Coexistence of synchrony and incoherence in oscillatory media under nonlinear global coupling

Synchronization transitions in ensembles of noisy oscillators with bi-harmonic coupling

We describe synchronization transitions in an ensemble of globally coupled phase oscillators with a bi-harmonic coupling function, and two sources of disorder - diversity of intrinsic oscillatory frequencies and external independent noise. Based on the self-consistent formulation, we derive analytic solutions for different synchronous states. We report on various non-trivial transitions from incoherence to synchrony where possible scenarios include: simple supercritical transition (similar to classical Kuramoto model), subcritical transition with large area of bistability of incoherent and syn…

The changing notion of chimera states, a critical review

Chimera states, states of coexistence of synchronous and asynchronous motion, have been a subject of extensive research since they were first given a name in 2004. Increased interest has lead to their discovery in ever new settings, both theoretical and experimental. Less well-discussed is the fact that successive results have also broadened the notion of what actually constitutes a chimera state. In this article, we critically examine how the results for different model types and coupling schemes, as well as varying implicit interpretations of terms such as coexistence, synchrony and incohere…

连续化学振子系统中嵌合体的非平衡热力学表征

Nonequilibrium thermodynamic characterization of chimeras in a continuum chemical oscillator system

本研究针对连续化学振子系统的嵌合体态涌现问题，通过全局耦合复金兹堡-朗道方程表征其非平衡热力学演化，发现熵产生率拍频模式等特征，揭示了信息不确定性原理对嵌合体能量学的引导作用。

Occurrence and stability of chimera states in multivariable coupled flows

Study of collective phenomenon in populations of coupled oscillators are a subject of intense exploration in physical, biological, neuronal and social systems. Here we propose a scheme for the creation of chimera states, namely the coexistence of distinct dynamical behaviors in an ensemble of multivariable coupled oscillatory systems and a novel scheme to study their stability. We target bifurcation parameters that can be tuned such that out of the two coupling parameters one pushes the system to synchrony while the other one takes it to the desynchronized state. The competition between these …

Chimera patterns in three-dimensional locally coupled systems

The coexistence of coherent and incoherent domains, namely the appearance of chimera states, is being studied extensively in many contexts of science and technology since the past decade, though the previous studies are mostly built on the framework of one-dimensional and two-dimensional interaction topologies. Recently, the emergence of such fascinating phenomena has been studied in three-dimensional (3D) grid formation while considering only the nonlocal interaction. Here we study the emergence and existence of chimera patterns in a three dimensional network of coupled Stuart-Landau limit cy…

Emergence of chimera in multiplex network

Chimera is a relatively new emerging phenomenon where coexistence of synchronous and asynchronous state is observed in symmetrically coupled dynamical units. We report observation of the chimera state in multiplex networks where individual layer is represented by 1-d lattice with non-local 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 emergence of coherent-incoherent bifurcation upon varying the control parameters, namely, the coupl…

分形 basins 作为灵巧大脑的一种机制

Fractal Basins as a Mechanism for the Nimble Brain

本文在基于真实人脑DTI网络的动力系统模型中，提出向量模式状态（VPS）方法识别chimera状态并映射basin结构，发现共存吸引子具有交织的分形basin边界且立即可达，从而解释大脑快速切换活动模式的能力。

Chimera states in population dynamics: networks with fragmented and hierarchical connectivities

We study numerically the development of chimera states in networks of nonlocally coupled oscillators whose limit cycles emerge from a Hopf bifurcation. This dynamical system is inspired from population dynamics and consists of three interacting species in cyclic reactions. The complexity of the dynamics arises from the presence of a limit cycle and four fixed points. When the bifurcation parameter increases away from the Hopf bifurcation the trajectory approaches the heteroclinic invariant manifolds of the fixed points producing spikes, followed by long resting periods. We observe chimera stat…

Basin stability for chimera states

Chimera states, namely complex spatiotemporal patterns that consist of coexisting domains of spatially coherent and incoherent dynamics, are investigated in a network of coupled identical oscillators. These intriguing spatiotemporal patterns were first reported in nonlocally coupled phase oscillators, and it was shown that such mixed type behavior occurs only for specific initial conditions in nonlocally and globally coupled networks. The influence of initial conditions on chimera states has remained a fundamental problem since their discovery. In this report, we investigate the robustness of …

Transitions from chimeras to coherence: An analytical approach by means of the coherent stability function

Chimera states have been a vibrant subject of research in the recent past, but the analytical treatment of transitions from chimeras to coherent states remains a challenge. Here we analytically derive the necessary conditions for this transition by means of the coherent stability function approach, which is akin to the master stability function approach that is traditionally used to study the stability of synchronization in coupled oscillators. In chimera states, there is typically at least one group of oscillators that evolves in a drifting, random manner, while other groups of oscillators fo…

双群体网络中广义 Kuramoto-Sakaguchi 振荡子的嵌合体动力学

Chimera Dynamics of Generalized Kuramoto-Sakaguchi Oscillators in Two-population Networks

本文研究了二维复空间双群体网络中广义 Kuramoto-Sakaguchi 振荡子的嵌合体动力学，发现随群体内耦合强度减弱，系统依次呈现稳态、呼吸、周期交替及守恒量破缺导致的非周期嵌合体状态。

在共同频率调制驱动下非耦合振荡器中最小奇异态的出现：理论与实验

Emergence of minimal chimera in uncoupled oscillators under common frequency-modulated driving: Theory and experiment

研究三个非耦合振荡器在频率调制驱动下最小奇异态的出现，通过调整调制参数实现不同状态转变，用相位约化等方法分析机制，经实验验证，为驱动非线性系统集体动力学提供新视角。