Article
Engineering, Electrical & Electronic
Shyam Krishan Joshi
Summary: This study focuses on finding sufficient conditions for synchronized bursts using coupled Hindmarsh-Rose model and verifies the outcomes through experiments and numerical simulations.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2022)
Article
Engineering, Electrical & Electronic
Shan Wang, Zhouchao Wei
Summary: This paper investigates the synchronization of memristive Hindmarsh-Rose neuron maps under different coupling conditions, including electrical synapses, chemical synapses, inner linking functions, and hybrid synapses. The study found that synchronization is achieved when the neurons are coupled through electrical and hybrid synapses, but not through chemical synapses. Moreover, it shows that a slightly lower coupling value is needed for synchronization through inner linking functions compared to electrical synapses.
AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS
(2023)
Article
Neurosciences
Danfeng Chen, Junsheng Li, Wei Zeng, Jun He
Summary: This article investigates the complex nonlinear behavior of the Hindmarsh-Rose neuron system and discusses the identification of nonlinear dynamics and topologies under unknown dynamical environment. It proposes a fast dynamical pattern recognition method based on system synchronization and demonstrates its effectiveness through simulations.
COGNITIVE NEURODYNAMICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Yuanyuan Yuan, Fang Han, Qinghua Zhu, Wenlian Lu
Summary: This study focuses on the existence of chimera states in two-layer networks of Hindmarsh-Rose neurons with different types of coupling. The results show that chimera states can occur by changing the synaptic coupling strength and the number of coupled neighbors. It is interesting to note that a new type of chimera state, called the interlayer semi-synchronous chimera state, is observed, where interlayer synchronous and asynchronous chimera states coexist. The findings indicate that the interaction between layers in neuronal networks can induce different types of chimera states and firing patterns, which can have implications for controlling neural firing patterns and understanding neuronal evolution.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Mathematics, Applied
L. Messee Goulefack, Marlon F. Ramos, R. Yamapi, C. Anteneodo
Summary: In this study, the dynamics of nonlocally coupled Hindmarsh-Rose neurons modified by coupling the induced magnetic flux to the membrane potential with a quadratic memristor of strength k were investigated. The nonlocal coupling involved the interaction of each neuron with its neighbors within a fixed radius, influencing the membrane potential with coupling intensity sigma. The study examined how variations of k and sigma affect the collective dynamics, finding that coherence typically increased when k and sigma were increased, except for small parameter ranges where the opposite behavior could occur. Moreover, varying k also affected the pattern of bursts and spikes, resulting in an increase in burst frequency, a decrease in the number and amplitude of spikes, and longer quiescent periods.
Article
Physics, Multidisciplinary
Franky Kevin Nando Tezoh, Adamou Dang Koko, H. P. Ekobena Fouda
Summary: Recent research has found that by considering the magnetic induction field brought by a memristor, two neurons can be coupled using the 2D Hindmarsh-Rose model. The memristor generates an induced current that flows through the neuronal network. By adding an external current to this induced current, the modes of electrical activities and the Hamiltonian energy of the coupled Hindmarsh-Rose model have been studied. Results showed that the neuronal network exhibits fast spiking behavior, which becomes even faster with an increase in the value of the external current. Additionally, it was observed that the neuronal network requires more energy to fire when the external current is added.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Physics, Multidisciplinary
Zhan-Hong Guo, Zhi-Jun Li, Meng-Jiao Wang, Ming-Lin Ma
Summary: A memristor-coupled heterogenous neural network consisting of 2D FitzHugh-Nagumo and Hindmarsh-Rose neurons with two time delays is established. The existence of Hopf bifurcation near the stable equilibrium point in four cases is theoretically derived and numerically verified. The time delays in FHN and HR neurons have different effects on the firing activity of the network, inducing complex firing patterns. Phase synchronization between the heterogeneous neurons is explored, revealing that the time delay in HR neurons has a greater effect on blocking synchronization. The theoretical analysis is verified by circuit simulations.
Article
Mathematics, Applied
Yuncheng You
Summary: A new model of neural networks based on the memristive Hindmarsh-Rose equations is proposed. It is proven that exponential synchronization at a uniform convergence rate occurs when the coupling strengths satisfy the threshold conditions quantitatively expressed by the parameters, through sharp and uniform grouping estimates and by leverage of integral and interpolation inequalities tackling the linear network coupling against the memristive nonlinearity.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2023)
Article
Engineering, Mechanical
Armand Sylvin Eteme, Conrad Bertand Tabi, Jean Felix Beyala Ateba, Henry Paul Ekobena Fouda, Alidou Mohamadou, Timoleon Crepin Kofane
Summary: The study demonstrates that the electromagnetic induction phenomenon can suppress chaotic states and enhance neural synchrony in neural systems. Increasing memristor strength can reduce the threshold for achieving synchronized states in electrically coupled neuron systems.
NONLINEAR DYNAMICS
(2021)
Article
Physics, Fluids & Plasmas
Jian-Fang Zhou, En-Hua Jiang, Bang-Lin Xu, Kesheng Xu, Changsong Zhou, Wu-Jie Yuan
Summary: By tuning synaptic strength, transitions between tonic and bursting neural activities can be realized. In networks with excitatory chemical synapses or electrical synapses, slow-wave activity similar to that observed during sleep can appear. Networks dominated by inhibitory chemical synapses result in desynchronized bursting activities.
Article
Physics, Multidisciplinary
Premraj Durairaj, Sathiyadevi Kanagaraj, P. Nageswara Rao, Anitha Karthikeyan, Karthikeyan Rajagopal
Summary: Magnetic flux and Josephson junctions are crucial in understanding the dynamics of biological neurons, leading to complex behaviors such as chaos and hyper-chaos. These dynamics depend on the coupling strength and junction coefficient.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Engineering, Multidisciplinary
Yuan YuanYuan, Yang Hao, Han Fang, Wang ZhiJie
Summary: This study investigates the traveling chimera states in memristive neuronal networks of locally coupled Hindmarsh-Rose neurons. Various traveling chimera patterns and firing modes are observed, including two kinds of traveling chimera states in opposite directions and a new type of chimera state called semi-traveling chimera state. Multi-head traveling chimera states and a firing pattern called mixed-amplitude bursting state are also observed. The study demonstrates the generation of traveling chimera states in real circuits and provides insights into the dynamics of neuronal networks.
SCIENCE CHINA-TECHNOLOGICAL SCIENCES
(2022)
Article
Mathematics, Applied
Fatemeh Parastesh, Mahtab Mehrabbeik, Karthikeyan Rajagopal, Sajad Jafari, Matjaz Perc
Summary: This study investigates the higher-order interactions among neurons and finds that second-order interactions can lead to synchronization under lower first-order coupling strengths. Additionally, the introduction of three-body interactions reduces the overall synchronization cost.
Article
Mathematics, Interdisciplinary Applications
A. Moujahid, F. Vadillo
Summary: Mathematical modeling is crucial for studying the impact of delay in neural systems and evaluating its effects on the signaling activity of coupled neurons. This study focuses on the energy perspective of delayed coupling in Hindmarsh-Rose burst neurons, examining the average energy consumption required to maintain cooperative behavior and quantifying the contribution of synapses to total energy consumption.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Physics, Multidisciplinary
Zeric Tabekoueng Njitacke, Sishu Shankar Muni, Soumyajit Seth, Jan Awrejcewicz, Jacques Kengne
Summary: This study focuses on the collective behavior of two HR neurons and a network of HR neurons. By connecting a traditional 3D HR neuron and a memristive 2D HR neuron through a gap junction, the collective behavior of the coupled neurons is obtained. Numerical simulations reveal that the coupled neurons exhibit various behaviors, including periodic, quasi-periodic, and chaotic bursting or spiking, by adjusting the control parameter. The network topology affects the spatiotemporal patterns, with cluster states observed in non-homogenous ring and star structures.
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)