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
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
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
Engineering, Multidisciplinary
Jerzy Wojewoda, Karthikeyan Rajagopal, Viet-Thanh Pham, Fatemeh Parastesh, Tomasz Kapitaniak, Sajad Jafari
Summary: This paper investigates the chimera states in a network of impact oscillators with nonlocal coupling, finding that the coupling strength and range affect the emergence of chimera states. The study also shows that coupling can help maintain oscillatory motion with lower amplitude in the case of excitation failure.
JOURNAL OF ZHEJIANG UNIVERSITY-SCIENCE A
(2021)
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, 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
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
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, 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
Nanoscience & Nanotechnology
Yoji Kawamura
Summary: The study investigates the stability of a system of nonlocally coupled phase oscillators, analyzing the plane wave solutions and demonstrating their stability under specific wavenumbers and natural frequency heterogeneity. The mathematical model is applicable in any spatial dimension and the theoretical findings are corroborated through numerical simulations.
Article
Mathematics, Applied
Elena Rybalova, Galina Strelkova
Summary: In this study, we numerically investigate the impact of heterogeneity in parameters on the dynamics of nonlocally coupled discrete-time systems. We explore the robustness of solitary states, which occur during the transition from coherence to incoherence, to heterogeneity in local dynamics or coupling strength. The results show that solitary states are suppressed when network parameters are modulated by noise, but they can persist in the case of static randomly distributed system parameters.
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
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
Physics, Multidisciplinary
Yibin Zhang, Peiyu Wang, Mei Zhang, Junzhong Yang
Summary: In this study, heterogeneity is introduced into a ring of nonlocally coupled bicomponent FitzHugh-Nagumo oscillators by randomly partitioning oscillators into two groups with different epsilon values. It is found that a synchronous chimera state appears at weak mismatch between epsilon values, while an asynchronous chimera state emerges at strong mismatch, which is not sensitive to the partition of oscillators. The existence of an asynchronous chimera state at strong mismatch of epsilon contradicts the common view that strong heterogeneity in non-identical oscillators is harmful to the chimera state.
Article
Mathematics, Applied
Mark R. Tinsley, Darrell Collison, Kenneth Showalter
Article
Mathematics, Applied
Kenneth Showalter, Irving R. Epstein
Article
Mathematics, Applied
Razan Snari, Mark R. Tinsley, Dan Wilson, Sadegh Faramarzi, Theoden Ivan Netoff, Jeff Moehlis, Kenneth Showalter
Article
Chemistry, Physical
Annette F. Taylor, Mark R. Tinsley, Kenneth Showalter
PHYSICAL CHEMISTRY CHEMICAL PHYSICS
(2015)
Article
Mathematics, Applied
Simbarashe Nkomo, Mark R. Tinsley, Kenneth Showalter
Article
Physics, Multidisciplinary
Tianran Chen, Mark R. Tinsley, Edward Ott, Kenneth Showalter
Article
Physics, Multidisciplinary
Jan Frederik Totz, Julian Rode, Mark R. Tinsley, Kenneth Showalter, Harald Engel
Review
Mathematics, Applied
Ulrike Feudel, Alexander N. Pisarchik, Kenneth Showalter
Article
Mathematics, Applied
Desmond Yengi, Mark R. Tinsley, Kenneth Showalter
Article
Mathematics, Applied
Dan Wilson, Sadegh Faramarzi, Jeff Moehlis, Mark R. Tinsley, Kenneth Showalter
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
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
Chemistry, Physical
Porramain Porjai, Malee Sutthiopad, Kritsana Khaothong, Metinee Phantu, Nakorn Kumchaiseemak, Jiraporn Luengviriya, Kenneth Showalter, Chaiya Luengviriya
PHYSICAL CHEMISTRY CHEMICAL PHYSICS
(2019)
