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We explore a recently proposed locally resonant granular system bearing harmonic internal resonators in a chain of beads interacting via Hertzian elastic contacts. In this system, we propose the existence of two types of configurations: (a)…

Pattern Formation and Solitons · Physics 2015-06-10 Lifeng Liu , Guillaume James , Panayotis Kevrekidis , Anna Vainchtein

Chimera states in spatiotemporal dynamical systems have been investigated in physical, chemical, and biological systems, and have been shown to be robust against random perturbations. How do chimera states achieve their robustness? We…

Adaptation and Self-Organizing Systems · Physics 2019-01-30 Nan Yao , Zi-Gang Huang , Hai-Peng Ren , Celso Grebogi , Ying-Cheng Lai

We consider ensembles of sine-coupled phase oscillators consisting of subpopulations of identical units, with a general heterogeneous coupling between subpopulations. Using the Watanabe-Strogatz ansatz we reduce the dynamics of the ensemble…

Adaptation and Self-Organizing Systems · Physics 2010-01-11 Arkady Pikovsky , Michael Rosenblum

Homogeneous populations of oscillators have recently been shown to exhibit stable coexistence of coherent and incoherent regions. Generalizing the concept of chimera states to the context of order-disorder transition in systems at thermal…

Statistical Mechanics · Physics 2015-05-20 Rajeev Singh , Subinay Dasgupta , Sitabhra Sinha

The paper addresses compact oscillatory states (compact breathers) in translationally-invariant lattices with flat dispersion bands. The compact breathers appear in such systems even in the linear approximation. If the interactions are…

Pattern Formation and Solitons · Physics 2020-08-31 Nathan Perchikov , O. V. Gendelman

We propose a robust universal approach to identify multiple dynamical states, including stationary and travelling chimera states based on an adaptive coherence measure. Our approach allows automatic disambiguation of synchronized clusters,…

Adaptation and Self-Organizing Systems · Physics 2021-11-24 Olesia Dogonasheva , Dmitry Kasatkin , Boris Gutkin , Denis Zakharov

The formation and evolution of stationary and moving breather solutions in (2+1)-dimensional O(3) nonlinear $\sigma$-model are investigated. The analytical form of oscillating solutions for (2+1)-dimensional sine-Gordon equation, which…

Pattern Formation and Solitons · Physics 2016-05-04 F. Sh. Shokirov

A group-theoretical approach for studying localized periodic and quasiperiodic vibrations in 2D and 3D lattice dynamical models is developed. This approach is demonstrated for the scalar models on the plane square lattice. The…

Pattern Formation and Solitons · Physics 2011-06-10 George Chechin , Galina Bezuglova , Petr Goncharov

We consider a previously experimentally realized discrete model that describes a mechanical metamaterial consisting of a chain of pairs of rigid units connected by flexible hinges. Upon analyzing the linear band structure of the model, we…

Pattern Formation and Solitons · Physics 2023-02-15 H. Duran , J. Cuevas-Maraver , P. G. Kevrekidis , A. Vainchtein

A breathing mode in a Hamiltonian system is a function on the phase space whose evolution is exactly periodic for all solutions of the equations of motion. Such breathing modes are familiar from nonlinear dynamics in harmonic traps or…

Mathematical Physics · Physics 2020-04-24 Oleg Evnin

We analyze nonlocally coupled networks of identical chaotic oscillators with either time-discrete or time-continuous dynamics (Henon map, Lozi map, Lorenz system). We hypothesize that chimera states, in which spatial domains of coherent…

Adaptation and Self-Organizing Systems · Physics 2016-01-20 Nadezhda Semenova , Anna Zakharova , Eckehard Schöll , Vadim Anishchenko

Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…

Chaotic Dynamics · Physics 2024-07-02 Marco Thiel

We study a theoretical model of closed quasi-hermitian chain of spins which exhibits quantum analogues of chimera states, i.e. long life classical states for which a part of an oscillator chain presents an ordered dynamics whereas another…

Quantum Physics · Physics 2016-01-08 David Viennot , Lucile Aubourg

We consider the nonlinear Schr\"odinger equation with non-local derivatives in a two-dimensional periodic domain. For certain orders of derivatives, we find a new type of breather solution dominating the field evolution at low nonlinearity…

Pattern Formation and Solitons · Physics 2022-09-20 Alexander Hrabski , Yulin Pan

We have identified the existence of globally clustered chimera states in delay coupled oscillator populations and find that these states can breathe periodically, aperiodically and become unstable depending upon the value of coupling delay.…

Adaptation and Self-Organizing Systems · Physics 2015-05-13 Jane H. Sheeba , V. K. Chandrasekar , M. Lakshmanan

We explore the dynamics of strongly localized periodic solutions (discrete solitons, or discrete breathers) in a finite one-dimensional chain of asymmetric vibro-impact oscillators. The model involves a parabolic on-site potential with…

Pattern Formation and Solitons · Physics 2017-01-12 I. Grinberg , O. V. Gendelman

Chimera states have been studied in 1D arrays, and a variety of different chimera states have been found using different models. Research has recently been extended to 2D arrays but only to phase models of them. Here, we extend it to a…

Chaotic Dynamics · Physics 2017-01-23 Changhai Tian , Xiyun Zhang , Zhenhua Wang , Zonghua Liu

We analyze the effect of adding a weak, localized, inhomogeneity to a two dimensional array of oscillators with nonlocal coupling. We propose and also justify a model for the phase dynamics in this system. Our model is a generalization of a…

Analysis of PDEs · Mathematics 2018-11-28 Gabriela Jaramillo , Shankar Venkataramani

Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate…

Statistical Mechanics · Physics 2018-08-15 Adam Rupe , James P. Crutchfield

The dynamics of a system composed of elastic hard particles confined by an isotropic harmonic potential are studied. In the low-density limit, the Boltzmann equation provides an excellent description, and the system does not reach…

Statistical Mechanics · Physics 2024-09-13 P. Maynar , M. I. García de Soria , D. Guéry-Odelin , E. Trizac