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Article
Engineering, Mechanical
D. Vignesh et al.
Summary: This article investigates the chaotic behavior of the 2-D vocal dynamical system using commensurate and incommensurate fractional order Caputo difference operator. The analysis shows that the behavior of the system changes with different fractional orders, highlighting the importance of employing incommensurate order models in real-life modeling.
NONLINEAR DYNAMICS
(2023)
Article
Multidisciplinary Sciences
Haitao Qiu et al.
Summary: In this paper, a novel three-dimensional chaotic system with strange characteristic is introduced by applying a construction method of a 3D chaotic circuit. The system exhibits multiple equilibria and abundant coexisting attractors. A mathematical model is developed and stability analyses for equilibrium points are conducted, yielding significant results of period-doubling bifurcation patterns confirmed by phase plane plots and Lyapunov exponent spectra. By varying the initial value and a unique controlled parameter, the double-scroll chaotic attractor is broken up into a pair of symmetric singular attractors. Furthermore, the local basins of attraction are investigated with respect to the initial condition. The circuit synthesis results generated by Multisim simulation tool validate the self-excitation characteristics of this system. Finally, the feedback control technique is utilized to study difference synchronization of this system, and the main conclusions confirm the validity and reliability of difference synchronization.
SCIENTIFIC REPORTS
(2023)
Article
Mathematics, Applied
D. Vignesh et al.
Summary: This article aims to construct a mathematical model of two-step reversible chemical reactions using a Caputo fractional difference operator. The reaction involves the breakdown of an ester compound in the presence of water and the formation of fatty acid salts from the reaction of a free fatty acid with alkali hydroxide. The chaotic response of the system is illustrated using bifurcation diagrams and the synchronization of the subsystems is achieved with nonlinear control functions.
Article
Mathematics, Interdisciplinary Applications
Qiuzhen Wan et al.
Summary: In this paper, a new method for generating symmetric multi-scroll attractors is proposed based on a magnetized Hopfield neural network (HNN). The mathematical model of magnetized HNN is established, and its dynamic characteristics are analyzed. The complex attractor structure changes of the magnetized HNN under external pulse controlled memristor, pulse current stimulation and their combined effects are discussed respectively. The numerical simulation results show that the magnetized HNN can produce multi-scroll chaotic and multi-scroll periodic strange attractors with symmetric structure under pulse controlled memristor or/and pulse current stimulation. The number of attractors can be changed by setting the different series of multi-level-logic pulse functions. The experimental results verify the validity of the numerical simulation results, and the magnetized HNN circuit is realized using discrete analog electronic devices.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Computer Science, Hardware & Architecture
C. A. Velazquez-Morales et al.
Summary: This paper proposes the derivation of novel electronic bridge circuits for emulating artificial synapse behavior using arbitrary-order memristors. These bridge circuits serve as the cornerstone for on-chip neural network design. Sixty-four topologies are generated based on the characteristics and configuration type (incremental or decremental) of each charge or flux-controlled arbitrary-order memristor. Simulations are conducted to investigate the features of the arbitrary-order memristive bridge synapses, which show significant improvement in terms of symmetry, control, and update of synaptic weights.
INTEGRATION-THE VLSI JOURNAL
(2023)
Review
Mathematics
Hairong Lin et al.
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
Mathematics, Interdisciplinary Applications
Hairong Lin et al.
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
Mathematics, Applied
D. Vignesh et al.
Summary: This article introduces a discrete time fractional order three-dimensional Rucklidge system with complex state variables and compares its dynamical properties and chaotic behavior with the Rucklidge system with real state variables and higher dimensional system derived from complex state variables. The stability of the proposed system is analyzed at equilibrium states by obtaining eigenvalues numerically. Chaotic dynamics exhibited by the system with real and complex variables are studied using bifurcation analysis, maximum Lyapunov exponents, and the Jacobian matrix method. Nonlinear controllers are implemented for chaos synchronization of the subsystems of the proposed system. The article also discusses the coexisting behavior of the attractors in the Rucklidge system with real state variables and coexisting bifurcation diagrams.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Physics, Multidisciplinary
Yan-Mei Lu et al.
Summary: This study constructed a new fractional-order discrete memristor model with significant nonlinearity for simulating the dynamical behaviors of neurons under electromagnetic radiation. The characteristics of integer-order and fractional-order systems were analyzed, showing that the fractional-order system has richer dynamics.
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
Computer Science, Artificial Intelligence
Shanrong Lin et al.
Summary: This article addresses the synchronization and pinning control problems of directly coupled reaction-diffusion neural networks (RDNNs). By using the weighted combination of NLEVec for multiple coupling matrices, synchronization and pinning control criteria with sufficiently large coupling strengths can be derived, and the issue of adaptive coupling strengths is also addressed.
Article
Physics, Multidisciplinary
Abderrahmane Abbes et al.
Summary: This research presents a novel discrete-time fractional Hopfield neural network (DTHNN) with incommensurate order. Analytical and numerical analysis are used to investigate the dynamic behavior of the proposed network and study the stability of the zero equilibrium point as well as the presence of chaos.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Mathematics, Interdisciplinary Applications
Shaochuan Xu et al.
Summary: In this work, a new fractional-order chaotic system based on the 4-neurons-based HNN model is proposed, and it is solved using the Adomain decomposition method. The proposed system exhibits rich dynamical characteristics with changing orders. A new construction method of multiple hash index chain is designed based on the pseudo-random numbers generated by the system, and an image encryption algorithm is developed using the multiple hash index chain. The experimental results demonstrate the feasibility of the theoretical analysis.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Engineering, Electrical & Electronic
Xiaoxuan Yang et al.
Summary: This survey gives an overview of research progress on memristors, including different types of memristor synaptic devices and their working mechanisms. Crossbar-based memristors have advantages in vector-matrix multiplication and neuromorphic system design. Despite non-ideal properties and reliability issues, studies in the field are focused on addressing these challenges.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
(2022)
Article
Mathematics, Interdisciplinary Applications
Qiang Lai et al.
Summary: This study constructs a new memristive neural network with the simplest circular loop, replacing synaptic weights with hyperbolic memristors. The network can generate chaos via period-doubling bifurcation and exhibit different stable and periodic states. Furthermore, it shows the coexistence of point, periodic, and chaotic attractors from different initial conditions.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Engineering, Industrial
Yun Chen et al.
Summary: This research addresses the challenges of project risk propagation control in large engineering projects (LEPs) by proposing a multilayer heterogeneous network model and an improved schedule risk analysis model. The study considers multiple uncertainties and provides comprehensive and valuable risk information, contributing to the extension of the current theory of risk propagation in complex systems.
JOURNAL OF MANAGEMENT IN ENGINEERING
(2022)
Article
Multidisciplinary Sciences
Qing Yang et al.
Summary: Social media marketing activities have a positive impact on brand equity and repurchase intention of high-tech products among Chinese consumers. Trendiness, interaction, and word of mouth have a significant effect on brand awareness, while customisation, trendiness, interaction, and word of mouth positively affect brand image. Brand awareness and brand image also influence repurchase intention, with trendiness being the most notable factor in developing brand awareness and brand image.
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
Engineering, Mechanical
Hairong Lin et al.
Summary: In this paper, a memristive ring neural network (MRNN) with special structure and a non-ideal flux-controlled memristor is introduced to simulate the effect of external electromagnetic radiation on neurons. The chaotic dynamics of the MRNN is investigated and verified through numerical simulations and circuit experiments. Based on the characteristics of the network, a medical image encryption scheme is proposed. Performance evaluations show that the scheme has advantages compared with other chaotic systems-based cryptosystems in terms of keyspace, information entropy, and key sensitivity.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Applied
Xiao-Li Zhang et al.
Summary: In this article, the problem of global Mittag-Leffler synchronization is addressed for a specific type of discrete-time fractional-order neural networks with delays. The article constructs a power law inequality for fractional difference using integration by parts, Young inequality, and properties of fractional-order difference. Based on this inequality, along with Lyapunov function theory and properties of nabla Mittag-Leffler function, novel adaptive and delay feedback controllers are proposed to achieve global Mittag-Leffler synchronization. Numerical modeling is conducted to demonstrate the effectiveness of the proposed methods.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Computer Science, Artificial Intelligence
Xinyu Mao et al.
Summary: This paper proposes a fractional-order model of quaternion-valued BAM neural networks (QVBAMNNs) with impulses and proportional delays in discrete-time case, and derives several criteria for the existence, uniqueness, and global exponential stability (GES) of equilibrium point by employing the homeomorphic mapping theorem, Lyapunov stability theory, and inequality technology. The novelty of these results lies in their generality for both fractional-order systems and integer-order ones.
Article
Engineering, Mechanical
Zhenghui Wen et al.
Summary: This paper investigates the effect of magnetic field coupling between neurons on neuron dynamics and finds that it can change the firing mode of neurons, providing new insights into the mechanism of information interaction between neurons.
NONLINEAR DYNAMICS
(2022)
Article
Optics
Shuying Wang et al.
Summary: This paper proposes an image encryption scheme using complex and time-delayed neural networks, which greatly enhances the security and resistance against attacks.
Article
Computer Science, Artificial Intelligence
Zhenyuan Guo et al.
Summary: This article discusses the multistability of switched neural networks with Gaussian activation functions under state-dependent switching, showing how the equilibrium points can be characterized using geometrical properties and local linearization. By deriving sufficient conditions, it is demonstrated that the networks can have up to 7(n) equilibria, with up to 4(n) of them being locally stable when p(1) = n. Proper selection of parameters can lead to a desired number of stable equilibria. Two numerical examples are provided to support the theoretical results.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Article
Computer Science, Hardware & Architecture
Xu Zhang et al.
Summary: This paper proposes a Multi-attention based Hybrid-convolution Spatial-temporal Recurrent Network (MHSRN) for region-based traffic flow prediction. The model leverages a hybrid-convolution module to capture shifting features and rich information at the nearest timestamps, and applies the downsampling procedure to reduce computation. Furthermore, a space-aware multi-attention module is used to re-perceive global and local spatial-temporal features. Experimental results demonstrate that MHSRN outperforms other baselines on various datasets.
Article
Computer Science, Artificial Intelligence
Martin J. A. Schuetz et al.
Summary: This paper demonstrates the application of graph neural networks to solve combinatorial optimization problems. By applying relaxation strategy to the problem Hamiltonian and training a graph neural network with unsupervised learning, we are able to achieve comparable or even superior performance to existing solvers on classical NP-hard problems, and scale beyond the state of the art to problems with millions of variables.
NATURE MACHINE INTELLIGENCE
(2022)
Article
Mathematics, Interdisciplinary Applications
Wafa Shammakh et al.
Summary: This study focuses on investigating the stability properties of the nonlinear fractional order generalized pantograph equation with discrete time using the Hilfer operator. By considering the hybrid fixed point theorem and Banach contraction theorem, the existence and uniqueness of solutions are studied. Stability results in the sense of Ulam and Hyers, as well as its generalized form for the initial value problem, are established, with numerical simulations demonstrating the impact of the fractional order on stability.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Fuqiang Wu et al.
Summary: Memristor is identified as a modulation factor to mimic neuronal synapse, inducing excitability transitions different from chemical methods in the Morris-Lecar model. The autapses of memristor and chemical play different roles in modulating neuronal electrical activities, contributing to the design and development of novel memristive synapses with excitatory or inhibitory effects.
CHAOS SOLITONS & FRACTALS
(2021)
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
Computer Science, Artificial Intelligence
Xiang Liu et al.
Summary: This paper investigates the quasi-projective synchronization and complete synchronization of fractional-order complex-valued neural networks with time delays without separating them into two real-valued systems. A generalized discrete fractional Halanay inequality with bounded time delays is first established, and then several novel synchronization conditions are derived based on this inequality and the Lyapunov functional method. Several examples are presented to illustrate the results.
NEURAL COMPUTING & APPLICATIONS
(2021)
Article
Materials Science, Multidisciplinary
Yuexi Peng et al.
Summary: This paper investigates an interesting second-order memristor-based map model using Caputo fractional-order difference, and explores its dynamic behaviors through various analysis methods. The numerical simulations show that the fractional-order system exhibits a range of complex behaviors, laying a solid foundation for future analysis and engineering applications of discrete memristors.
RESULTS IN PHYSICS
(2021)
Review
Nanoscience & Nanotechnology
Weilin Xu et al.
Summary: This paper provides an overview of memristor device characteristics, models, synapse circuits, and neural network applications, as well as research summaries, comparisons, limitations, challenges, and future work opportunities.
FRONTIERS IN NANOTECHNOLOGY
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NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
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EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
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NONLINEAR DYNAMICS
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(2015)
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(2015)
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(2011)
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INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2011)
Review
Mathematics, Interdisciplinary Applications
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INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2008)
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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2008)
