Article
Mathematics, Interdisciplinary Applications
S. G. Ngueuteu Mbouna, Tanmoy Banerjee, Rene Yamapi, Paul Woafo
Summary: This paper investigates the impact of fractional derivation on the symmetry-breaking dynamics of a network of coupled fractional-order Stuart-Landau oscillators. The study finds that the value of the fractional derivatives order has a significant influence on the network dynamics. Decreasing the derivatives order results in complex dynamical patterns and extends the lifetime of amplitude chimeras.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Physics, Fluids & Plasmas
Seungjae Lee, Katharina Krischer
Summary: Twisted state is an important and simple form of collective dynamics in oscillatory medium, characterized by inhomogeneous profiles of amplitudes and phase gradients. In this study, we investigate a non-trivial twisted state in a system of nonlocally coupled Stuart-Landau oscillators using various methods including linear stability analysis, Lyapunov exponents, and covariant Lyapunov vectors. We show that the non-trivial twisted state is robust and can be born or annihilated in saddle-node bifurcations and change stability in Hopf bifurcations.
Article
Physics, Multidisciplinary
Rok Cestnik, Arkady Pikovsky
Summary: We study the collective behavior of phase oscillators in the thermodynamic limit and propose an Ansatz for the circular moments of the distribution that allows for truncation at any number of modes. By simulating a Josephson junction array, we demonstrate the higher-dimensional behavior facilitated by dynamics on extended manifolds.
PHYSICAL REVIEW LETTERS
(2022)
Article
Mathematics, Interdisciplinary Applications
Wang Yi, Xue Yu, Wang Xue, Cen Bing-ling, Qiao Yan-feng
Summary: The paper presents a two-layer coupled oscillator model, in which the driven layer transitions from unsynchronized state to synchronized state with parameter changes, revealing the existence of chimer state. The dynamic behavior of the system has been studied and the critical value for the state transition has been identified.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
David Mersing, Shannyn A. Tyler, Benjamas Ponboonjaroenchai, Mark R. Tinsley, Kenneth Showalter
Summary: The study investigates photochemically coupled micro-oscillators in star networks, showing that synchronization can be achieved through adjusting coupling strength. Both experimental and theoretical analysis provide insights into the synchronization mechanism, where phase divergence in heterogeneous oscillators can be realigned by perturbations from hub oscillator.
Article
Physics, Fluids & Plasmas
Kazuha Itabashi, Quoc Hoan Tran, Yoshihiko Hasegawa
Summary: By proposing a topological approach to characterize the phase dynamics in coupled oscillators, this study gains insights into the collective dynamics of complex systems. The method extracts quantitative features describing the shape of the phase data and extends these features to time-variant characteristics. Combining these features with the kernel method allows for characterization of multiclustered synchronized dynamics and qualitative explanation of chimera states.
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
Mathematics, Applied
Anjuman Ara Khatun, Haider Hasan Jafri
Summary: The study explores the coexistence of synchronous and asynchronous dynamical behaviors in an ensemble of nonlinear oscillators coupled through different variables, resulting in chimera states. By tuning the coupling parameter in a different variable, the region of multistability can be shifted, providing an additional means to create chimera states. In an ensemble of coupled Rossler systems, multiple attractors and intertwined basins are observed, with the strength of incoherence (SI) serving as a useful order parameter for characterizing chimera states.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Mathematics, Applied
Dawid Dudkowski, Krzysztof Czolczynski, Tomasz Kapitaniak
Summary: This paper introduces a novel type of chimera state, known as multi-headed loop chimera, by studying a network of pendulum clocks. The study examines the occurrence and stability of these chimera states, analyzing the geometrical regions of the system with the highest probability of their occurrence, discussing the mechanisms of their creation, and exploring the influence of global coupling on their stability. The paper also investigates the bifurcation analysis of these states and generalizes their appearance into large networks of oscillators.
Article
Mathematics, Applied
Guillermo H. Goldsztein, Lars Q. English, Emma Behta, Hillel Finder, Alice N. Nadeau, Steven H. Strogatz
Summary: Using theory, experiment, and simulation, this study examines the dynamics of two coupled metronomes on a moving platform. The experiments show that the platform motion is damped by a dry friction force of Coulomb type, contrary to previous assumptions of viscous linear friction force. A new mathematical model is developed based on previous models but with a different treatment of friction. The model analysis reveals various long-term behaviors, including synchronization, phase locking, and suppression, shedding light on the dynamics of coupled metronomes.
Article
Physics, Fluids & Plasmas
Biswabibek Bandyopadhyay, Tanmoy Banerjee
Summary: This study investigates the impact of Kerr anharmonicity on the symmetry-breaking phenomena of coupled quantum oscillators, revealing that Kerr nonlinearity hinders the process of symmetry breaking in both cases. The findings provide a means to control and engineer symmetry-breaking states for quantum technology.
Article
Mathematics, Interdisciplinary Applications
E. Njinkeu Nganso, S. G. Ngueuteu Mbouna, R. Yamapi, G. Filatrella, J. Kurths
Summary: In this paper, the authors study a network of van der Pol oscillators with extended nonlinearity to explore symmetry-breaking phenomena. The van der Pol oscillator with extended nonlinearity is widely used as a model for coherent oscillations in enzyme-substrate systems, exhibiting multistability known as birhythmicity. The coupled dynamics of this model show various symmetry-breaking phenomena, including peculiar chimera and solitary states involving two types of attractors. This study deepens our understanding of pattern formation in coupled multistable systems.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Engineering, Mechanical
Mingxue Yang, Shuangjian Guo, Yirui Chen, Qionglin Dai, Haihong Li, Junzhong Yang
Summary: This study identified a two-frequency chimera state in which oscillators in different coherent domains oscillate at different velocities. Oscillators in coherent domains with higher mean phase velocity almost synchronize, while those in domains with lower mean phase velocity are randomly partitioned into two groups in antiphase. Additionally, the dynamics of local mean fields in these two types of coherent domains are found to be different.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
Hyunsuk Hong, Erik A. Martens
Summary: This study investigated the phase coherence dynamics in coupled oscillators based on the correlation between frequencies and coupling strengths. Results showed that in the case of correlated disorder, the oscillator population splits into two subpopulations, while in the uncorrelated case, it may split into four phase-locked subpopulations, leading to periodic global synchronization motion. In both cases of disorder, an incoherent state exists, with instability observed in the correlated case and neutral stability in the uncorrelated case.
Article
Physics, Fluids & Plasmas
A. Ragavan, M. Manoranjani, D. V. Senthilkumar, V. K. Chandrasekar
Summary: We have observed the emergence of distinct multistable chimera states, in addition to chimera death and synchronized states, in a smallest population of three globally coupled oscillators with mean-field diffusive coupling. A series of torus bifurcations result in the manifestation of distinct periodic orbits, leading to the creation of chimera states with two synchronized oscillators coexisting with an asynchronous oscillator. Subsequent Hopf bifurcations lead to homogeneous and inhomogeneous steady states, resulting in desynchronized steady states and chimera death state among the coupled oscillators. The stability of periodic orbits and steady states is lost through a sequence of saddle-loop and saddle-node bifurcations, ultimately resulting in a stable synchronized state. We have also extended these findings to N coupled oscillators and derived the variational equations corresponding to perturbation transverse to the synchronization manifold, confirming the synchronized state in the two-parameter phase diagrams using its largest eigenvalue. Chimera states in three coupled oscillators emerge as a solitary state in N coupled oscillator ensemble.
Article
Mathematics, Applied
Stanislaw Drozdz, Ludovico Minati, Pawel Oswiecimka, Marek Stanuszek, Marcin Watorek
Article
Neurosciences
Carlo Nicolini, Giulia Forcellini, Ludovico Minati, Angelo Bifone
Article
Engineering, Mechanical
Pawel Oswiecimka, Stanislaw Drozdz, Mattia Frasca, Robert Gebarowski, Natsue Yoshimura, Luciano Zunino, Ludovico Minati
NONLINEAR DYNAMICS
(2020)
Article
Mathematics, Applied
Alessio Perinelli, Michele Castelluzzo, Ludovico Minati, Leonardo Ricci
Article
Mathematics, Interdisciplinary Applications
L. Minati, L. Gambuzza, W. J. Thio, J. C. Sprott, M. Frasca
CHAOS SOLITONS & FRACTALS
(2020)
Article
Automation & Control Systems
Lucia Valentina Gambuzza, Mattia Frasca
Summary: The paper addresses the problem of steering a multiagent system to multiconsensus, utilizing distributed proportional controllers. It investigates the stability and conditions for gain of the controllers in achieving multiconsensus state. Furthermore, the approach is extended to controllers that alter the original structure while preserving weak connectedness in the resulting graph.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2021)
Article
Computer Science, Artificial Intelligence
Yuri Antonacci, Ludovico Minati, Luca Faes, Riccardo Pernice, Giandomenico Nollo, Jlenia Toppi, Antonio Pietrabissa, Laura Astolfi
Summary: Studying the application of artificial neural networks and stochastic gradient descent algorithm in Granger causality analysis can effectively address the issue of reduced accuracy in situations with low data points and VAR parameters ratio. Additionally, the selection of different parameter combinations has a significant impact on the performance of GC estimation, indicating that choosing the appropriate regularization parameter can enhance the sparsity and accuracy of network estimation.
PEERJ COMPUTER SCIENCE
(2021)
Article
Computer Science, Information Systems
Ettore Tiraboschi, Ludovico Minati, Simone Monachino, Mattia Frasca, Albrecht Haase
Summary: We demonstrate an interdisciplinary approach to derive a mesoscopic-scale functional model of a biological system, which can be used to design analog electronic circuits. We focus on the sensory processing in honey bees and use high temporal resolution calcium imaging to track the dynamics of odor-evoked activity. By applying a transfer function approach, we capture the signal transformations between odor input and glomerular response, and between glomerular signals and somata activity. Through Granger causality and machine learning techniques, we map somata to glomeruli and group responses based on common properties. The obtained low-order transfer functions closely resemble the biological system's input-output properties and can be used for designing corresponding analog electronic circuits.
Article
Engineering, Electrical & Electronic
Xinkai Fan, Ekaterina Dudkina, Lucia Valentina Gambuzza, Mattia Frasca, Emanuele Crisostomi
Summary: In this work, a novel model based on a structure-preserving approach is developed to describe a power grid. The model takes into consideration classic voltage and frequency protection mechanisms. By studying the Italian power grid, it is found that more realistic models are crucial in determining the size of cascading failures and the sequence of involved links.
ELECTRIC POWER SYSTEMS RESEARCH
(2022)
Article
Mathematics, Applied
Alessandra Corso, Lucia Valentina Gambuzza, Pietro De Lellis, Mattia Frasca
Summary: In this work, a multilayer control protocol is proposed for achieving synchronization of network dynamical systems with limited resources. In addition to the backbone network where system interactions take place, a second adaptive layer is introduced with edge snapping mechanism to add or remove edges. The modified edge dynamics with capped number of activated edges are studied for local stability of the network dynamics. The effectiveness and robustness of the proposed approach are demonstrated on a network of Rossler oscillators and a model of the Italian high-voltage power grid.
Article
Robotics
Cinzia Tomaselli, Dario C. Guastella, Giovanni Muscato, Mattia Frasca, Lucia Valentina Gambuzza
Summary: This paper proposes a multi-robot system for experimental investigations of face-to-face interaction dynamics. The study finds that the system reproduces the main features of face-to-face dynamics and remains robust under different experimental settings and challenging operating conditions.
IEEE ROBOTICS AND AUTOMATION LETTERS
(2023)
Article
Engineering, Multidisciplinary
Lucia Valentina Gambuzza, Mattia Frasca, Francesco Sorrentino, Louis M. Pecora, Stefano Boccaletti
Summary: Symmetries play a crucial role in regulating collective dynamics in complex networks, and this study focuses on controlling network symmetries and enforcing patterned states of synchronization. By perturbing the original network connectivity with minimal changes, desirable clustering of nodes can be achieved. The stability conditions of enforced patterns are derived and the method's performance is illustrated with examples relevant to various practical scenarios.
IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING
(2021)
Article
Computer Science, Information Systems
Ludovico Minati, Korkut Kaan Tokgoz, Mattia Frasca, Yasuharu Koike, Jacopo Iannacci, Natsue Yoshimura, Kazuya Masu, Hiroyuki Ito
Article
Mathematics, Interdisciplinary Applications
Bo Li, Tian Huang
Summary: This paper proposes an approximate optimal strategy based on a piecewise parameterization and optimization (PPAO) method for solving optimization problems in stochastic control systems. The method obtains a piecewise parameter control by solving first-order differential equations, which simplifies the control form and ensures a small model error.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Guram Mikaberidze, Sayantan Nag Chowdhury, Alan Hastings, Raissa M. D'Souza
Summary: This study explores the collective behavior of interacting entities, focusing on the co-evolution of diverse mobile agents in a heterogeneous environment network. Increasing agent density, introducing heterogeneity, and designing the network structure intelligently can promote agent cohesion.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Gengxiang Wang, Yang Liu, Caishan Liu
Summary: This investigation studies the impact behavior of a contact body in a fluidic environment. A dissipated coefficient is introduced to describe the energy dissipation caused by hydrodynamic forces. A new fluid damping factor is derived to depict the coupling between liquid and solid, as well as the coupling between solid and solid. A new coefficient of restitution (CoR) is proposed to determine the actual physical impact. A new contact force model with a fluid damping factor tailored for immersed collision events is proposed.
CHAOS SOLITONS & FRACTALS
(2024)
