Review
Mathematics
Hairong Lin, Chunhua Wang, Fei Yu, Jingru Sun, Sichun Du, Zekun Deng, Quanli Deng
Summary: Since the discovery of the Lorenz chaotic system in 1963, the construction of chaotic systems with complex dynamics has been a hot topic in chaos research. Recently, memristive Hopfield neural networks (MHNNs) have shown great potential in designing complex, chaotic systems due to their unique network structures, hyperbolic tangent activation function, and memory property. This review provides an analysis of different modeling methods, reviews pioneering works and recent important papers, and surveys the progress of MHNN-based chaotic systems in various applications. It aims to be a reference and resource for both chaos researchers and those interested in applying chaotic systems.
Article
Physics, Multidisciplinary
M. Emin Sahin
Summary: This paper proposes an image encryption model that utilizes different chaotic systems, including the logistic map, Lorenz chaotic system, and memristor-based hyperchaotic system, combined with AES and RSA encryption algorithms. The proposed scheme applies bit-based pixel diffusion and confusion techniques to enhance the security of encrypted images. Statistical and security tests are conducted to compare the performance of different encryption systems and algorithms, and the experimental results demonstrate the effectiveness of the proposed image encryption scheme in terms of security, speed, and reliability, offering valuable insights for future chaos-based encryption systems.
Article
Physics, Applied
Ke Cao, Qiang Lai
Summary: This paper proposes a new memristive chaotic system with a relatively simple structure and complex dynamic behavior. The system's dynamic characteristics and an image encryption algorithm are studied, and the physical existence of the system is verified through numerical simulations and circuit implementation.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2022)
Article
Mathematics, Interdisciplinary Applications
Shaohui Yan, Yu Ren, Binxian Gu, Qiyu Wang, Ertong Wang
Summary: In this paper, a four-dimensional chaotic system based on a flux-controlled memristor with a cosine function is constructed. It has infinitely many equilibria. The distribution of infinitely many single-wing and double-wing attractors along the u-coordinate is obtained by changing the initial values of the system and keeping the parameters constant, verifying the initial-offset boosting behavior of the system. Additionally, the complex dynamical behavior of the system is studied in detail through various analysis techniques, and the proposed chaotic system is applied to image encryption and shows good security performance.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2023)
Article
Mathematics, Interdisciplinary Applications
Hairong Lin, Chunhua Wang, Jingru Sun, Xin Zhang, Yichuang Sun, Herbert H. C. Iu
Summary: This article focuses on the bionic model and chaotic dynamics of the asymmetric neural network, as well as its engineering application. The proposed memristor-coupled asymmetric neural network (MANN) exhibits multiple complex dynamical characteristics and is observed to have phenomena such as infinitely wide hyperchaos and hyperchaotic multi-structure attractors for the first time in neural networks. Additionally, a color image encryption scheme based on the MANN is designed and shows advantages in correlation, information entropy, and key sensitivity.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Computer Science, Information Systems
Sara M. Mohamed, Wafaa S. Sayed, Ahmed H. Madian, Ahmed G. Radwan, Lobna A. Said
Summary: This paper extends a memristive chaotic system with transcendental nonlinearities to the fractional-order domain. The chaotic properties of the extended system are validated through bifurcation analysis and spectral entropy. The presented system is employed in the substitution stage of an image encryption algorithm, demonstrating its efficiency through statistical tests, key sensitivity analysis, and resistance to brute force and differential attacks. The proposed system includes reconfigurable coordinate rotation digital computer (CORDIC) and Grunwald-Letnikov (GL) architectures for trigonometric and hyperbolic functions and fractional-order operator implementations, respectively. It achieved a throughput of 0.396 Gbit/s on the Artix-7 FPGA board.
Article
Mathematics, Interdisciplinary Applications
Qiang Lai, Zhijie Chen
Summary: The paper establishes a four-dimensional multi-scroll chaotic system by adding a flux-controlled non-volatile memristor to a simple three-dimensional chaotic system. The system is extended to generate grid-scroll chaotic attractors by replacing the linear term with a triangular wave function. The evolution of chaos is studied and the existence of coexisting attractors is observed. In addition, the proposed system can be controlled by adjusting the parameters and the circuit implementation results are consistent with numerical simulations.
CHAOS SOLITONS & FRACTALS
(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
Computer Science, Hardware & Architecture
Mingshu Chen, Zhen Wang, Fahimeh Nazarimehr, Sajad Jafari
Summary: This paper presents a memristive 4D chaotic oscillator with multistability and hidden attractor. The chaotic attractor and dynamical behaviors of the oscillator are discussed. It also demonstrates proper performance in image encryption, and the system is realized using FPGA.
INTEGRATION-THE VLSI JOURNAL
(2021)
Article
Computer Science, Hardware & Architecture
Hairong Lin, Chunhua Wang, Cong Xu, Xin Zhang, Herbert H. C. Iu
Summary: In this article, a novel method for designing multistructure chaotic attractors in memristive neural networks is proposed. By utilizing a multipiecewise memristive synapse control in a Hopfield neural network (HNN), various complex multistructure chaotic attractors can be produced. Theoretical analysis and numerical simulation demonstrate that multiple multistructure chaotic attractors with different topologies can be generated by conducting the memristive synapse-control in different synaptic coupling positions. Meanwhile, the number of structures can be easily controlled with the memristor control parameters. Furthermore, a module-based analog memristive neural network circuit is designed, allowing the arbitrary number of multistructure attractors to be obtained by selecting corresponding control voltages. Finally, a novel image encryption cryptosystem with a permutation-diffusion structure is designed and evaluated, exhibiting its excellent encryption performances, especially the extremely high key sensitivity.
IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS
(2023)
Article
Engineering, Mechanical
Yue Deng, Shaoyan Li, Peng Zhang, Fang Yuan, Yuxia Li
Summary: This research presents a series of physical memristors with different TiO2 thicknesses, exploring their characteristics and mathematical models in the context of constructing nonlinear and chaotic circuits. A fifth-order memristive circuit is built to reveal the complex coexisting behaviors of multiple kinds of attractors. The numerical simulations are verified through the implementation of a hardware circuit.
NONLINEAR DYNAMICS
(2023)
Article
Optics
Chenyang Hu, Zean Tian, Qiao Wang, Xiefu Zhang, Bo Liang, Canling Jian, Xianming Wu
Summary: This article introduces a new chaotic system based on asymmetric memristors, with high complexity and various attractor shapes. A circuit was designed to verify its physical feasibility, applied to image encryption, and analyzed from a security perspective.
Article
Optics
Qiang Lai, Hui Zhang
Summary: This paper presents a new image encryption method based on a novel two-dimensional memristive-coupled hyperchaotic Sine map. The proposed map shows a higher propensity for hyperchaotic behavior in multiple parameter ranges, making it suitable for image encryption. The algorithm involves permutation and diffusion processes, which disorder the pixel arrangement and propagate changes across the entire cipher-image using a new bit-based double-loop-shift exclusive-OR (XOR) mechanism. The algorithm's encryption and decryption effects are numerically investigated, and its security is fully evaluated. Performance evaluations demonstrate its key sensitivity, robustness, and superiority over related algorithms in terms of information entropy, correlation coefficient, and resistance against differential attacks.
OPTICS AND LASER TECHNOLOGY
(2023)
Article
Automation & Control Systems
Fang Yuan, Shaoyan Li, Yue Deng, Yuxia Li, Guanrong Chen
Summary: In this article, a Cu-doped TiO2-x nanoscale memristor is built and its accurate mathematical model is established. The reliable performance of the memristor and the correctness of its mathematical model are demonstrated through numerical simulations and hardware experiments, revealing its chaotic system dynamics.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
(2023)
Article
Computer Science, Information Systems
Zain-Aldeen S. A. Rahman, Basil H. Jasim, Yasir I. A. Al-Yasir, Raed A. Abd-Alhameed
Summary: Fractional-order chaotic systems have more complex dynamics compared to integer-order chaotic systems. A novel three-dimensional fractional-order memristive chaotic system with a single unstable equilibrium point is proposed in this article. The system's nonlinear dynamic characteristics have been studied analytically and numerically, demonstrating high robustness against different types of pirate attacks.
Article
Physics, Multidisciplinary
Feifei Yang, Jun Ma
Summary: The collaboration of neurons in the nervous system is crucial for information processing and encoding, and synchronization stability reflects their cooperative and competitive behaviors. Adjusting the synchronization state of neurons through external stimulation is an effective method, which can lead to energy balance. A study introduced a light-sensitive neuron model into a neural circuit and designed a star network with electric synapses, showing complete synchronization and energy balance among neurons in different firing patterns.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2022)
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, Applied
Feifei Yang, Ying Xu, Jun Ma
Summary: Connecting memristors enhances potential controllability; magnetic flux-controlled memristor estimates electromagnetic induction effect; charge-controlled memristor estimates external electric field effect.
Article
Mathematics, Interdisciplinary Applications
Guoping Sun, Feifei Yang, Guodong Ren, Chunni Wang
Summary: Some nonlinear circuits, such as the Fitzhugh-Nagumo neural circuit with a phototube and additive induction coil, can mimic the dynamical properties of biological neurons and be used for studying neural activities. The circuit can perceive external illumination and changes in the magnetic field and control the synaptic connection and energy balance. These findings provide insights into the growth mechanism of synapse connection and the control of collective behaviors of neurons through external energy injection.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Feifei Yang, Ya Wang, Jun Ma
Summary: The field energy in neuron can be changed under shape deformation due to external energy injection. Stimulating neurons in the same region enables energy pumping through electromagnetic field superposition, and synaptic connection can be created for local energy balance. Neurons in the network maintain energy balance through continuous energy propagation and exchange, with identical neurons forming a homogeneous state and non-identical ones supporting gradient spatial patterns. This study improves the Fitzhugh-Nagumo neural circuit by adding a thermistor and a phototube, making the neuron sensitive to light and temperature. The energy diversity between neurons controls heterogeneity and defects in the network, and local energy injection regulates the firing patterns by modulating wave propagation.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Physics, Condensed Matter
Feifei Yang, Xikui Hu, Guodong Ren, Jun Ma
Summary: A simple neural circuit coupled by magnetic flux-controlled memristor is used to describe the electromagnetic effect and radiation on biological neurons. The effect of external electric field on biophysical neurons is identified by adding a charge-controlled memristor into a nonlinear circuit. The firing patterns of the memristive circuit can be adjusted by tuning the angular frequency of an external voltage source, and the physical field energy and equivalent Hamilton energy are dependent on the firing modes of neural activities. The exchange and propagation of field energy in clustered neurons is achieved by regulating the charge flow, and coupling intensity is controlled by the energy difference between adjacent neurons for perfect energy balance and saturation.
EUROPEAN PHYSICAL JOURNAL B
(2023)
Article
Mathematics, Applied
Yitong Guo, Fuqiang Wu, Feifei Yang, Jun Ma
Summary: This study investigates the control mechanism of neuron membrane potential and the adaptive characteristics of neurons. By simulating the physical properties of cell membranes and adding an induction channel, coherence resonance and mode selection under adaptive excitation are discovered. An adaptive control law is proposed to explain the controllability of cell membranes under external stimuli.
Article
Mathematics, Interdisciplinary Applications
Junen Jia, Feifei Yang, Jun Ma
Summary: This paper introduces an equivalent neural circuit for biological neurons, composed of two capacitors, and a smooth nonlinear resistor with a cubic term is introduced to describe its capacitive effect. A magnetic flux-controlled memristor is connected to the circuit to evaluate its memristive effect on dynamics and energy flow. The circuit is transformed into equivalent neuron models, which can exhibit similar spiking and bursting patterns as biological neurons. The study confirms that energy flow can be controlled to regulate neural electric activities, and higher energy levels are obtained in neuron periodic patterns under coherence resonance.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Neurosciences
Feifei Yang, Qun Guo, Jun Ma
Summary: The nonlinear properties of the cell membrane play a crucial role in simulating the behavior of biological neurons. By using a nonlinear circuit model, the characteristics of the membrane can be described, leading to a better understanding of the energy flow and firing patterns inside and outside the cell.
COGNITIVE NEURODYNAMICS
(2023)
Article
Engineering, Mechanical
Feifei Yang, Guodong Ren, Jun Tang
Summary: The propagation and exchange of electrical signals between neurons rely on the controllability of synapses. Introducing memristors allows for the evaluation of the energy effect from the physical field on neurons. By constructing a memristive neural circuit, we can perceive and modulate external electric and magnetic fields. The results of the experiment show that this neural circuit is self-adaptive and coherent resonance may occur in the presence of an electromagnetic field.
NONLINEAR DYNAMICS
(2023)
Article
Optics
Feifei Yang, Jun Ma
Summary: A controllable photosensitive neuron model is built by incorporating two phototubes in parallel in the FitzHugh-Nagumo neural circuit. The generated photocurrents from the different illuminations activate different firing modes in this light-sensitive neuron. Switching between the two phototubes induces significant pattern transitions in the neural activity.
OPTICS AND LASER TECHNOLOGY
(2023)
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
Physics, Multidisciplinary
Feifei Yang, Jun Ma
Summary: In this study, a neural circuit was rebuilt using a thermistor and a photocell, making it sensitive to external temperature and illumination. A magnetic flux-controlled memristor was used to connect the neural circuits, with its coupling channel adaptively controlled by energy diversity. The involvement of memristive synapses activated the ability for energy pumping and storage via magnetic field, allowing for controlled energy propagation along the memristive channel. It was found that by enhancing the magnetic field coupling via memristor, neurons could achieve complete synchronization and energy balance.
PRAMANA-JOURNAL OF PHYSICS
(2023)
Article
Physics, Multidisciplinary
F. Yang, Y. Wang, J. Ma
Summary: Due to the diversity in excitability and intrinsic parameters, neurons present different firing patterns and energy diversity. In this work, four FHN neurons in chain and ring networks are connected via memristive synapses, and their collective activities are controlled by adaptively taming the memristive coupling. Bifurcation analysis, Lyapunov exponent spectrum and Hamilton energy are calculated to investigate the dynamics dependence on external stimulus and parameters.
INDIAN JOURNAL OF PHYSICS
(2023)
