaviors of the circuit are analyzed in detail under two different parameters. Moreover, the exceptional phenomenon of multistability is discovered in the new circuit. The circuit is implemented on a DSP platform, and the experimental results are in accordance with the simulation results. The analysis shows that the new mix chaotic circuit has complex dynamical characteristics and can be used in the field of encryption.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Review
Computer Science, Interdisciplinary Applications
Daniel Clemente-Lopez et al.
Summary: This article comprehensively reviews the FPGA-based and embedded physical realization of fractional-order continuous-time chaotic systems under singular kernel fractional derivatives. The main numerical algorithms for computing a solution of the fractional-order continuous-time chaotic systems are studied in-depth, and their computational cost and accuracy on digital hardware are analyzed. Two methodologies for obtaining suitable digital implementations using FPGAs and embedded hardware are also discussed and demonstrated. The existing open problems in both computational and hardware are discussed, and the research opportunities in this exciting scientific area are forecasted.
ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING
(2023)
Article
Physics, Multidisciplinary
Mengxin Jin et al.
Summary: A novel fractional-order hyperchaotic complex system is proposed by introducing the Caputo fractional-order derivative operator and a constant term to the complex simplified Lorenz system. The dynamics and synchronization of the proposed system are investigated through various analyses and simulations, revealing the presence of extreme multistability and hidden attractors. The theoretical results provide a foundation for practical applications of the proposed system.
Article
Physics, Multidisciplinary
Xinyu Gao et al.
Summary: We propose a color image encryption scheme by combining hyperchaotic map, cross-plane operation, and gene theory. The hyperchaotic map used in the scheme is analyzed and studied, and a color image encryption scheme is designed based on its dynamics. A DNA mutation operation is applied at the end of the encryption process to enhance image randomness and improve algorithm security. Simulation experiments, performance analysis, and attack tests validate the effectiveness and security of the proposed algorithm. This work explores the potential application of chaos theory and gene theory in image encryption.
Article
Mathematics, Interdisciplinary Applications
Xintong Han et al.
Summary: In this paper, a discrete model of memristor is adopted and analyzed. The new discrete maps are built by introducing this discrete memristor model into a two-dimensional discrete map. Interestingly, introducing this discrete memristor model from different locations can lead to two new chaotic map models. The dynamical behaviors of the two maps are studied by means of bifurcation diagrams, phase diagrams and Lyapunov exponential spectra (LEs). The simulation results show that both chaotic systems have rich dynamical behaviors. In addition, they are experimentally found to have multi-stable properties, where the M-XM map has infinite attractors coexistence. Finally, we complete the hardware implementation of the two maps based on Digital Signal Processing (DSP) platform for the application of discrete chaotic systems.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Interdisciplinary Applications
Yanjie Ma et al.
Summary: In this paper, a new discrete chaotic map is constructed by introducing a discrete memristor into two-dimensional generalized square maps to enhance its chaotic performance. The fixed points of the new maps are analyzed and the effects of different parameters on the system performance are investigated. The coexistence of various types of attractors, including hyperchaos and cycles, is found in the present maps. Furthermore, symmetric chaotic attractors with different positive and negative parameters are discovered, along with state transition phenomenon between chaos and cycles. Finally, the discrete maps are designed and implemented using a DSP platform, providing a reference for the application of discrete amnesic chaotic maps.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Interdisciplinary Applications
Xinyu Gao et al.
Summary: This paper proposes a hybrid encryption scheme for multi-image that can encrypt different types and different sizes of images simultaneously. The order of the discrete map is extended from integer order to unequal fractional order to exhibit chaotic behavior. The plain images are pixel substituted using chaotic sequences generated by the unequal fractional-order discrete map, and additional encryption steps such as DNA encoding, selective diffusion, and gene exchange are performed. Simulation experiments and security test results demonstrate the effectiveness and security of the designed multi-image hybrid encryption algorithm.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Interdisciplinary Applications
Yuwen Sha et al.
Summary: With the development of modern cryptography, it is necessary to protect sensitive information using secure and efficient algorithms. The Hopfield neural network (HNN) has been found to possess stronger memory and can exhibit rich kinetic behavior, especially when incorporating fractional-order operators. Therefore, this study proposes a chaotic image encryption method based on fractional-order HNN (FO-HNN) as a key generator. Spatial permutation strategy and a new diffusion technique using a Three-input logic valve are utilized to eliminate pixel correlation and guide the diffusion process, respectively. Simulation results and security analysis demonstrate the superior security performance of the HNN-based image cryptosystem.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Engineering, Mechanical
Tao Ma et al.
Summary: A new tri-cellular neural network system based on double memristors is constructed in this paper. Instead of the conventional segmentation function, a hyperbolic tangent function is used. The rich and complex dynamical characteristics of the system are presented through various analyses and experiments. The improved system provides a theoretical foundation in other fields of application, particularly for secure communications.
NONLINEAR DYNAMICS
(2023)
Article
Optics
Linian Wang et al.
Summary: In this paper, a color image encryption algorithm is presented, which utilizes double-layer Joseph's scramble, XOR diffusion, and is built on a laser chaos system. The algorithm shows good practicality and security performance based on simulation results and security analysis. The proposed scheme provides better technical support for the wide applications of image encryption.
Article
Physics, Multidisciplinary
Lujie Ren et al.
Summary: In this paper, a new fractional-order complex chaotic system (FOCCS) is proposed and studied. The dissipativity and stability are discussed, and the dynamical characteristics of the system with parameter and order changes are analyzed. Multiple attractor coexistence and its dependence on initial conditions are found. The implementation on analog circuit and DSP platform is also explored. This study provides valuable insights for chaos research and application.
Article
Mathematics, Interdisciplinary Applications
Lujie Ren et al.
Summary: This research constructs a new discrete memristor model and couples it with a new three-dimensional hyperchaotic map to discuss its stability and analyze its dynamical characteristics. The study demonstrates the coexistence of periodic, quasi-periodic, chaotic, and hyperchaotic attractors in the model, and successfully implements the hyperchaotic map on DSP hardware platforms. Finally, the discrete hyperchaotic map is applied to image encryption.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Automation & Control Systems
Xinyu Gao et al.
Summary: In this research, a multi-image (MI) hybrid encryption algorithm is proposed to flexibly encrypt color and grayscale images of different sizes. The algorithm combines back-propagation neural network compression technology and the MI hybrid encryption algorithm to obtain an MI hybrid compression-encryption (MIHCE) scheme, which reduces the pressure of simultaneous transmission and storage of multiple cipher images. Two chaotic maps are used in the scheme design process, exhibiting rich variations in the behavior of the chaotic maps. After the MIHCE is completed, the obtained cipher images are stored and transmitted. Security analysis and compression performance analysis prove the feasibility and safety of the designed compression-encryption scheme.
IEEE TRANSACTIONS ON CYBERNETICS
(2023)
Article
Physics, Multidisciplinary
Nadjette Debbouche et al.
Summary: This paper investigates the nonlinear dynamics of a biological system modeled by fractional incommensurate order Van der Pol equations, analyzing the stability of the proposed fractional non-autonomous system by varying the fractional order derivative and system parameters. Interesting phenomena such as symmetry, multi-stability, and coexistence of attractors are discovered, and numerical simulations using the Caputo fractional derivative are performed to report the results through bifurcation diagrams, computation of the largest Lyapunov exponent, and phase portraits in 2D and 3D projections.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2022)
Article
Computer Science, Artificial Intelligence
Mei Guo et al.
Summary: In this paper, a physical Sr0.97Ba0.03TiO3-x (SBT) memristor with voltage threshold characteristic was prepared and an adaptive voltage threshold memristor model was proposed to accurately characterize its electrical characteristics. The synaptic plasticity of SBT memristor under different pulse stimulation was analyzed. A Pavlov associative memory circuit was designed using the LTSPICE environment, which consisted of neuron and memristive synaptic circuits. The experimental results demonstrated the feasibility and applicability of SBT memristor as an electronic synapse in neuromorphic applications, providing a path for the development of artificial neural networks.
Article
Engineering, Mechanical
Chunlai Li et al.
Summary: This paper introduces a nonvolatile locally active memristor with three stable equilibrium states for three-bit-per-cell memory device functionality. A neural network model composed of three Hopfield neurons is presented, showing that the distribution of system equilibrium points depends on the coupling weight of the memristor synapse. The bifurcation diagram reveals the coexistence phenomenon of multiple stable modes, with complex bursting oscillation emerging in the neural network when there is a step difference between the system's natural frequency and the external excitation frequency.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Kamal Shah et al.
Summary: This research work investigates the analysis of a general fractional order system under Atangana, Baleanu, and Caputo (ABC) fractional order derivative. The study focuses on existence theory, stability, and numerical analysis. The Krasnoselskii and Banach contraction theorems are used for the existence theory, and necessary results for Ulam Hyer's (UH) stability are developed using nonlinear analysis. The approximate solution is computed using the Adam's-Bashforth numerical technique, and three concrete examples with numerical and graphical interpretations are provided for validation.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Physics, Multidisciplinary
Shaobo He et al.
Summary: This paper investigates the mathematical models of discrete memristors based on Caputo fractional difference and G-L fractional difference, and shows the hysteresis loop characteristics under different input signals. It analyzes the relationship between hysteresis area and input signal frequency and derivative order, discusses the memory effect, characteristics and physical realization of the discrete memristors, and designs a discrete memristor with short memory effects. Furthermore, discrete memristive systems are constructed by introducing fractional-order and integer-order discrete memristors, and the complexity of the systems is controlled. Finally, FPGA digital circuit implementation demonstrates the potential application value of discrete memristors in engineering applications.
Article
Physics, Multidisciplinary
Tao Ma et al.
Summary: This paper investigates the nonlinear characteristics of a new 4D Hopfield neural network model with two nonlinear synaptic weights by introducing memristors in the model. Rich and complex dynamical behaviors of the HNNs were analyzed, including periodic windows, chaos, and coexistence of asymmetric attractors. Hardware circuit implementation on a DSP platform showed good consistent performance with Matlab simulations, providing a theoretical basis for the application of HNNs to human brain dynamics.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Mathematics, Interdisciplinary Applications
Xingce Liu et al.
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 et al.
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
Mathematics, Interdisciplinary Applications
Akif Akgul et al.
Summary: In this paper, a novel fractional-order chaotic circuit with a memristor and a memcapacitor with a linear inductor was created. Various dynamical properties of the system were investigated and it was applied to secure communication systems for the first time, showing rich dynamic properties suitable for different engineering applications.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Pei-Ying Xiong et al.
Summary: A vast amount of research has been devoted to chaotic systems due to their diverse applications. This study investigates a multi-stable fractional-order chaotic system and proposes a new control method using a neural network for synchronization and disturbance rejection. The results demonstrate the effectiveness and disturbance rejection capability of the proposed method.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Shuangquan Gu et al.
Summary: In this study, a new fractional-order chaotic system based on the ADM is proposed, which exhibits hidden nonlinear characteristics and multistability. By numerical simulations, the evolution of conservative, quasi-conservative, and dissipative phase trajectories are analyzed in detail, showing controlled initial-offset boosting behavior. The system's physical implementability is demonstrated through a circuit implementation on a DSP.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics
Zain-Aldeen S. A. Rahman et al.
Summary: This article introduces a novel four-dimensional autonomous fractional-order chaotic system and studies its dynamics, deriving adaptive control laws for chaos synchronization based on Lyapunov theory. The numerical simulations demonstrate the validity and potential of using this new FOCS in high-level security communication systems, showing its capability in real-world applications. Additionally, the developed synchronization mechanism leads to a secure communication scheme that is highly resistant to pirate attacks, confirmed through security analysis metric tests.
Article
Physics, Multidisciplinary
Chenguang Ma et al.
Summary: A new 2-dimensional chaotic map with a simple algebraic form is proposed in this paper, and the numerical solution of the corresponding fractional-order map is derived. The new map still exhibits chaotic behaviors when expanded to fractional-order and improper fractional-order, and it has multiple coexisting attractors.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2021)
Article
Automation & Control Systems
Yucheng Chen et al.
Summary: This work proposes a model-free adaptive sliding mode control method for chaotic fractional-order systems (FOSs), and a new medical image encryption scheme is tentatively proposed based on this synchronization method. The effectiveness of the encryption scheme is verified through numerical simulations, and performance and security analyses confirm its superiority.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2021)
Review
Computer Science, Information Systems
Francisco J. Romero et al.
Summary: The concept of memristor was introduced by Prof. L. Chua in 1971 as a new circuit element, later extended to memcapacitors and meminductors. The non-linear and non-volatile properties of these devices have attracted interest for various applications.
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(2020)
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EUROPEAN PHYSICAL JOURNAL PLUS
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(2018)
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PRAMANA-JOURNAL OF PHYSICS
(2017)
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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2014)
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
(2013)
Article
Mathematics, Interdisciplinary Applications
S. K. Agrawal et al.
CHAOS SOLITONS & FRACTALS
(2012)
Editorial Material
Engineering, Electrical & Electronic
Pinaki Mazumder et al.
PROCEEDINGS OF THE IEEE
(2012)
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