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
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
Zhen Su, Juergen Kurths, Yaru Liu, Serhiy Yanchuk
Summary: Extreme multistability refers to the appearance of infinitely many coexisting attractors or continuous families of stable states in dynamical systems. In this study, we investigate a model of pendulum clocks coupled by springs and suspended on an oscillating base to demonstrate how extreme multistability can be induced through specifically designed coupling. Symmetric coupling is found to increase the dynamical complexity, leading to the generation of multiple isolated attractors and continuous families of stable periodic states. These coexisting states exhibit different levels of phase synchronization and can display splitting behavior.
Article
Mathematics, Applied
Georgi S. Medvedev, Matthew S. Mizuhara, Andrew Phillips
Summary: In this study, we investigate a system of coupled phase oscillators driven by random intrinsic frequencies near a saddle-node on invariant circle bifurcation. The system undergoes a phase transition and changes its qualitative properties of collective dynamics under the variation of control parameters. By using Ott-Antonsen reduction and geometric techniques for ordinary differential equations, we identify heteroclinic bifurcation in a family of vector fields on a cylinder, which explains the change in collective dynamics. Specifically, we demonstrate that heteroclinic bifurcation separates two topologically distinct families of limit cycles: contractible limit cycles before bifurcation and noncontractible ones after bifurcation. Both families are stable in the model at hand.
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
Computer Science, Interdisciplinary Applications
Mingxue Yang, Yirui Chen, Wenchen Han, Junzhong Yang
Summary: In this study, the multi-stability of multi-clustered chimera states in a ring of nonlocally coupled Brusselators is investigated. It is found that the phenomenon is insensitive to the coupling radius. The mechanisms behind the multi-stability of different types of multi-clustered chimera states are explored.
INTERNATIONAL JOURNAL OF MODERN PHYSICS C
(2023)
Article
Physics, Multidisciplinary
K. Premalatha, V. K. Chandrasekar, L. Senthilkumar, M. Lakshmanan
Summary: We investigate the impact of shear on the emergence of symmetry-breaking dynamical states in a globally coupled Stuart-Landau oscillator system with attractive and repulsive interactions. Without shear, the system displays synchronization, nontrivial oscillation death states, and oscillation death states. However, the introduction of shear leads to diverse dynamical patterns, such as amplitude clusters, solitary states, complete synchronization, and nontrivial oscillation death states.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Physics, Multidisciplinary
M. Bataille-Gonzalez, M. G. Clerc, E. Knobloch, O. E. Omel'chenko
Summary: Systems of coupled nonlinear oscillators often exhibit states of partial synchrony, referred to as chimera states, in which some oscillators oscillate coherently while the rest remain incoherent. This study investigates stationary and moving chimera states in planar phase oscillator arrays using numerical simulations and the corresponding continuum limit. The results reveal the existence and properties of traveling spiral wave chimeras and the transition from stationary to moving chimeras, accompanied by the appearance of complex filamentary structures within the incoherent spiral wave core.
NEW JOURNAL OF PHYSICS
(2023)
Article
Chemistry, Multidisciplinary
Zhengyuan Zhang, Liming Dai
Summary: This research explores the impact of synaptic pruning on a ring-shaped neural network with non-locally coupled FitzHugh-Nagumo (FHN) oscillators. Neurons in the pruned region synchronize and repel the coherent domain of chimera states. The width of the pruned region determines the precision and efficiency of controlling the position of coherent domains.
APPLIED SCIENCES-BASEL
(2022)
Article
Mathematics, Applied
Nikita V. Barabash, Vladimir N. Belykh, Grigory V. Osipov, Igor V. Belykh
Summary: This study analyzes the stability of partial synchronization in the second-order finite-dimensional Kuramoto model of heterogeneous oscillators with inertia using an auxiliary system method. Results show explicit bounds relating maximum natural frequency mismatch, inertia, and network size to support stable partial synchronization, as well as predicting threshold-like stability loss caused by increasing inertia. The auxiliary system method is potentially applicable to cluster synchronization with multiple coherent clusters and more complex network topology.
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
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
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
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
Physics, Multidisciplinary
Manashita Borah, Binoy Krishna Roy, Tomasz Kapitaniak, Karthikeyan Rajagopal, Christos Volos
Summary: This paper revisits the Bombay Plague epidemic of India and presents six fractional-order models of the epidemic based on observational data. Suitable controllers based on fuzzy logic concept are designed to stabilise chaos and forecast the course of the Covid-19 outbreak, with crucial parameters including memory and heredity indices.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2022)
Article
Engineering, Mechanical
Sandra Zarychta, Tomasz Sagan, Marek Balcerzak, Artur Dabrowski, Andrzej Stefanski, Tomasz Kapitaniak
Summary: This paper presents a novel numerical method based on Fourier series for optimizing open-loop control. The method is flexible and can be applied to a wide range of systems, including discontinuous or black box systems with unknown equations. The paper provides the mathematical background, algorithm details, and a practical example to demonstrate the effectiveness of the proposed method. It is expected to facilitate research in the control of non-smooth, discontinuous, or black box systems.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2022)
Article
Mechanics
Zhanqing Wang, Yongge Li, Yong Xu, Tomasz Kapitaniak, Juergen Kurths
Summary: This paper investigates the collective dynamical behaviors of a network of identical Hindmarsh-Rose neurons under small-world schemes and with the addition of alpha-stable Levy noise. The firing patterns of each neuron are used to distinguish the network into different states. The study shows the presence of coherence resonance in time and chimera states in space, known as coherence-resonance chimeras (CRC).
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2022)
Article
Engineering, Mechanical
Dawid Dudkowski, Krzysztof Czolczynski, Tomasz Kapitaniak
Summary: The dynamics of a 3 DOF model of two self-excited pendula suspended on an oscillating beam were studied to analyze the multistability of synchronous configurations. The study revealed regions of different behaviors and the influence of model parameters on their occurrence. The system exhibited classical phase-locked synchronization of pendula with phase shift depending on the oscillation angle of the beam.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Mathematics, Applied
S. Leo Kingston, Tomasz Kapitaniak, Syamal K. K. Dana
Summary: This article presents the distinction between hyperchaos and chaos in dynamical systems, with the former having at least two positive Lyapunov exponents. The authors demonstrate a general scenario where the attractor of continuous dynamical systems undergoes a sudden large expansion at a critical parameter, resulting in intermittent large-amplitude spiking or bursting events in the temporal dynamics. Experimental validation is provided through three paradigmatic models.
Article
Physics, Multidisciplinary
Tayebeh Moalemi, Fatemeh Parastesh, Tomasz Kapitaniak
Summary: This paper investigates networks with bounded synchronization stability regions and finds that blinking connections can lead to synchronized states in specific asynchronous networks. By setting a normalized coupling parameter and identifying the proper substitute connections, periodic switching of the identified connections can achieve network synchronization.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2022)
Article
Engineering, Mechanical
Zi-Fei Lin, Yan-Ming Liang, Jia-Li Zhao, Jiao-Rui Li, Tomasz Kapitaniak
Summary: In this study, the prediction of dynamic systems driven by strong noise intensities was investigated using deep learning algorithms. The proposed improved algorithm proved to be feasible and effective for predicting strongly noise-driven dynamic systems. Additionally, the influence of neural network construction on the performance of machine learning techniques was discussed.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Patrycja Jaros, Roman Levchenko, Tomasz Kapitaniak, Juergen Kurths, Yuri Maistrenko
Summary: Based on the symmetric circular model, this study shows that the stability of power grids can be destroyed by elementary violations of the network architecture, causing cascading failures and blackouts. The findings highlight that a symmetric topology is crucial for the stability of power grids.
Article
Mathematics, Applied
Dawid Dudkowski, Patrycja Jaros, Tomasz Kapitaniak
Summary: We study the extreme transient dynamics of four self-excited pendula coupled via the movable beam. The research investigates the problem of transient dynamics preceding the stabilization of the network on a final synchronous attractor, showing that the width of transient windows can become extremely long. The relation between the behavior of the system within the transient regime and its initial conditions is examined and described.
Article
Mathematics, Interdisciplinary Applications
Abhirup Banerjee, Arindam Mishra, Syamal K. Dana, Chittaranjan Hens, Tomasz Kapitaniak, Juergen Kurths, Norbert Marwan
Summary: This study proposes a reservoir computation-based framework that can predict the preceding structure or pattern in the time evolution of the active variable leading to extreme events using information from the passive variable. The magnitude of extreme events and the appearance of a coherent pattern before the arrival of the extreme event in a time series affect the prediction skill.
FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS
(2022)
Article
Mathematics, Applied
S. Leo Kingston, Marek Balcerzak, Syamal K. Dana, Tomasz Kapitaniak
Summary: A discontinuous transition to hyperchaos occurs in the Zeeman laser model for quasiperiodic breakdown to chaos, quasiperiodic intermittency, and Pomeau-Manneville intermittency. Hyperchaos emerges with an expansion of the system's attractor at a critical parameter and coincides with occasional and recurrent large-intensity pulses. The transition via Pomeau-Manneville intermittency shows hysteresis, while the other two processes do not exhibit hysteresis. The phenomenon is robust to weak noise, but the critical parameter shifts with noise strength.
Article
Mathematics, Applied
Dawid Dudkowski, Patrycja Jaros, Tomasz Kapitaniak
Summary: In this paper, we study the complex dynamics of a system composed of rotating pendula arranged in a simple mechanical structure. Through global and local coupling mechanisms, the behaviors of the system vary depending on the distribution of the rotating pendula. We use classical bifurcation analysis and a sample-based approach to determine the regions of existence and co-existence of different solutions. Various states, such as synchronization patterns, coherent dynamics, and irregular motion, are presented and discussed. Our study reveals the emergence of new co-existing patterns when considering the local coupling structure, leading to complex dynamics of the system.
Article
Nanoscience & Nanotechnology
Zi-Fei Lin, Jia-Li Zhao, Yan-Ming Liang, Tomasz Kapitaniak
Summary: We propose a new method, the RC-FODS algorithm, for solving fractional order nonlinear dynamical systems using reservoir computing. The method demonstrates advantages in terms of computation time and accuracy compared to traditional methods. By comparing it with recurrent neural network and echo state network algorithms, we find that the RC-FODS algorithm achieves higher accuracy and shorter computation time. The method's accuracy is validated using the largest Lyapunov exponent, and we analyze the pros and cons of different deep learning models. Our study concludes that the RC-FODS algorithm is a promising method for solving fractional order nonlinear dynamical systems with high accuracy and low error rate.
Article
Engineering, Multidisciplinary
Sebastian Garus, Bartlomiej Blachowski, Wojciech Sochacki, Anna Jaskot, Pawel Kwiaton, Mariusz Ostrowski, Michal Sofer, Tomasz Kapitaniak
Summary: This review paper discusses prospective research directions in the field of mechanical vibrations, including energy harvester devices, structure design using vibrations, vibration in multi-body systems and modal analysis, and the properties of granulated materials. These studies are of great importance for environmental protection and technological advancement.
BULLETIN OF THE POLISH ACADEMY OF SCIENCES-TECHNICAL SCIENCES
(2022)
