Magnetron Modes and the Chimera State

2018 ◽  
pp. 35-65 ◽  
Author(s):  
Victor J. Law ◽  
Denis P. Dowling
Keyword(s):  
Chimera State

A continuous chimera state in an optical comb

2013 ◽  
Author(s):  
E. A. Viktorov ◽  
T. Habruseva ◽  
S. P. Hegarty ◽  
G. Huyet ◽  
B. Kelleher
Keyword(s):  
Chimera State

From collective oscillation to chimera state in a nonlocally coupled excitable system

2018 ◽  
Vol 91 (3) ◽  
pp. 1723-1731 ◽  
Author(s):  
Qionglin Dai ◽  
Mengya Zhang ◽  
Hongyan Cheng ◽  
Haihong Li ◽  
Fagen Xie ◽  
...  
Keyword(s):  
Collective Oscillation ◽  
Chimera State ◽  
Excitable System

scholarly journals Emergence of Chimera in Multiplex Network

2016 ◽  
Vol 26 (07) ◽  
pp. 1650120 ◽  
Author(s):  
Saptarshi Ghosh ◽  
Sarika Jalan
Keyword(s):  
Real World ◽  
Coupling Strength ◽  
Network Size ◽  
Initial Condition ◽  
Control Parameters ◽  
Critical Coupling ◽  
Individual Layer ◽  
Chimera State ◽  
Multiplex Network ◽  
Multilayer Architecture

Chimera is a relatively new emerging phenomenon where coexistence of synchronous and asynchronous states is observed in symmetrically coupled dynamical units. We report the observation of the chimera state in multiplex networks where individual layer is represented by 1-d lattice with nonlocal interactions. While, multiplexing does not change the type of the chimera state and retains the multi-chimera state displayed by the isolated networks, it changes the regions of the incoherence. We investigate the emergence of coherent–incoherent bifurcation upon varying the control parameters, namely, the coupling strength and the network size. Additionally, we investigate the effect of initial condition on the dynamics of the chimera state. Using a measure based on the differences between the neighboring nodes which distinguishes smooth and nonsmooth spatial profiles, we find the critical coupling strength for the transition to the chimera state. Observing chimera in a multiplex network with one-to-one inter layer coupling is important to gain insight to many real world complex systems which inherently posses multilayer architecture.

scholarly journals Cascades of Multiheaded Chimera States for Coupled Phase Oscillators

2014 ◽  
Vol 24 (08) ◽  
pp. 1440014 ◽  
Author(s):  
Yuri L. Maistrenko ◽  
Anna Vasylenko ◽  
Oleksandr Sudakov ◽  
Roman Levchenko ◽  
Volodymyr L. Maistrenko
Keyword(s):  
Periodic Orbit ◽  
Coupled Oscillators ◽  
Phase Oscillators ◽  
Invariant Circle ◽  
Saddle Node Bifurcation ◽  
Chimera States ◽  
Chimera State ◽  
Self Organized ◽  
Saddle Node ◽  
Different Types

Chimera state is a recently discovered dynamical phenomenon in arrays of nonlocally coupled oscillators, that displays a self-organized spatial pattern of coexisting coherence and incoherence. We discuss the appearance of the chimera states in networks of phase oscillators with attractive and with repulsive interactions, i.e. when the coupling respectively favors synchronization or works against it. By systematically analyzing the dependence of the spatiotemporal dynamics on the level of coupling attractivity/repulsivity and the range of coupling, we uncover that different types of chimera states exist in wide domains of the parameter space as cascades of the states with increasing number of intervals of irregularity, so-called chimera's heads. We report three scenarios for the chimera birth: (1) via saddle-node bifurcation on a resonant invariant circle, also known as SNIC or SNIPER, (2) via blue-sky catastrophe, when two periodic orbits, stable and saddle, approach each other creating a saddle-node periodic orbit, and (3) via homoclinic transition with complex multistable dynamics including an "eight-like" limit cycle resulting eventually in a chimera state.

scholarly journals Asymmetric couplings enhance the transition from chimera state to synchronization

2017 ◽  
Vol 96 (5) ◽  
Author(s):  
Changhai Tian ◽  
Hongjie Bi ◽  
Xiyun Zhang ◽  
Shuguang Guan ◽  
Zonghua Liu
Keyword(s):  
Chimera State

scholarly journals Connecting the Kuramoto Model and the Chimera State

2017 ◽  
Vol 119 (26) ◽  
Author(s):  
Tejas Kotwal ◽  
Xin Jiang ◽  
Daniel M. Abrams
Keyword(s):  
Kuramoto Model ◽  
Chimera State ◽  
The Kuramoto Model

scholarly journals Pattern selection in multi-layer network with adaptive coupling

2021 ◽  
Author(s):  
Peihua Feng ◽  
Ying Wu
Keyword(s):  
Adaptive Dynamics ◽  
Transient State ◽  
Neuron Network ◽  
Neuron System ◽  
Feed Forward ◽  
Chimera States ◽  
Chimera State ◽  
Narrow Region ◽  
Multiple Network ◽  
Full Synchronization

Abstract Feed-forward effect modulates collective behavior of a multiple neuron network and facilitates strongly synchronization of their firing in deep layers. However, full synchronization of neuron system corresponds to functional disorder. In this work, we investigate coexistence of synchronized and incoherent neurons in deeper layer (called chimera state) in order to avoid the contradiction between facilitation of full synchronization and complete functional failure of neuron system. We focus on a multiple network containing two layers and confirm that chimera state in layer 1 could also induce that in layer 2 when the feed-forward effect is strong enough. Cluster also is discovered as a transient state which separates full synchronization and chimera state and occupy a narrow region. Both feed-forward and back-forward effect together emerge of chimera states in both layer 1 and 2 under same parameter in large range of parameters selection. Further, we introduce adaptive dynamics into inter-layer rather than intra-layer couplings. Under this circumstance chimera state still can be induced and coupling matrix will be self-organized under suitable phase parameter to guarantee chimera formation. Indeed, chimera states exist and transit to deeper layer in a regular multiple network with very strict parameter selection. The results helps understanding better the neuron firing propagating and encoding scheme in a multi-layer neuron network.

scholarly journals Chimera state in coupled map lattice of matrices

2021 ◽  
Vol 62 ◽  
pp. 57-63
Author(s):  
Kotryna Mačernytė ◽  
Rasa Šmidtaitė
Keyword(s):  
Initial Conditions ◽  
State Parameter ◽  
Coupled Map Lattice ◽  
Supplementary Variable ◽  
Chimera States ◽  
Chimera State ◽  
Nilpotent Matrix ◽  
Wide Range ◽  
The Matrix ◽  
Iterative Maps

In recent years, a lot of research has focused on understanding the behavior of when synchronous and asynchronous phases occur, that is, the existence of chimera states in various networks. Chimera states have wide-range applications in many disciplines including biology, chemistry, physics, or engineering. The object of research in this paper is a coupled map lattice of matrices when each node is described by an iterative map of matrices of order two. A regular topology network of iterative maps of matrices was formed by replacing the scalar iterative map with the iterative map of matrices in each node. The coupled map of matrices is special in a way where we can observe the effect of divergence. This effect can be observed when the matrix of initial conditions is a nilpotent matrix. Also, the evolution of the derived network is investigated. It is found that the network of the supplementary variable $\mu$ can evolve into three different modes: the quiet state, the state of divergence, and the formation of divergence chimeras. The space of parameters of node coupling including coupling strength $\varepsilon$ and coupling range $r$ is also analyzed in this study. Image entropy is applied in order to identify chimera state parameter zones.

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