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Related papers: From Turing patterns to chimera states in the 2D B…

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Chimera state is defined as a mixed type of collective state in which synchronized and desynchronized subpopulations of a network of coupled oscillators coexist and the appearance of such anomalous behavior has strong connection to diverse…

Adaptation and Self-Organizing Systems · Physics 2018-02-07 Srilena Kundu , Soumen Majhi , Bidesh K. Bera , Dibakar Ghosh , M. Lakshmanan

In this paper, we consider a coupled Brusselator model of chemical reactions, for which no symmetry for the coupling matrices is assumed. We show that the model can undergoes a Hopf bifurcation, and consequently periodic solutions can arise…

Dynamical Systems · Mathematics 2023-05-30 Shanshan Chen , Yihuan Sun

We study an oscillatory medium with a nonlinear global coupling that gives rise to a harmonic mean-field oscillation with constant amplitude and frequency. Two types of cluster states are found, each undergoing a symmetry-breaking…

Pattern Formation and Solitons · Physics 2015-06-11 Lennart Schmidt , Katharina Krischer

Biomolecular processes are typically modeled using chemical reaction networks coupled to infinitely large chemical reservoirs. A difference in chemical potential between these reservoirs can drive the system into a non-equilibrium steady…

Statistical Mechanics · Physics 2020-06-17 Jonas H. Fritz , Basile Nguyen , Udo Seifert

In this article, we study the Brusselator partial differential equation (PDE) in the limit in which the diffusivity of the activator is much smaller than that of the inhibitor. The PDE robustly exhibits a subcritical Turing bifurcation…

Dynamical Systems · Mathematics 2025-09-08 Robert Jencks , Arjen Doelman , Tasso J. Kaper , Theodore Vo

Nonlocally coupled oscillator systems can exhibit an exotic spatiotemporal structure called chimera, where the system splits into two groups of oscillators with sharp boundaries, one of which is phase-locked and the other is…

Pattern Formation and Solitons · Physics 2007-05-23 Yoji Kawamura

Applying the Lyapunov-Schmidt reduction approach introduced by Mielke and Schneider in their analysis of the fourth-order scalar Swift-Hohenberg equation, we carry out a rigorous small-amplitude stability analysis of Turing patterns for the…

Analysis of PDEs · Mathematics 2018-01-17 Alim Sukhtayev , Kevin Zumbrun , Soyeun Jung , Raghavendra Venkatraman

In this paper the Turing pattern formation mechanism of a two component reaction-diffusion system modeling the Schnakenberg chemical reaction coupled to linear cross-diffusion terms is studied. The linear cross-diffusion terms favors the…

Pattern Formation and Solitons · Physics 2017-05-08 G. Gambino , S. Lupo , M. Sammartino

We present an approach to generate chimera dynamics (localized frequency synchrony) in oscillator networks with two populations of (at least) two elements using a general method based on delayed interactions with linear and quadratic terms.…

Adaptation and Self-Organizing Systems · Physics 2017-10-25 Christian Bick , Michael Sebek , István Z. Kiss

Chimera states, representing a spontaneous break-up of a population of identical oscillators that are identically coupled, into sub-populations displaying synchronized and desynchronized behavior, have traditionally been found to exist in…

Chaotic Dynamics · Physics 2015-06-18 Gautam C Sethia , Abhijit Sen

We report and classify the rich variety of patterns forming spontaneously in the oxide layer during the oscillatory photoelectrodissolution of n-type doped silicon electrodes under limited illumination. Remarkably, these patterns are often…

Pattern Formation and Solitons · Physics 2014-06-16 Konrad Schoenleber , Carla Zensen , Andreas Heinrich , Katharina Krischer

The instability of mixing in the Kuramoto model of coupled phase oscillators is the key to understanding a range of spatiotemporal patterns, which feature prominently in collective dynamics of systems ranging from neuronal networks, to…

Chaotic Dynamics · Physics 2022-02-23 Georgi S. Medvedev , Matthew S. Mizuhara

We derive a necessary and sufficient condition for Turing instabilities to occur in two-component systems of reaction-diffusion equations with Neumann boundary conditions. We apply this condition to reaction-diffusion systems built from…

Mathematical Physics · Physics 2007-05-23 Rui Dilao

We report a novel mechanism for the formation of chimera states, a peculiar spatiotemporal pattern with coexisting synchronized and incoherent domains found in ensembles of identical oscillators. Considering Stuart-Landau oscillators we…

Chaotic Dynamics · Physics 2015-06-18 Lennart Schmidt , Konrad Schönleber , Katharina Krischer , Vladimir García-Morales

In coupled reaction-diffusion systems, modes with two different length scales can interact to produce a wide variety of spatiotemporal patterns. Three-wave interactions between these modes can explain the occurrence of spatially complex…

Pattern Formation and Solitons · Physics 2020-04-14 Jennifer K. Castelino , Daniel J. Ratliff , Alastair M. Rucklidge , Priya Subramanian , Chad M. Topaz

Formation of diverse patterns in spatially extended reaction-diffusion systems is an important aspect of study which is pertinent to many chemical and biological processes. Of special interest is the peculiar phenomenon of chimera state…

Adaptation and Self-Organizing Systems · Physics 2021-06-16 Srilena Kundu , Paulsamy Muruganandam , Dibakar Ghosh , M. Lakshmanan

This paper is concerned with analysis of coupled fractional reaction-diffusion equations. It provides analytical comparison for the fractional and regular reaction-diffusion systems. As an example, the reaction-diffusion model with cubic…

Adaptation and Self-Organizing Systems · Physics 2007-05-23 Vasyl Gafiychuk , Bohdan Datsko , Vitaliy Meleshko

Systems of nonlocally coupled oscillators can exhibit complex spatio-temporal patterns, called chimera states, which consist of coexisting domains of spatially coherent (synchronized) and incoherent dynamics. We report on a novel form of…

Adaptation and Self-Organizing Systems · Physics 2018-02-02 Iryna Omelchenko , Oleh E. Omel'chenko , Philipp Hövel , Eckehard Schöll

Chimera states, which consist of coexisting domains of coherent and incoherent parts, have been observed in a variety of systems. Most of previous works on chimera states have taken into account specific form of interaction between…

Adaptation and Self-Organizing Systems · Physics 2016-11-15 Hongyan Cheng , Qionglin Dai , Nianping Wu , Yuee Feng , Haihong Li , Junzhong Yang

Schemes for optical-state truncation of two cavity modes are analysed. The systems, referred to as the nonlinear quantum scissors devices, comprise two coupled nonlinear oscillators (Kerr nonlinear coupler) with one or two of them pumped by…

Quantum Physics · Physics 2009-08-03 Adam Miranowicz , Wieslaw Leonski