Chimeras on a social-type network

Cascades of Multi-headed Chimera States for Coupled Phase Oscillators

Chimera state is a recently discovered dynamical phenomenon in arrays of nonlocally coupled oscillators, that displays a self-organized spatial pattern of co-existing 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 st…

Minimal Chimera States in Phase-Lag Coupled Mechanical Oscillators

We obtain experimental chimera states in the minimal network of three identical mechanical oscillators (metronomes), by introducing phase-lagged all-to-all coupling. For this, we have developed a real-time model-in-the-loop coupling mechanism that allows for flexible and online change of coupling topology, strength and phase-lag. The chimera states manifest themselves as a mismatch of average frequency between two synchronous and one desynchronized oscillator. We find this kind of striking chimeric behavior is robust in a wide parameter region. At other parameters, however, chimera state can l…

通过傅里叶分析和无监督学习对奇点态进行分类

Classification of Chimera States via Fourier Analysis and Unsupervised Learning

本文提出基于傅里叶分析和无监督学习的方法，用于识别参数空间中产生奇点态的区域并区分其类型，应用于Rayleigh振子网络。

Traveling chimera patterns in two-dimensional neuronal network

We study the emergence of the traveling chimera state in a two-dimensional network of Hindmarsh-Rose burst neurons with the mutual presence of local and non-local couplings. We show that in the unique presence of the non-local chemical coupling modeled by a nonlinear function, the traveling chimera phenomenon occurs with a displacement in both directions of the plane of the grid. The introduction of local electrical coupling shows that the mutual influence of the two types of coupling can, for certain values, generate traveling chimera, imperfect-traveling, traveling multi-clusters, and altern…

Dynamics of a 2D lattice of van der Pol oscillators with nonlinear repulsive coupling

We describe spatiotemporal patterns in a network of identical van der Pol oscillators coupled in a two-dimensional geometry. In this study, we show that the system under study demonstrates a plethora of different spatiotemporal structures including chimera states when the coupling parameters are varied. Spiral wave chimeras are formed in the network when the coupling strength is rather large and the coupling range is short enough. Another type of chimeras is a target wave chimera. It is shown that solitary states play a crucial role in forming an incoherence cluster of this chimera state. They…

Mixed-Mode Chimera states in Pendula Networks

We report the emergence of peculiar chimera states in networks of identical pendula with global phase-lagged coupling. The states reported include both rotating and quiescent modes, i.e. with non-zero and zero average frequencies. This kind mixed-mode chimeras may be interpreted as images of bump states known in neuroscience in the context of modelling the working memory. We illustrate this striking phenomenon for a network of N=100 coupled pendula, followed by a detailed description of the minimal non-trivial case of N=3. Parameter regions for five characteristic types of the system behavior …

耦合主动转子系统中的凸起态、嵌合态与图灵斑图

Bumps, chimera states, and Turing patterns in systems of coupled active rotators

该研究聚焦耦合主动转子系统中的凸起态等相干-非相干斑图，揭示其从完全相干图灵斑图经超临界分岔、准周期及混沌行为的演化路径，并用短程激活长程抑制范式解释斑图形成。

Chimera states in networks of locally and non-locally coupled SQUIDs

Planar and linear arrays of SQUIDs (superconducting quantum interference devices), operate as nonlinear magnetic metamaterials in microwaves. Such {\em SQUID metamaterials} are paradigmatic systems that serve as a test-bed for simulating several nonlinear dynamics phenomena. SQUIDs are highly nonlinear oscillators which are coupled together through magnetic dipole-dipole forces due to their mutual inductance; that coupling falls-off approximately as the inverse cube of their distance, i.~e., it is non-local. However, it can be approximated by a local (nearest-neighbor) coupling which in many c…

Effect of diluted connectivities on cluster synchronization of adaptively coupled oscillator networks

Synchronization in networks of oscillatory units is an emergent phenomenon present in various systems, such as biological, technological, and social systems. Many real-world systems have adaptive properties, meaning that their connectivities change with time, depending on the dynamical state of the system. Networks of adaptively coupled oscillators show various synchronization phenomena, such as hierarchical multifrequency clusters, traveling waves, or chimera states. While these self-organized patterns have been previously studied on all-to-all coupled networks, this work extends the investig…

Stability of rotatory solitary states in Kuramoto networks with inertia

Solitary states emerge in oscillator networks when one oscillator separates from the fully synchronized cluster and becomes incoherent with the rest of the network. Such chimera-type patterns with an incoherent state formed by a single oscillator were observed in various oscillator networks; however, there is still a lack of understanding of how such states can stably appear. Here, we study the stability of solitary states in Kuramoto networks of identical two-dimensional phase oscillators with inertia and a phase-lagged coupling. The presence of inertia can induce rotatory dynamics of the pha…