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
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
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, Interdisciplinary Applications
Ryong-Son Kim, Gi-Hun Tae, Chol-Ung Choe
Summary: A stripe-core mixed spiral chimera state is reported in a system of nonlocally coupled phase oscillators on a spherical surface. The stability and existence of this state are rigorously analyzed based on the Ott-Antonsen reduction theory, showing that it emerges as a unique attractor and loses stability via the Hopf bifurcation. The theoretical results are verified using direct numerical simulations of the model system.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(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
Chemistry, Physical
Vladimir K. Vanag, Ivan S. Proskurkin
Summary: This is a theoretical and experimental study on a network of four excitable cells with the Belousov-Zhabotinsky (BZ) reaction. The cells are coupled by pulses with time delays and the coupling strengths are constant except for the coupling strength between cells #1 and #2 (C-12). The value of C-12 is controlled by pulses from two other cells, and the network exhibits three dynamic modes depending on the values of the time delays. The ability to tune C-12 through Hebb and anti-Hebb modes introduces memory and enables learning in the chemical network. The theoretical network is implemented experimentally using microcells with the BZ reaction and optical links for pulse coupling.
PHYSICAL CHEMISTRY CHEMICAL PHYSICS
(2023)
Article
Mathematics, Applied
Bing-Wei Li, Yuan He, Ling-Dong Li, Lei Yang, Xingang Wang
Summary: Spiral wave chimeras (SWCs) are a new type of dynamical pattern that can be observed even in locally coupled systems, according to a study using an experimentally feasible model. SWCs may become unstable in scenarios of core breakup and core expansion, with the latter leading to the emergence of shadowed spirals where regular spiral waves are embedded in a completely disordered background.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Physics, Fluids & Plasmas
Bojun Li, Nariya Uchida
Summary: The study shows that the multichimera state disappears when the phase delay parameter alpha exceeds a critical value, but reappears when further increased. A transition from multichimera to multitwisted states is observed, involving five collective phases.
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
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
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
Chol-Ung Choe, Ryong-Son Kim, Hun Jo
Summary: Spiral wave chimeras are a remarkable spatiotemporal pattern in a two-dimensional array of oscillators, in which coherent spiral arms coexist with incoherent cores. This phenomenon has also been observed in globally coupled phase oscillators with heterogeneous phase lags.
PHYSICA D-NONLINEAR PHENOMENA
(2021)
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.
Review
Mathematics, Applied
Ulrike Feudel, Alexander N. Pisarchik, Kenneth Showalter
Article
Mathematics, Applied
Desmond Yengi, Mark R. Tinsley, Kenneth Showalter
Article
Physics, Multidisciplinary
Sonja Totz, Jakob Loeber, Jan Frederik Totz, Harald Engel
NEW JOURNAL OF PHYSICS
(2018)
Article
Multidisciplinary Sciences
Hannah Jeckel, Eric Jelli, Raimo Hartmann, Praveen K. Singh, Rachel Mok, Jan Frederik Totz, Lucia Vidakovic, Bruno Eckhardt, Joern Dunkel, Knut Drescher
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2019)
Article
Mathematics, Applied
Enrico Fengler, Jan Frederik Totz, Pablo Kaluza, Harald Engel
Article
Multidisciplinary Sciences
Jan Frederik Totz, Mark R. Tinsley, Harald Engel, Kenneth Showalter
SCIENTIFIC REPORTS
(2020)
Article
Mathematics, Applied
Syed Jazli Syed Jamaluddin, Kritsana Khaothong, Mark R. Tinsley, Kenneth Showalter
Article
Multidisciplinary Sciences
Dumitru Calugaru, Jan Frederik Totz, Erik A. Martens, Harald Engel
Article
Developmental Biology
Marlis Denk-Lobnig, Jan F. Totz, Natalie C. Heer, Jorn Dunkel, Adam C. Martin
Summary: The study shows that transcription factors Twist and Snail regulate a multicellular pattern of F-actin density, influencing cell shape changes and tissue bending. The width of the Myosin-2 gradient depends on a gradient in RhoA activation, refined through the balance between RhoGEF2 and RhoGAP C-GAP.
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
Boshir Ahmed, David Mersing, Mark R. Tinsley, Kenneth Showalter
Summary: This article investigates the unique spatiotemporal behavior of propagating precipitation waves resulting from the coupling of reaction, diffusion, and precipitation in a system with sodium hydroxide and aluminum hydroxide electrolytes. Complex spatiotemporal waves, including counter-rotating spiral waves, target patterns, and wave annihilation on collision, occur within the propagating precipitation band in a redissolution Liesegang system. Experiments in thin gel slices reveal diagonal precipitation waves within the primary precipitation band, which exhibit a wave merging phenomenon. Computational modeling aids in understanding the intricate dynamical behavior.
Article
Multidisciplinary Sciences
Jinghui Liu, Jan F. Totz, Pearson W. Miller, Alasdair D. Hastewell, Yu-Chen Chao, Jorn Dunkel, Nikta Fakhri
Summary: The study reveals that the spiral wave cores in starfish egg cells undergo spontaneous braiding dynamics, which are correlated with cellular activity and consistent with predictions from a generic field theory. The analysis further uncovers the generation and annihilation of virtual quasi-particle excitations during defect scattering events, suggesting phenomenological parallels between quantum and living matter.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2021)
Article
Chemistry, Physical
Porramain Porjai, Malee Sutthiopad, Kritsana Khaothong, Metinee Phantu, Nakorn Kumchaiseemak, Jiraporn Luengviriya, Kenneth Showalter, Chaiya Luengviriya
PHYSICAL CHEMISTRY CHEMICAL PHYSICS
(2019)