Robust chimera states in SQUID metamaterials with local interactions

We report on the emergence of robust multi-clustered chimera states in a dissipative-driven system of symmetrically and locally coupled identical SQUID oscillators. The "snake-like" resonance curve of the single SQUID (Superconducting QUantum Interference Device) is the key to the formation of the chimera states and is responsible for the extreme multistability exhibited by the coupled system that leads to attractor crowding at the geometrical resonance (inductive-capacitive) frequency. Until now, chimera states were mostly believed to exist for nonlocal coupling. Our findings provide theoretical evidence that nearest neighbor interactions are indeed capable of supporting such states in a wide parameter range. SQUID metamaterials are the subject of intense experimental investigations and we are highly confident that the complex dynamics demonstrated in this manuscript can be confirmed in the laboratory

Delay-induced multistability near a global bifurcation

We study the effect of a time-delayed feedback within a generic model for a saddle-node bifurcation on a limit cycle. Without delay the only attractor below this global bifurcation is a stable node. Delay renders the phase space infinite-dimensional and creates multistability of periodic orbits and the fixed point. Homoclinic bifurcations, period-doubling and saddle-node bifurcations of limit cycles are found in accordance with Shilnikov's theorems.Comment: Int. J. Bif. Chaos (2007), in prin

The Effect of Intra- and Inter-ring Couplings in Leaky Integrate-and-Fire Multiplex Networks

We study the dynamics of identical Leaky Integrate-and-Fire (LIF) neurons on a multiplex composed of two ring networks with symmetric nonlocal coupling within each ring and one-to-one connections between rings. We investigate the impact of different intra-ring coupling strengths in the two rings for attractive and repulsive inter-ring coupling and show that they can lead to subthreshold oscillations. The corresponding parameter spaces where this phenomenon occurs are determined numerically. Moreover, we show that depending on whether the couplings between the two rings are attractive or repulsive, the interaction produces qualitatively different behavior in the synchronization patterns and the mean frequency profiles.Comment: 12 pages; 6 figure

Chimeras in Leaky Integrate-and-Fire Neural Networks: Effects of Reflecting Connectivities

The effects of nonlocal and reflecting connectivity are investigated in coupled Leaky Integrate-and-Fire (LIF) elements, which assimilate the exchange of electrical signals between neurons. Earlier investigations have demonstrated that non-local and hierarchical network connectivity often induces complex synchronization patterns and chimera states in systems of coupled oscillators. In the LIF system we show that if the elements are non-locally linked with positive diffusive coupling in a ring architecture the system splits into a number of alternating domains. Half of these domains contain elements, whose potential stays near the threshold, while they are interrupted by active domains, where the elements perform regular LIF oscillations. The active domains move around the ring with constant velocity, depending on the system parameters. The idea of introducing reflecting non-local coupling in LIF networks originates from signal exchange between neurons residing in the two hemispheres in the brain. We show evidence that this connectivity induces novel complex spatial and temporal structures: for relatively extensive ranges of parameter values the system splits in two coexisting domains, one domain where all elements stay near-threshold and one where incoherent states develop with multileveled mean phase velocity distribution.Comment: 12 pages, 12 figure

Multi-channel pulse dynamics in a stabilized Ginzburg-Landau system

We study the stability and interactions of chirped solitary pulses in a system of nonlinearly coupled cubic Ginzburg-Landau (CGL) equations with a group-velocity mismatch between them, where each CGL equation is stabilized by linearly coupling it to an additional linear dissipative equation. In the context of nonlinear fiber optics, the model describes transmission and collisions of pulses at different wavelengths in a dual-core fiber, in which the active core is furnished with bandwidth-limited gain, while the other, passive (lossy) one is necessary for stabilization of the solitary pulses. Complete and incomplete collisions of pulses in two channels in the cases of anomalous and normal dispersion in the active core are analyzed by means of perturbation theory and direct numerical simulations. It is demonstrated that the model may readily support fully stable pulses whose collisions are quasi-elastic, provided that the group-velocity difference between the two channels exceeds a critical value. In the case of quasi-elastic collisions, the temporal shift of pulses, predicted by the analytical approach, is in semi-quantitative agrement with direct numerical results in the case of anomalous dispersion (in the opposite case, the perturbation theory does not apply). We also consider a simultaneous collision between pulses in three channels, concluding that this collision remains quasi-elastic, and the pulses remain completely stable. Thus, the model may be a starting point for the design of a stabilized wavelength-division-multiplexed (WDM) transmission system.Comment: a text file in the revtex4 format, and 16 pdf files with figures. Physical Review E, in pres

Metastable and chimera-like states in the C.elegans brain network

We model the neuronal activity of the C.elegans network by coupling Hindmarsh-Rose oscillators through the adjacency matrix obtained from its corresponding brain connectivity. By means of numerical simulations, we produce the parameter spaces for quantities related to synchronization, metastability and chimera-like dynamics, identifying, thus, interesting complex patterns of collective behaviour