Article
Engineering, Mechanical
Hairong Lin, Chunhua Wang, Li Cui, Yichuang Sun, Xin Zhang, Wei Yao
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
Qiang Lai, Shicong Guo
Summary: This paper aims to construct a class of memristive neural networks (MNNs) with a simple circular connection relationship and complex dynamics by introducing a generic memristor as synapse. One remarkable feature of the proposed MNNs is that they can yield complex dynamics, in particular, abundant coexisting attractors and large-scale parameter-relied amplitude control, by comparing with some existing MNNs. The complex dynamics and circuit implementation of one of the MNNs are studied, and a microcontroller-based hardware circuit is given to realize the network, which verifies the correctness of the numerical results and experimental results.
Article
Mathematics, Interdisciplinary Applications
Xiaochen Mao, Fuchen Lei
Summary: This paper examines the dynamics of a nonlinear network with multiple interacting neural populations and time-delayed couplings in the presence of electromagnetic radiation. The impact of the electromagnetic radiation is described using flux-controlled memristors. By decomposing and analyzing the characteristic equations, the paper determines the delay-induced instability and bifurcated periodic oscillations of the memristive multiplex network. Bifurcation diagrams are presented, showcasing complex dynamical behaviors such as multi-periodic orbits and period doubling bifurcations. These intriguing phenomena are also observed in circuit realizations. The study finds that both time delay and electromagnetic radiation have significant effects on the network's performance, including synchronization transitions and the coexistence of multistability.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Materials Science, Multidisciplinary
F. M. Allehiany, Emad E. Mahmoud, Lone Seth Jahanzaib, Pushali Trikha, Hammad Alotaibi
Summary: The manuscript introduces the dynamics of fractional order neural network under electromagnetic radiation, showing high sensitivity to external stimuli and improvement in neural functioning under the right amount of electromagnetic radiations. Control of chaos in the studied dynamical system around its unique stagnation point using SMC controllers in the presence of uncertainties and disturbances is also explored. These results could provide insights into neuron related problems.
RESULTS IN PHYSICS
(2021)
Review
Engineering, Mechanical
Hairong Lin, Chunhua Wang, Quanli Deng, Cong Xu, Zekun Deng, Chao Zhou
Summary: The study of dynamics on artificial neurons and neuronal networks is crucial for understanding brain functions and developing neuromorphic systems. Memristive neuron and neural network models show great potential in investigating neurodynamics, researching various chaotic dynamics phenomena, and are categorized into five types based on different biological function mechanisms. Pioneering works and recent important papers related to these types are introduced, along with presenting some open problems in the field for future exploration.
NONLINEAR DYNAMICS
(2021)
Article
Physics, Multidisciplinary
Ai-Xue Qi, Bin-Da Zhu, Guang-Yi Wang
Summary: This paper presents a new hyperbolic-type memristor model and verifies its performance through numerical simulations and analog circuit experiments. Based on this model, a cellular neural network with complex dynamic behaviors is designed and the complexity and chaotic characteristics are validated.
Article
Engineering, Mechanical
Qiuzhen Wan, Zidie Yan, Fei Li, Jiong Liu, Simiao Chen
Summary: This paper investigates a Hopfield neural network under external electromagnetic radiation and dual bias currents, discussing its basic properties and nonlinear dynamic characteristics. The network shows high sensitivity to system parameters and initial conditions due to the presence of radiation and dual bias currents. The study reveals the existence of hidden attractors such as periodic, quasi-periodic, chaotic, and transient chaotic attractors in the proposed network. Additionally, the network exhibits transient chaos with different chaotic times based on varying neuron membrane magnetic flux, and parallel bifurcation behaviors with changing system parameters are observed.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Qing Dong, Shihua Zhou, Qiang Zhang, Nikola K. Kasabov
Summary: This paper introduces a five-dimensional non-Hamiltonian conservative hyperchaos system and investigates its dynamic properties. The results show that the system exhibits multi-stable characteristics as well as intermittent chaos and quasi-periodic characteristics, with sequences of good pseudo-randomness.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Engineering, Mechanical
Hao Ming, Hanping Hu, Jun Zheng
Summary: This paper introduces a new coupled chaotic model with a wide chaotic parameter range. By exploring dynamical behaviors with various coupling structures, it is found that the coupled model exhibits more complex and stable chaotic performance when there exists a loop in its topological structure.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Christophe Letellier, Nataliya Stankevich, Otto E. Roessler
Summary: Accurately characterizing chaotic behaviors is a complex problem that requires classification and labeling to determine the shared properties and differences between chaotic behaviors. Starting from the Lyapunov exponent spectrum, we extended the description of chaotic behaviors, proposed higher-level classification methods, and expanded the description to multi-component attractors using a linker.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(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
Mathematics, Interdisciplinary Applications
Vladimir V. Klinshov, Andrey V. Kovalchuk, Igor Franovic, Matjaz Perc, Milan Svetec
Summary: This study investigates the emergence of rate chaos in three different scenarios and finds that only the scenario involving slow dynamics of synapses results in an extension of the network's dynamic memory.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Debarghya Pattanayak, Arindam Mishra, Nandadulal Bairagi, Syamal K. Dana
Summary: This paper discusses the statistics of transient dynamics in a classic tri-trophic food chain with bistability. It is found that the distribution of the transient time to predator extinction exhibits interesting patterns of inhomogeneity and anisotropy in the basin of the predator-free state. Two new metrics, homogeneity index and local isotropic index, are introduced to characterize the distinctive features of the distribution. The paper also explains the origin of multimodal distributions and presents their ecological implications.
Article
Neurosciences
S. Kamyar Tavakoli, Andre Longtin
Summary: Neural circuits operate with delays over a range of time scales, and the inclusion of multiple delays in a high-dimensional chaotic neural network can lead to a reduction in dynamical complexity known as multi-delay complexity collapse (CC). CC occurs when multiple small local delays are combined with moderate global delayed inhibitory feedback and random initial conditions, leading to the settling of transient chaos onto a limit cycle. Interestingly, an increase in the distribution width of local delays, even to unrealistically large values, does not cause CC, nor does adding more local delays.
FRONTIERS IN SYSTEMS NEUROSCIENCE
(2021)
Article
Engineering, Multidisciplinary
MengYan Ge, GuoWei Wang, Ya Jia
Summary: Iterative methods were used to simulate in vitro feedforward neural networks in physiological experiments. The study investigated the effect of Gaussian colored noise and electromagnetic radiation on the propagation of subthreshold excitatory postsynaptic current signals. It was found that electromagnetic radiation slightly reduces the propagation of weak signals and an increase in feedback gain leads to longer propagation time. The feedforward neural network studied is a simple model, while more complex structures can be observed in real biological systems.
SCIENCE CHINA-TECHNOLOGICAL SCIENCES
(2021)
Article
Neurosciences
Cong Xu, Meiling Liao, Chunhua Wang, Jingru Sun, Hairong Lin
Summary: This paper proposes a memristor-based competitive Hopfield neural network circuit for image segmentation. The circuit utilizes a memristive cross array to store synaptic weights and perform matrix operations, resulting in improved processing speed and segmentation accuracy compared to other methods. The proposed circuit also demonstrates good robustness to noise and memristive variation.
COGNITIVE NEURODYNAMICS
(2023)
Article
Engineering, Mechanical
Zhou Chao, Chunhua Wang, Wei Yao
Summary: In this paper, the quasi-synchronization problem of stochastic memristive neural networks subject to deception attacks is investigated using hybrid impulsive control. Attack conditions are described using stochastic variables, and a new inequality is proposed for dealing with quasi-synchronization in impulsive systems. Sufficient conditions and error bounds are obtained for validating the quasi-synchronization, and the effects of attacks and their mitigation are discussed.
NONLINEAR DYNAMICS
(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
Engineering, Electrical & Electronic
Hairong Lin, Chunhua Wang, Yichuang Sun, Ting Wang
Summary: This paper presents a novel method for generating n-scroll chaotic attractors. It models a magnetized Hopfield neural network (HNN) with three neurons by introducing an improved multi-piecewise memristor to describe the effect of electromagnetic induction. Theoretical analysis and numerical simulation demonstrate that the memristor-based magnetized HNN can generate multi-scroll chaotic attractors with any number of scrolls, which can be easily adjusted by controlling the memristor parameters. Additionally, complex initial offset boosting behavior is observed in the magnetized HNN. The designed magnetized HNN circuit is capable of generating various typical attractors.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2023)
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
Mathematics, Interdisciplinary Applications
Xiaojuan Ma, Chunhua Wang, Wenlu Qiu, Fei Yu
Summary: In this paper, a fast hyperchaotic image encryption scheme based on RSVM and step-by-step scrambling-diffusion is proposed. The scheme utilizes the RSVM algorithm to generate random one-dimensional arrays of the pixel matrix, which are then used to scramble-diffuse the rows/columns of the pixel matrix. The control parameters of the RSVM algorithm are determined by the SHA-256 of the plaintext pixels, ensuring that even small changes in the plaintext pixels result in significant differences in the ciphertext images. Additionally, the overall time complexity of the scheme is quite low, reducing the time cost significantly.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2023)
Article
Mathematics, Applied
Shaohua Zhang, Cong Wang, Hongli Zhang, Hairong Lin
Summary: Propose a multiplier-free implementation of the Rulkov neuron model and utilize a periodic memristor to achieve the biomimetic modeling of the non-autonomous memristive Rulkov neuron. Numerical simulations show that the mRulkov neuron can exhibit parameter-dependent local spiking, local hidden spiking, and periodic bursting firing behaviors. Furthermore, the novel boosted extreme multistability is discovered in the Rulkov neuron for the first time.
Article
Mathematics, Interdisciplinary Applications
Hairong Lin, Chunhua Wang, Sichun Du, Wei Yao, Yichuang Sun
Summary: In this paper, a simplified multi-piecewise memristor is used to design a family of memristive multibutterfly chaotic systems (MMBCSs). Three MMBCSs are constructed by coupling different numbers of the simplified multi-piecewise memristors into a modified Sprott C system. The constructed MMBCSs can generate connected and unconnected 1D, 2D, and 3D multibutterfly chaotic attractors, and the number and position of butterfly attractors can be easily controlled.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Computer Science, Hardware & Architecture
Zekun Deng, Chunhua Wang, Hairong Lin, Yichuang Sun
Summary: In this article, a selective supervised algorithm inspired by the selective attention mechanism is proposed, and memristive neural circuits are designed based on this algorithm. The proposed algorithm shows excellent performance on sequence learning. Additionally, attention encoding circuits are designed to encode external stimuli into attention spikes. The memristive spiking neural network circuit can achieve high accuracy on the MNIST and Fashion-MNIST datasets after learning a small number of labeled samples, reducing manual annotation cost and improving supervised learning efficiency.
IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS
(2023)
Article
Computer Science, Artificial Intelligence
Wei Yao, Chunhua Wang, Yichuang Sun, Shuqing Gong, Hairong Lin
Summary: This paper investigates the robust exponential synchronization of inertial memristive neural networks (IMNNs) with time-varying delays and parameter disturbance through event-triggered control (ETC) scheme. The delayed IMNNs are transformed into first-order MNNs with parameter disturbance by constructing proper variable substitutions. Then, a state feedback controller is designed for response IMNNs with parameter disturbance, and ETC methods are provided to decrease the update times of controller.
Article
Mathematics, Interdisciplinary Applications
Minglin Ma, Yaping Lu, Zhijun Li, Yichuang Sun, Chunhua Wang
Summary: To enrich the dynamic behaviors of discrete neuron models and mimic biological neural networks more effectively, this paper proposes a bistable locally active discrete memristor (LADM) model to simulate synapses. By introducing the LADM into two identical Rulkov neurons, the dynamic behaviors of neural networks are explored. Numerical simulation shows that the neural network exhibits multistability and new firing behaviors under different system parameters and initial values. In addition, the synchronization between the neurons is also investigated.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Peter Frolkovic, Nikola Gajdosova
Summary: This paper presents compact semi-implicit finite difference schemes for solving advection problems using level set methods. Through numerical tests and stability analysis, the accuracy and stability of the proposed schemes are verified.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Md. Rajib Arefin, Jun Tanimoto
Summary: Human behaviors are strongly influenced by social norms, and this study shows that injunctive social norms can lead to bi-stability in evolutionary games. Different games exhibit different outcomes, with some showing the possibility of coexistence or a stable equilibrium.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Dingyi Du, Chunhong Fu, Qingxiang Xu
Summary: A correction and improvement are made on a recent joint work by the second and third authors. An optimal perturbation bound is also clarified for certain 2 x 2 Hermitian matrices.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Pingrui Zhang, Xiaoyun Jiang, Junqing Jia
Summary: In this study, improved uniform error bounds are developed for the long-time dynamics of the nonlinear space fractional Dirac equation in two dimensions. The equation is discretized in time using the Strang splitting method and in space using the Fourier pseudospectral method. The major local truncation error of the numerical methods is established, and improved uniform error estimates are rigorously demonstrated for the semi-discrete scheme and full-discretization. Numerical investigations are presented to verify the error bounds and illustrate the long-time dynamical behaviors of the equation with honeycomb lattice potentials.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kuan Zou, Wenchen Han, Lan Zhang, Changwei Huang
Summary: This research extends the spatial PGG on hypergraphs and allows cooperators to allocate investments unevenly. The results show that allocating more resources to profitable groups can effectively promote cooperation. Additionally, a moderate negative value of investment preference leads to the lowest level of cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kui Du
Summary: This article introduces two new regularized randomized iterative algorithms for finding solutions with certain structures of a linear system ABx = b. Compared to other randomized iterative algorithms, these new algorithms can find sparse solutions and have better performance.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Shadi Malek Bagomghaleh, Saeed Pishbin, Gholamhossein Gholami
Summary: This study combines the concept of vanishing delay arguments with a linear system of integral-algebraic equations (IAEs) for the first time. The piecewise collocation scheme is used to numerically solve the Hessenberg type IAEs system with vanishing delays. Well-established results regarding regularity, existence, uniqueness, and convergence of the solution are presented. Two test problems are studied to verify the theoretical achievements in practice.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Qi Hu, Tao Jin, Yulian Jiang, Xingwen Liu
Summary: Public supervision plays an important role in guiding and influencing individual behavior. This study proposes a reputation incentives mechanism with public supervision, where each player has the authority to evaluate others. Numerical simulations show that reputation provides positive incentives for cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Werner M. Seiler, Matthias Seiss
Summary: This article proposes a geometric approach for the numerical integration of (systems of) quasi-linear differential equations with singular initial and boundary value problems. It transforms the original problem into computing the unstable manifold at a stationary point of an associated vector field, allowing efficient and robust solutions. Additionally, the shooting method is employed for boundary value problems. Examples of (generalized) Lane-Emden equations and the Thomas-Fermi equation are discussed.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Lisandro A. Raviola, Mariano F. De Leo
Summary: We evaluated the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations and showed that the proposed methods are effective in terms of accuracy and computational cost. They can be applied to both irreversible models and dissipative solitons, offering a promising alternative for solving a wide range of evolutionary partial differential equations.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Yong Wang, Jie Zhong, Qinyao Pan, Ning Li
Summary: This paper studies the set stability of Boolean networks using the semi-tensor product of matrices. It introduces an index-vector and an algorithm to verify and achieve set stability, and proposes a hybrid pinning control technique to reduce computational complexity. The issue of synchronization is also discussed, and simulations are presented to demonstrate the effectiveness of the results obtained.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Ling Cheng, Sirui Zhang, Yingchun Wang
Summary: This paper considers the optimal capacity allocation problem of integrated energy systems (IESs) with power-gas systems for clean energy consumption. It establishes power-gas network models with equality and inequality constraints, and designs a novel full distributed cooperative optimal regulation scheme to tackle this problem. A distributed projection operator is developed to handle the inequality constraints in IESs. The simulation demonstrates the effectiveness of the distributed optimization approach.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Abdurrahim Toktas, Ugur Erkan, Suo Gao, Chanil Pak
Summary: This study proposes a novel image encryption scheme based on the Bessel map, which ensures the security and randomness of the ciphered images through the chaotic characteristics and complexity of the Bessel map.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Xinjie Fu, Jinrong Wang
Summary: In this paper, we establish an SAIQR epidemic network model and explore the global stability of the disease in both disease-free and endemic equilibria. We also consider the control of epidemic transmission through non-instantaneous impulsive vaccination and demonstrate the sustainability of the model. Finally, we validate the results through numerical simulations using a scale-free network.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Maria Han Veiga, Lorenzo Micalizzi, Davide Torlo
Summary: The paper focuses on the iterative discretization of weak formulations in the context of ODE problems. Several strategies to improve the accuracy of the method are proposed, and the method is combined with a Deferred Correction framework to introduce efficient p-adaptive modifications. Analytical and numerical results demonstrate the stability and computational efficiency of the modified methods.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
