Chimera states, a symmetry-breaking spatiotemporal pattern in nonlocally coupled identical dynamical units, prevail in a variety of systems. Here, we consider a population of nonlocally coupled bicomponent phase oscillators in which oscillators with natural frequency $ω_0$ (positive oscillators) and $-ω_0$ (negative oscillators) are randomly distributed along a ring. We show the existence of chimera states no matter how large $ω_0$ is and the states manifest themselves in the form that oscillators with positive/negative frequency support their own chimera states. There are two types of chimera states, synchronous chimera states at small $ω_0$ in which coherent positive and negative oscillators share a same mean phase velocity and asynchronous chimera states at large $ω_0$ in which coherent positive and negative oscillators have different mean phase velocities. Increasing $ω_0$ induces a desynchronization transition between synchronous chimera states and asynchronous chimera states.
Chimera states in the systems of nonlocally coupled phase oscillators are considered stable in the continuous limit of spatially distributed oscillators. However, it is reported that in the numerical simulations without taking such limit, chimera states are chaotic transient and finally collapse into the completely synchronous solution. In this paper, we numerically study chimera states by using the coupling function different from the previous studies and obtain the result that chimera states can be stable even without taking the continuous limit, which we call the persistent chimera state.
Chimera states, which consist of coexisting domains of spatially coherent and incoherent dynamics, have been widely found in nonlocally coupled oscillatory systems. We demonstrate for the first time that chimera states can emerge from excitable systems under nonlocal coupling in which isolated units only allow for the equilibrium. We theoretically reveal that nonlocal coupling induced collective oscillation is behind the occurrence of the chimera states. We find two different types of chimera states, phase-chimera state and excitability-chimera states, depending on the coupling strength. At we…
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 oscillators, for example sinusoidal coupling or diffusive coupling. Here, we investigate chimera dynamics in nonlocally coupled phase oscillators with biharmonic interaction. We find novel chimera states with features such as that oscillators in the same coherent cluster may split into two groups with a phase difference between them at around pi/2 and that oscillato…
We study numerically the dynamics of a network made of two coupled one-dimensional ensembles of discrete-time systems. The first ensemble is represented by a ring of nonlocally coupled Henon maps, and the second one - by a ring of nonlocally coupled Lozi maps. We find that the network of coupled ensembles can realize all the spatio-temporal structures which are observed both in the Henon map ensemble and in the Lozi map ensemble when uncoupled. Moreover, we reveal a new type of spatiotemporal structure, a solitary state chimera, in the considered network. We also establish and describe the eff…
Chimera states, a symmetry-breaking spatiotemporal pattern in nonlocally coupled dynamical units, prevail in a variety of systems. However, the interaction structures among oscillators are static in most of studies on chimera state. In this work, we consider a population of agents. Each agent carries a phase oscillator. We assume that agents perform Brownian motions on a ring and interact with each other with a kernel function dependent on the distance between them. When agents are motionless, the model allows for several dynamical states including two different chimera states (the type-I and …
We investigate the emergence of different kinds of imperfect synchronized states and chimera states in two interacting populations of nonlocally coupled Stuart-Landau oscillators. We find that the complete synchronization in population-I and existence of solitary oscillators which escape from the synchronized group in population-II lead to imperfect synchronized states for sufficiently small values of nonisochronicity parameter. Interestingly, on increasing the strength of this parameter further there occurs an onset of mixed imperfect synchronized states where the solitary oscillators occur f…
We investigate the significance of nonisochronicity parameter in a network of nonlocally coupled Stuart-Landau oscillators with symmetry breaking form. We observe that the presence of nonisochronicity parameter leads to structural changes in the chimera death region while varying the strength of the interaction. This gives rise to the existence of different types of chimera death states such as multi-chimera death state, type-I periodic chimera death (PCD) state and, type-II periodic chimera death (PCD) state. We also find that the number of periodic domains in both the types of PCD states exp…
Chimera states for the one-dimensional array of nonlocally coupled phase oscillators in the continuum limit are assumed to be stationary states in most studies, but a few studies report the existence of breathing chimera states. We focus on multichimera states with two coherent and incoherent regions, and numerically demonstrate that breathing multichimera states, whose global order parameter oscillates temporally, can appear. Moreover, we show that the system exhibits a Hopf bifurcation from a stationary multichimera to a breathing one by the linear stability analysis for the stationary multi…
We study numerically synchronization phenomena of spatiotemporal structures, including chimera states, in a two layer network of nonlocally coupled nonlinear chaotic discrete-time systems. Each of the interacting ensembles represents a one layer ring network of nonlocally coupled logistic maps in the chaotic regime. The coupled networks differ in their control parameters that enables one to observe distinct spatiotemporal dynamics in the networks when there is no coupling between them. We explore in detail external and mutual synchronization of chimera structures. The identity of synchronous s…
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 …
Chimera states in one-dimensional nonlocally coupled phase oscillators are mostly assumed to be stationary, but breathing chimeras can occasionally appear, branching from the stationary chimeras via Hopf bifurcation. In this paper, we demonstrate two types of breathing chimeras: The type I breathing chimera looks the same as the stationary chimera at a glance, while the type II consists of multiple coherent regions with different average frequencies. Moreover, it is shown that the type I changes to the type II by increasing the breathing amplitude. Furthermore, we develop a self-consistent ana…
Since the discovery of chimera states, the presence of a nonzero phase lag parameter turns out to be an essential attribute for the emergence of chimeras in a nonlocally coupled identical Kuramoto phase oscillators' network with pairwise interactions. In this letter, we report the emergence of chimeras without phase lag in nonlocally coupled identical Kuramoto network owing to the introduction of non-pairwise interactions. The influence of added nonlinearity in the coupled system dynamics in the form of simplicial complexes mitigates the requisite of a nonzero phase lag parameter for the emerg…
Nonlocally coupled oscillators with a phase lag self-organize into various patterns such as global synchronization, the twisted state, and the chimera state. In this paper, we consider nonlocally coupled oscillators that move on a ring by randomly exchanging their positions with the neighbors, and investigate the combined effects of phase lag and mobility on the collective phase dynamics. Spanning the whole range of phase lag and mobility, we show that mobility promotes synchronization for an attractive coupling, while it destroys coherence for a repulsive coupling. The transition behaviors ar…
About two decades ago it was discovered that systems of nonlocally coupled oscillators can exhibit unusual symmetry-breaking patterns composed of coherent and incoherent regions. Since then such patterns, called chimera states, have been the subject of intensive study but mostly in the stationary case when the coarse-grained system dynamics remains unchanged over time. Nonstationary coherence-incoherence patterns, in particular periodically breathing chimera states, were also reported, however not investigated systematically because of their complexity. In this paper we suggest a semi-analytic…
We report the emergence of a collective dynamical state, namely phase-flip chimera, from an en- semble of identical nonlinear oscillators that are coupled indirectly via the dynamical variables from a common environment, which in turn are nonlocally coupled. The phase-flip chimera is character- ized by the coexistence of two adjacent out-of-phase synchronized coherent domains interspersed by an incoherent domain, in which the nearby oscillators are in out-of-phase synchronized states. At- tractors of the coherent domains are either from the same or different basins of attractions depending on …
Complex multiplex networks consist of several subnetwork layers, which interact via pairwise inter-layer connections. Relay synchronization between distant layers which are not directly connected, but only via a relay layer, can be observed in multiplex networks. We study three-layer networks of discrete logistic maps, where each individual layer is a nonlocally coupled ring, and demonstrate scenarios of relay synchronization of complex patterns in the outer layers which interact via an intermediate layer. We find regimes of relay synchronization for chimera states, i.e., patterns of coexistin…
An ensemble of nonlocally coupled excitable FitzHugh-Nagumo systems is studied. In the presence of noise the explored system can exhibit a special kind of chimera states called coherence-resonance chimera. As previously thought, noise plays principal role in forming these structures. It is shown in the present paper that these regimes appear because of the specific coupling between the elements. The action of coupling involve a spatial wave regime, which occurs in ensemble of excitable nodes even if the noise is switched off. In addition, a new chimera state is obtained in an excitable regime.…
Nonlinearity of local dynamics promotes multi-chimeras
嵌合态是一种复杂的时空模式，其中同步和异步动力学域共存于耦合的振荡器系统中。我们研究如何影响嵌合体状态的单个元素的字符通过研究网络的非局部耦合范德波尔振荡器。通过改变Van der Pol系统的分岔参数，我们可以在正则正弦和强非线性弛豫振荡之间进行插值，并证明了更显著的非线性会导致具有多个非相干域的多嵌合态。我们发现，多嵌合态的稳定性制度和振荡器的平均相速度分布的变化显着的非线性变得更强。此外，我们揭示了时间延迟对嵌合体模式的影响。
We show that amplitude-mediated phase chimeras and amplitude chimeras can occur in the same network of nonlocally coupled identical oscillators. These are two different partial synchronization patterns, where spatially coherent domains coexist with incoherent domains and coherence/incoherence refer to both amplitude and phase or only the amplitude of the oscillators, respectively. By changing the coupling strength the two types of chimera patterns can be induced. We find numerically that the amplitude chimeras are not short-living transients but can have a long lifetime. Also, we observe varia…
We show the existence of chimera-like states in two distinct groups of identical populations of globally coupled Stuart-Landau oscillators. The existence of chimera-like states occurs only for a small range of frequency difference between the two populations and these states disappear for an increase of mismatch between the frequencies. Here the chimera-like states are characterized by the synchronized oscillations in one population and desynchronized oscillations in another population. We also find that such states observed in two distinct groups of identical populations of nonlocally coupled…
We report the emergence of stable amplitude chimeras and chimera death in a two-layer network where one layer has an ensemble of identical nonlinear oscillators interacting directly through local coupling and indirectly through dynamic agents that form the second layer. The nonlocality in the interaction among the dynamical agents in the second layer induces different types of chimera related dynamical states in the first layer. The amplitude chimeras developed in them are found to be extremely stable, while chimera death states are prevalent for increased coupling strengths. The results prese…
We discuss synchronization patterns in networks of FitzHugh-Nagumo and Leaky Integrate-and-Fire oscillators coupled in a two-dimensional toroidal geometry. Common feature between the two models is the presence of fast and slow dynamics, a typical characteristic of neurons. Earlier studies have demonstrated that both models when coupled nonlocally in one-dimensional ring networks produce chimera states for a large range of parameter values. In this study, we give evidence of a plethora of two-dimensional chimera patterns of various shapes including spots, rings, stripes, and grids, observed in …
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 neuronal developments. Most of the previous studies on chimera states are not extensively done in two-dimensional ensembles of coupled oscillators by taking neuronal systems with nonlinear coupling function into account while such ensembles of oscillators are more realistic from a neurobiological point of view. In this paper, we report the emergence and exis…
