Article
Physics, Multidisciplinary
Adrian Arellano-Delgado, Rosa Martha Lopez-Gutierrez, Miguel Angel Murillo-Escobar, Cornelio Posadas-Castillo
Summary: This work presents the problem of master-slave outer synchronization in different inner-outer network topologies. It focuses on particular scenarios concerning the topologies to reveal a suitable coupling strength for achieving outer synchronization. The novel MACM chaotic system is employed as a node in the coupled networks, which demonstrates robustness in its bifurcation parameters. Extensive numerical simulations are conducted to analyze the stability of the inner-outer network topologies using a master stability function approach.
Article
Mathematics, Interdisciplinary Applications
Zahra Dayani, Fatemeh Parastesh, Sajad Jafari, Eckehard Schoell, Juergen Kurths, Julien Clinton Sprott
Summary: This paper investigates various chaotic systems and finds the simplest cases that exhibit similar synchronization patterns, based on the master stability function approach.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2023)
Article
Mathematics, Interdisciplinary Applications
Andrey Andreev, Vladimir A. Maksimenko, Alexander N. Pisarchik, Alexander E. Hramov
Summary: Developing mathematical models to describe neuronal interactions in the brain is a challenging task in nonlinear dynamics. Recent advances in biochemistry and neuroscience have improved our understanding of neuron functioning and synaptic connections, but the mechanisms behind synchronization of different brain areas remain unknown and require further investigation.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Bo Yan, Fatemeh Parastesh, Shaobo He, Karthikeyan Rajagopal, Sajad Jafari, Matjaz Perc
Summary: This study investigates synchronization in multiplex neuronal networks composed of fractional-order Hindmarsh-Rose neurons and finds that fractional-order models achieve better synchronization compared to integer-order models. By reducing the derivative order of the model, the required coupling strengths for interlayer or intralayer synchronization can be weakened, and the dependence of synchronization on coupling strength decreases.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Engineering, Mechanical
Qian Zhou, Du Qu Wei
Summary: Electric and chemical synapses play a crucial role in signal exchange between neurons. This paper introduces the magnetic field and electric field into the traditional neuron model to study the collective dynamics of neuronal network, and finds that varying electrical synapse coupling can change the effects of magnetic coupling strength and cell size on synchronization. Additionally, for lower magnetic field coupling strength and cell size, electrical synapse coupling can induce synchronization more effectively. The results obtained provide new insights into signal coding and transition between neurons.
NONLINEAR DYNAMICS
(2021)
Article
Engineering, Multidisciplinary
Yuanyuan Liu, Zhongkui Sun, Xiaoli Yang, Wei Xu
Summary: In this paper, a multilayer neuronal network with ephaptic coupling between layers is constructed, and the dynamical robustness of the network is analyzed at different scales. The study reveals that inter-layer ephaptic coupling enhances the dynamical robustness of each layer and the entire network, contrasting with electrical coupling that tends to spoil the robustness. The firing patterns of neurons and their switching behaviors are also investigated. The findings provide new insights into the mechanism of collective phenomena in realistic neuronal systems.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Mathematics, Interdisciplinary Applications
Mohadeseh Shafiei Kafraj, Fahimeh Nazarimehr, Dibakar Ghosh, Karthikeyan Rajagopal, Sajad Jafari, J. C. Sprott
Summary: Obtaining the master stability function is a well-established method for studying synchronization in networks of chaotic oscillators. This study examines the effect of oscillator dynamics on the master stability function using a flexible oscillator with adjustable parameters. The results show that the amplitude of the oscillations has no significant effect on the master stability function, but oscillators with larger maximal Lyapunov exponent require higher coupling strength for synchronization. Interestingly, there is no linear relationship between the Kaplan-Yorke dimension and the coupling strength needed for complete synchronization.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Computer Science, Artificial Intelligence
Qiang Jia, Eric S. Mwanandiye, Wallace K. S. Tang
Summary: This paper investigates the master-slave synchronization problem of delayed neural networks with general time-varying control. The main theorem is established in terms of the time average of the control gain by using the Lyapunov-Razumikhin theorem, and some useful corollaries are deduced. The theorem also provides a solution for regaining stability under control failure, which is further demonstrated with numerical examples.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2021)
Article
Mathematical & Computational Biology
Sridevi Sriram, Hayder Natiq, Karthikeyan Rajagopal, Ondrej Krejcar, Hamidreza Namazi
Summary: Investigating the effect of changes in neuronal connectivity on the brain's behavior is a crucial topic in neuroscience. Complex network theory provides a powerful tool to study these changes. This paper focuses on the effect of asymmetry coupling changes on the behaviors of a multi-layer neuronal network.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Physics, Multidisciplinary
Fatemeh Parastesh, Zahra Dayani, Alireza Bahramian, Sajad Jafari, Guanrong Chen
Summary: This paper investigates the conventional PID control method for synchronizing a network of chaotic systems. The approach uses the master stability function and hyperjerk systems to overcome difficulties in calculating integral and derivative couplings. It is found that the most efficient coupling for network synchronization is the proportional-integral coupling.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2023)
Article
Automation & Control Systems
Luca Dieci, Cinzia Elia
Summary: This paper studies a network of identical piecewise smooth bimodal systems, known as systems of Filippov type, which synchronize along the asymptotically stable periodic orbit of a single agent. The fundamental matrix solution of the network along the synchronous solution is explicitly characterized, and the Master Stability Function tool is extended to the case of non-smooth dynamics of Filippov type.
Article
Mathematics, Interdisciplinary Applications
A. S. Reis, E. L. Brugnago, R. L. Viana, A. M. Batista, K. C. Iarosz, F. A. S. Ferrari, I. L. Caldas
Summary: In this study, a model of a clustered network formed by scale-free subnetworks is used to investigate the synchronization of neuronal activity. The spatial distribution of vertices in the cerebral cortex is simulated using the fitness model. The cortical connections in the network are established based on a human connectivity matrix obtained from experimental data. The results demonstrate that the fitness model and a three-stage switching control with time-delayed feedback are effective in suppressing synchronization in clustered networks.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Multidisciplinary Sciences
Elmer Guzman, Zhuowei Cheng, Paul K. Hansma, Kenneth R. Tovar, Linda R. Petzold, Kenneth S. Kosik
Summary: This study developed a non-invasive method to detect synaptic relationships among neurons from in vitro networks, using extracellular action potential propagation to identify short latency spiking relationships between neurons. The method allows for assembling a functional subset of neuronal connectivity in cultures.
SCIENTIFIC REPORTS
(2021)
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
Mathematics, Applied
Yuankai Ha, Yao Guo, Wei Lin
Summary: In this article, the dynamics of a non-Bayesian social learning model with periodically switching structures are investigated. Unlike previous studies, the model configurations are relaxed and it is validated that the dynamics of the model still converge to a true state of social learning in a particular sense of probability under such relaxed configurations. Estimations on the convergence rate for successful social learning in the model are provided, and the efficacy of the established conditions and estimations are numerically demonstrated using representative examples with switching structures. These results could potentially be useful for illustrating real-world social activities.
Article
Engineering, Mechanical
Kaipeng Hu, Zhouhong Li, Lei Shi, Matjaz Perc
Summary: In the rich variety of biological interaction patterns, the state of an individual often does not depend solely on immediate factors but is significantly associated also with interactions or circumstances from the past. In evolutionary game theory, delayed reciprocity is a common phenomenon that affects the evolution of cooperation. This paper studies three different two-species evolutionary models and finds that the type of interaction, whether it's intraspecific or interspecific, as well as the delay period, can have different effects on the stability and convergence of the system.
NONLINEAR DYNAMICS
(2023)
Article
Computer Science, Information Systems
Gayathri Vivekanandhan, Hayder Natiq, Yaser Merrikhi, Karthikeyan Rajagopal, Sajad Jafari
Summary: In this paper, a memristor is added to the two-dimensional neural model Chialvo to consider the effects of electromagnetic induction. The dynamics of the system are analyzed by obtaining bifurcation diagrams and Lyapunov spectra. The study shows that the magnetic strength and injected current are the most effective parameters on the dynamics. The memristive Chialvo can exhibit different neural behaviors and has coexisting attractors, similar to the primary Chialvo model. Furthermore, it is found that electrical coupling is essential for synchronization in the network of memristive Chialvo, while chemical coupling alone does not lead to synchronization.
Article
Mathematics, Applied
Mahtab Mehrabbeik, Sajad Jafari, Riccardo Meucci, Matjaz Perc
Summary: This paper studies the synchronization of globally coupled identical laser models via linear and nonlinear forms of diffusive couplings. The results show that complete synchronization can be achieved in laser models under linear diffusive function but not under nonlinear diffusive function. Multistability is observed in different network states such as cluster synchronization, chimera, and solitary states.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Physics, Multidisciplinary
Maja Duh, Marko Gosak, Matjaz Perc
Summary: In hyperbolic networks, the public goods game is influenced by network mixing and interdependence between networks. It is found that cooperation may have opposite effects in different networks. Optimal conditions for this phenomenon can be determined by considering mixing frequency and network interconnectedness.
Article
Computer Science, Hardware & Architecture
Zhen Wang, Fatemeh Parastesh, Huaigu Tian, Sajad Jafari
Summary: This paper investigates the synchronization behavior of multistable chaotic systems with coexisting symmetric attractors. It focuses on the attractive and repulsive couplings of the attractors in single-variable couplings. The results show that in self-couplings, both attractors have the same synchronization pattern either in the attractive or repulsive coupling. In cross-couplings, the synchronization pattern of the attractors depends on the variables involved and the symmetry transformation. If only one variable participates in the symmetry transformation, the synchronization patterns of the symmetric attractors are symmetric in the attractive and repulsive couplings. The master stability function is applied to four chaotic systems with different symmetry transformations to represent the results. The corresponding chaotic circuit of two coupled symmetric systems is also implemented and their symmetric responses are shown.
INTEGRATION-THE VLSI JOURNAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Atefeh Ahmadi, Sriram Parthasarathy, Nikhil Pal, Karthikeyan Rajagopal, Sajad Jafari, Esteban Tlelo-Cuautle
Summary: This paper proposes a novel five-dimensional autonomous chaotic system with hidden attractors and extreme multistability and extreme events. The features of this system are examined using dynamical analysis tools and its reliability is confirmed through analog electrical circuit design. This system can find applications in various engineering fields.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2023)
Article
Computer Science, Interdisciplinary Applications
Burhaneddin Izgi, Murat Ozkaya, Nazim Kemal Ure, Matjaz Perc
Summary: In this paper, a novel machine learning-driven framework for solving large-scale zero-sum matrix games is proposed. The framework combines the estimations from the extended matrix norm method and the payoff matrix, and provides rapid estimation of the game value through a neural network architecture. Experimental results demonstrate that the framework can accurately predict the values for games with up to 50 strategies, and real-time solution predictions can be obtained after the network training, making it useful for real-world applications.
JOURNAL OF COMPUTATIONAL SCIENCE
(2023)
Article
Computer Science, Interdisciplinary Applications
Bartu Yesilkaya, Ebru Sayilgan, Yilmaz Kemal Yuce, Matjaz Perc, Yalcin Isler
Summary: We propose a manifold learning framework to classify SSVEP data by reducing the number of features and comparing lower dimensional matrices with well-known machine learning algorithms. Among five manifold learning methods and nine machine learning algorithms, Principal Component Analysis shows the best classifier performance and achieves the highest accuracy when combined with the Naive Bayes classifier for a 7-class classification problem.
JOURNAL OF COMPUTATIONAL SCIENCE
(2023)
Article
Neurosciences
Murside Degirmenci, Yilmaz Kemal Yuce, Matjaz Perc, Yalcin Isler
Summary: In recent studies, researchers in the field of Brain-Computer Interface (BCI) have focused on Motor Imagery tasks, specifically on the classification of Electroencephalogram (EEG) signals. The study investigates the effect of statistical significance-based feature selection on the classification of Motor Imagery EEG signals, using various time-domain, frequency-domain, time-frequency domain, and non-linear parameters. By analyzing the results, it is found that the statistical significance-based feature selection approach improves the classifier performance in Motor Imagery task classification.
FRONTIERS IN HUMAN NEUROSCIENCE
(2023)
Article
Biology
Sridevi Sriram, Simin Mirzaei, Mahtab Mehrabbeik, Karthikeyan Rajagopal, Mehdi Rostami, Sajad Jafari
Summary: This paper investigates the effect of electrical, inner-linking, chemical, and hybrid coupling functions on the synchronization state of a neuronal network with regular structure using the memristive Chialvo (mChialvo) neuron map. The results suggest that chemical synapses facilitate mChialvo neurons' synchronization. Further studies reveal that coupled mChialvo neurons can reach different synchronization states based on the active synapses.
JOURNAL OF THEORETICAL BIOLOGY
(2023)
Article
Mathematics
Jayaraman Venkatesh, Alexander N. Pchelintsev, Anitha Karthikeyan, Fatemeh Parastesh, Sajad Jafari
Summary: This paper presents a study on a memristive two-neuron-based Hopfield neural network with fractional-order derivatives. The equilibrium points of the system are identified and their stability is analyzed. Bifurcation diagrams are obtained by varying the magnetic induction strength and the fractional-order derivative. The study also explores the application of the fractional-order model for image encryption and verifies its efficiency and resistance.
Article
Physics, Fluids & Plasmas
Kaipeng Hu, Pengyue Wang, Junzhou He, Matjaz Perc, Lei Shi
Summary: This study investigates the interactions among individuals in different populations, finding that interactions across multiple populations can promote the evolution of cooperation depending on the level of interaction asymmetry. If interactions within and between populations are symmetric, the presence of multiple populations alone can promote the evolution of cooperation. Asymmetric interactions can further promote cooperation but at the expense of the coexistence of competing strategies.
Article
Physics, Fluids & Plasmas
Simin Mirzaei, Md Sayeed Anwar, Fatemeh Parastesh, Sajad Jafari, Dibakar Ghosh
Summary: This paper introduces a general coupling condition based on the linear matrix of dynamical systems to achieve complete synchronization in purely repulsive coupled oscillators. The proposed coupling scheme is validated through simulations and linear stability analysis, and is shown to work effectively for a large ensemble of oscillators.
Article
Mathematics, Applied
Gokulakrishnan Sriram, Fatemeh Parastesh, Hayder Natiq, Karthikeyan Rajagopal, Riccardo Meucci, Sajad Jafari
Summary: This paper investigates the effects of a switching parameter on the dynamics of a multistable laser model. It is found that the attractor of a fast blinking system may differ from the average attractor.
Article
Physics, Multidisciplinary
Atiyeh Bayani, Prasina Alexander, Hamed Azarnoush, Karthikeyan Rajagopal, Sajad Jafari, Fahimeh Nazarimehr
Summary: This study demonstrates the impact of Laplacian eigenvalue on the type of synchronization transition observed in complex systems. The sparsity of the Laplacian eigenvalues is found to be the key factor in designing explosive or continuous synchronization transitions. The results highlight a pivotal characteristic that indicates the synchronization transition is not mainly dependent on the internal dynamics of the nodes, providing insights for the precise control of complex networks.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(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)
