Chimera and globally clustered chimera: Impact of time delay

Following a short report of our preliminary results [Phys. Rev. E 79, 055203(R) (2009)], we present a more detailed study of the effects of coupling delay in diffusively coupled phase oscillator populations. We find that coupling delay induces chimera and globally clustered chimera (GCC) states in delay coupled populations. We show the existence of multi-clustered states that act as link between the chimera and the GCC states. A stable GCC state goes through a variety of GCC states, namely periodic, aperiodic, long-- and short--period breathers and becomes unstable GCC leading to global synchronization in the system, on increasing time delay. We provide numerical evidence and theoretical explanations for the above results and discuss possible applications of the observed phenomena.Comment: 10 pages, 10 figures, Accepted in Phys. Rev.

Derivation of Non-isotropic Phase Equations from a General Reaction-Diffusion Equation

A non-isotropic version of phase equations such as the Burgers equation, the K-dV-Burgers equation, the Kuramoto-Sivashinsky equation and the Benney equation in the three-dimensional space is systematically derived from a general reaction-diffusion system by means of the renormalization group method.Comment: 21pages,no figure

Spin-dependent neutrino-induced nucleon knockout

We study neutrino-induced nucleon knockout off atomic nuclei and examine the polarization properties of the ejectile. A detailed study of the spin dependence of the outgoing nucleon is presented. The numerical results are derived within a non-relativistic plane-wave impulse-approximation approach. Our calculations reveal large polarization asymmetries, and clear dissimilarities between neutrino- and antineutrino-induced reactions. They reflect the fact that neutrino-induced nucleon knockout is dominated by the transverse axial current and gains its major contributions from forward nucleon emission and backward lepton scattering.Comment: 9 pages, 7 figures, accepted for publication in Phys. Rev.

Loss of coherence in dynamical networks: spatial chaos and chimera states

We discuss the breakdown of spatial coherence in networks of coupled oscillators with nonlocal interaction. By systematically analyzing the dependence of the spatio-temporal dynamics on the range and strength of coupling, we uncover a dynamical bifurcation scenario for the coherence-incoherence transition which starts with the appearance of narrow layers of incoherence occupying eventually the whole space. Our findings for coupled chaotic and periodic maps as well as for time-continuous R\"ossler systems reveal that intermediate, partially coherent states represent characteristic spatio-temporal patterns at the transition from coherence to incoherence.Comment: 4 pages, 4 figure

An experimental route to spatiotemporal chaos in an extended 1D oscillators array

We report experimental evidence of the route to spatiotemporal chaos in a large 1D-array of hotspots in a thermoconvective system. Increasing the driving force, a stationary cellular pattern becomes unstable towards a mixed pattern of irregular clusters which consist of time-dependent localized patterns of variable spatiotemporal coherence. These irregular clusters coexist with the basic cellular pattern. The Fourier spectra corresponding to this synchronization transition reveals the weak coupling of a resonant triad. This pattern saturates with the formation of a unique domain of great spatiotemporal coherence. As we further increase the driving force, a supercritical bifurcation to a spatiotemporal beating regime takes place. The new pattern is characterized by the presence of two stationary clusters with a characteristic zig-zag geometry. The Fourier analysis reveals a stronger coupling and enables to find out that this beating phenomena is produced by the splitting of the fundamental spatiotemporal frequencies in a narrow band. Both secondary instabilities are phase-like synchronization transitions with global and absolute character. Far beyond this threshold, a new instability takes place when the system is not able to sustain the spatial frequency splitting, although the temporal beating remains inside these domains. These experimental results may support the understanding of other systems in nature undergoing similar clustering processes.Comment: 12 pages, 13 figure

Dynamics of the Singlet-Triplet System Coupled with Conduction Spins -- Application to Pr Skutterudites

Dynamics of the singlet-triplet crystalline electric field (CEF) system at finite temperatures is discussed by use of the non-crossing approximation. Even though the Kondo temperature is smaller than excitation energy to the CEF triplet, the Kondo effect appears at temperatures higher than the CEF splitting, and accordingly only quasi-elastic peak is found in the magnetic spectra. On the other hand, at lower temperatures the CEF splitting suppresses the Kondo effect and inelastic peak develops. The broad quasi-elastic neutron scattering spectra observed in PrFe_4P_{12} at temperatures higher than the quadrupole order correspond to the parameter range where the CEF splittings are unimportant.Comment: 16 pages, 12 figures, 1 tabl

Globally clustered chimera states in delay--coupled populations

We have identified the existence of globally clustered chimera states in delay coupled oscillator populations and find that these states can breathe periodically, aperiodically and become unstable depending upon the value of coupling delay. We also find that the coupling delay induces frequency suppression in the desynchronized group. We provide numerical evidence and theoretical explanations for the above results and discuss possible applications of the observed phenomena.Comment: Accepted in Phys. Rev. E as a Rapid Communicatio

Heterogeneity Induced Order in Globally Coupled Chaotic Systems

Collective behavior is studied in globally coupled maps with distributed nonlinearity. It is shown that the heterogeneity enhances regularity in the collective dynamics. Low-dimensional quasiperiodic motion is often found for the mean-field, even if each element shows chaotic dynamics. The mechanism of this order is due to the formation of an internal bifurcation structure, and the self-consistent dynamics between the structures and the mean-field. Keywords: Globally Coupled Map with heterogeneity, Collective behaviorComment: 11 pages (Revtex) + 4 figures (PostScript,tar+gzip

A new approach to partial synchronization in globally coupled rotators

We develop a formalism to analyze the behaviour of pulse--coupled identical phase oscillators with a specific attention devoted to the onset of partial synchronization. The method, which allows describing the dynamics both at the microscopic and macroscopic level, is introduced in a general context, but then the application to the dynamics of leaky integrate-and-fire (LIF) neurons is analysed. As a result, we derive a set of delayed equations describing exactly the LIF behaviour in the thermodynamic limit. We also investigate the weak coupling regime by means of a perturbative analysis, which reveals that the evolution rule reduces to a set of ordinary differential equations. Robustness and generality of the partial synchronization regime is finally tested both by adding noise and considering different force fields.Comment: 5 pages, 3 eps figure