For a network of generic oscillators with nonlocal topology and symmetry-breaking coupling we establish novel partially coherent inhomogeneous spatial patterns, which combine the features of chimera states (coexisting incongruous coherent and incoherent domains) and oscillation death (oscillation suppression), which we call chimera death. We show that due to the interplay of nonlocality and breaking of rotational symmetry by the coupling two distinct scenarios from oscillatory behavior to a stationary state regime are possible: a transition from an amplitude chimera to chimera death via in-phase synchronized oscillations, and a direct abrupt transition for larger coupling strength. Spontaneous symmetry breaking in a complex dynamical system is a fundamental and universal phenomenon which occurs in diverse fields such as physics, chemistry, and biology [1]. It implies that processes occurring in nature favor a less symmetric configuration, although the underlying principles can be symmetric. This intriguing concept has recently gained renewed interest generated by the enormous burst of works on chimera states and on oscillation death, which have emerged independently. In this Letter we draw a relation between these two.Chimera states correspond to the situation when an ensemble of identical elements self-organizes into two coexisting and spatially separated domains with dramatically different behavior, i.e., spatially coherent and incoherent oscillations [2,3]. They have been the subject of intensive theoretical investigations, e.g. [4][5][6][7][8][9][10][11][12][13][14][15]. Experimental evidence of chimeras has only recently been provided for optical [16], chemical [17], mechanical [18] and electronic [19] systems. These peculiar hybrid states may also account for the observation of partial synchrony in neural activity [20], like unihemispheric sleep, i.e., the ability of some birds or dolphins to sleep with one half of their brain while the other half remains aware [21,22]. Chimera states have been initially found for phase oscillators [2], and they typically occur in networks with nonlocal coupling. Recently, for globally coupled oscillators it has been shown that such spatio-temporal patterns can be also connected to the amplitude dynamics (amplitude-mediated chimeras) [23,24]. However, the global coupling topology does not provide a clear notion of space, which is crucial for chimera states. A further open question is whether chimeras can be extended to more general symmetry breaking states.Another fascinating effect which requires the break-up of the system's symmetry as a crucial ingredient is oscillation death which refers to stable inhomogeneous steady states (IHSS) which are created through the coupling of self-sustained oscillators. This regime occurs when a ho- * corresponding author: schoell@physik.tu-berlin.de mogeneous steady state splits into at least two distinct branches -upper and lower -which represent a newly created IHSS [25][26][27][28]. For a network of coupled elements oscillation death ...

We demonstrate that chimera behavior can be observed in nonlocally coupled networks of excitable systems in the presence of noise. This phenomenon is distinct from classical chimeras, which occur in deterministic oscillatory systems, and it combines temporal features of coherence resonance, i.e., the constructive role of noise, and spatial properties of chimera states, i.e., coexistence of spatially coherent and incoherent domains in a network of identical elements. Coherence-resonance chimeras are associated with alternating switching of the location of coherent and incoherent domains, which might be relevant in neuronal networks. Chimera states are intriguing spatio-temporal patterns made up of spatially separated domains of synchronized (spatially coherent) and desynchronized (spatially incoherent) behavior, arising in networks of identical units. Originally discovered in a network of phase oscillators with a simple symmetric non-local coupling scheme [1,2], this sparked a tremendous activity of theoretical investigations . The first experimental evidence on chimera states was presented only one decade after their theoretical discovery [28][29][30][31][32][33][34][35][36][37][38]. In realworld systems chimera states might play a role, e.g., in power grids [39], in social systems [40], in the unihemispheric sleep of birds and dolphins [41], or in epileptic seizures [42]. In the context of the latter two applications it is especially relevant to explore chimera states in neuronal networks under conditions of excitability. However, while chimera states have previously been reported for neuronal networks in the oscillatory regime, e.g., in the FitzHugh-Nagumo system [17], they have not been detected in the excitable regime even for specially prepared initial conditions [17]. Therefore, the existence of chimera states for excitable elements remains unresolved.One of the challenging issues concerning chimera states is their behavior in the presence of random fluctuations, which are unavoidable in real-world systems. The robustness of chimeras with respect to external noise has been studied only very recently [43]. An even more intriguing question is whether the constructive role of noise in nonlinear systems, manifested for example in the counterintuitive increase of temporal coherence due to noise in coherence resonance [44][45][46][47], can be combined with the chimera behavior in spatially extended systems and networks. Coherence resonance, originally discovered for excitable systems like the FitzHugh-Nagumo model, implies that noise-induced oscillations become more regular for an optimum intermediate value of noise intensity. A question naturally arising in this context is whether noise can * corresponding author: anna.zakharova@tu-berlin.de also have a beneficial effect on chimera states. No evidence for the constructive role of noise for chimeras has been previously provided. Therefore, an important issue we aim to address here is to establish a connection between two intriguing counter-intuitive phenomena wh...

We investigate the influence of additive Gaussian white noise on two different bistable self-sustained oscillators: Duffing-Van der Pol oscillator with hard excitation and a model of a synthetic genetic oscillator. In the deterministic case, both oscillators are characterized with a coexistence of a stable limit cycle and a stable equilibrium state. We find that under the influence of noise, their dynamics can be well characterized through the concept of stochastic bifurcation, consisting in a qualitative change of the stationary amplitude distribution. For the Duffing-Van der Pol oscillator analytical results, obtained for a quasiharmonic approach, are compared with the result of direct computer simulations. In particular, we show that the dynamics is different for isochronous and anisochronous systems. Moreover, we find that the increase of noise intensity in the isochronous regime leads to a narrowing of the spectral line. This effect is similar to coherence resonance. However, in the case of anisochronous systems, this effect breaks down and a new phenomenon, anisochronous-based stochastic bifurcation occurs.

Chimera states are complex spatiotemporal patterns in networks of identical oscillators, characterized by the coexistence of synchronized and desynchronized dynamics. Here we propose to extend the phenomenon of chimera states to the quantum regime, and uncover intriguing quantum signatures of these states. We calculate the quantum fluctuations about semiclassical trajectories and demonstrate that chimera states in the quantum regime can be characterized by bosonic squeezing, weighted quantum correlations, and measures of mutual information. Our findings reveal the relation of chimera states to quantum information theory, and give promising directions for experimental realization of chimera states in quantum systems.PACS numbers: 05.45. Xt,05.30.Rt, 42.50.Lc, 42.65.Sf In classical systems of coupled nonlinear oscillators, the phenomenon of chimera states, which describes the spontaneous emergence of coexisting synchronized and desynchronized dynamics in networks of identical elements, has recently aroused much interest [1]. These intriguing spatio-temporal patterns were originally discovered in models of coupled phase oscillators. In this case, they exist due to nonlocal coupling between identical elements of the ensemble [2, 3]. There has been extensive work on the theoretical investigation of chimera states [4][5][6][7][8][9][10][11][12][13][14][15][16] While synchronization of classical oscillators has been well studied since the early observations of Huygens in the 17th century [26], synchronization in quantum mechanics has only very recently become a focus of interest. For example, quantum signatures of synchronization in a network of globally coupled Van der Pol oscillators have been investigated [27,28]. Related works focus on the dynamical phase transitions of a network of nanomechanical oscillators with arbitrary topologies characterized by a coordination number [29], and the semiclassical quantization of the Kuramoto model by using path integral methods [30].Contrary to classical mechanics, in quantum mechanics the notion of phase-space trajectory is not well defined. As a consequence, one has to define new measures of synchronization for continuous variable systems like optomechanical arrays [29]. These measures are based on quadratures of the coupled systems and allow one to extend the notion of phase synchronization to the quantum regime [31] [35,36], and mutual information [37]. Despite the intensive theoretical investigation of quantum signatures of synchronized states, to date, studies of the quantum manifestations of chimera states are still lacking.In this Letter we study the emergence of chimera states in a network of coupled quantum Van der Pol oscillators. Unlike in previous work [38], we address here the fundamental issue of the dynamical properties of chimera states in a continuous variable system. Considering the chaotic nature of chimera states [11], we study the shorttime evolution of the quantum fluctuations at the Gaussian level. This approach allows us to use powerful tools of quan...

Complex spatiotemporal patterns, called chimera states, consist of coexisting coherent and incoherent domains and can be observed in networks of coupled oscillators. The interplay of synchrony and asynchrony in complex brain networks is an important aspect in studies of both brain function and disease. We analyse the collective dynamics of FitzHugh-Nagumo neurons in complex networks motivated by its potential application to epileptology and epilepsy surgery. We compare two topologies: an empirical structural neural connectivity derived from diffusion-weighted magnetic resonance imaging and a mathematically constructed network with modular fractal connectivity. We analyse the properties of chimeras and partially synchronized states, and obtain regions of their stability in the parameter planes. Furthermore, we qualitatively simulate the dynamics of epileptic seizures and study the influence of the removal of nodes on the network synchronizability, which can be useful for applications to epileptic surgery.