Emergence of second coherent regions for breathing chimera states

Self-induced-stochastic-resonance breathing chimeras

The study by Semenova et al. [Phys. Rev. Lett. 117, 014102 (2016)0031-900710.1103/PhysRevLett.117.014102] discovered a type of chimera state known as coherence-resonance chimera (CRC), which combines the effects of coherence resonance (CR) and the spatial property of classical chimeras. In this Letter, we present yet another form of chimera, which we refer to as self-induced-stochastic-resonance breathing chimera (SISR-BC), which differs fundamentally from the CRC in that it combines the mechanism and effects of self-induced stochastic resonance (SISR, previously shown by DeVille et al. [Phys. Rev. E 72, 031105 (2005)1539-375510.1103/PhysRevE.72.031105] to be intrinsically different from CR), the symmetry breaking in the rotational coupling between the slow and fast subsystems of the coupled oscillators, and the property of breathing chimera-a form of chimera state characterized by nonstationary periodic dynamics of coherent-incoherent patterns with a periodically oscillating global order parameter. Unlike other types of chimeras, including CRC, SISR-BC demonstrates remarkable resilience to a relatively wide range of stochastic perturbations and persists even when the purely excitable system is significantly distant from the Hopf bifurcation threshold-thanks to the mechanism of SISR-and globally attracts random distributions of initial conditions. Considering its potential impact on information processing in neuronal networks, SISR-BC could have special significance and applications.

Explosive transitions to synchronization in networks of frequency dipoles

We reveal that an introduction of frequency-weighted inter-layer coupling term in networks of frequency dipoles can induce explosive synchronization transitions. The reason for explosive synchronization is that the oscillators with synchronization superiority are moderately suppressed. The findings show that a super-linear correlation induces explosive synchronization in networks of frequency dipoles, while a linear or sub-linear correlation excites chimera-like states. Clearly, the synchronization transition mode of networks of frequency dipoles is controlled by the power-law exponent. In addition, by means of the mean-field approximation, we obtain the critical values of the coupling strength within and between layers in two limit cases. The results of theoretical analysis are in good agreement with those of numerical simulation. Compared with the previous models, the model proposed in this paper retains the topological structure of network and the intrinsic properties of oscillators, so it is easy to realize pinning control.

Amplitude-mediated chimera states in nonlocally coupled Stuart-Landau oscillators

Chimera states achieve the coexistence of coherent and incoherent subgroups through symmetry breaking and emerge in physical, chemical, and biological systems. We show the presence of amplitude-mediated multicluster chimera states in nonlocally coupled Stuart-Landau oscillators. We clarify the prerequisites for having different types of chimera states by analytically and numerically studying how phase transitions occur between these states. Our results demonstrate how the oscillation amplitudes interact with the phase degrees of freedom in chimera states and significantly advance our understanding of the generation mechanisms of such states in coupled oscillator systems.

Self-Organized Multifrequency Clusters in an Oscillating Electrochemical System with Strong Nonlinear Coupling

We study the spatiotemporal dynamics of the oscillatory photoelectrodissolution of n-type Si in a fluoride-containing electrolyte under anodic potentials using in situ ellipsometric imaging. When lowering the illumination intensity stepwise, we successively observe uniform oscillations, modulated amplitude clusters, and the coexistence of multifrequency clusters, i.e., regions with different frequencies, with a stationary domain. We argue that the multifrequency clusters emerge due to an adaptive, nonlinear, and nonlocal coupling, similar to those found in the context of neural dynamics.