Non-universal results induced by diversity distribution in coupled excitable systems

We consider a system of globally coupled active rotators near the excitable regime. The system displays a transition to a state of collective firing induced by disorder. We show that this transition is found generically for any diversity distribution with well defined moments. Singularly, for the Lorentzian distribution (widely used in Kuramoto-like systems) the transition is not present. This warns about the use of Lorentzian distributions to understand the generic properties of coupled oscillators

Multistable attractors in a network of phase oscillators with three-body interaction

Three-body interactions have been found in physics, biology, and sociology. To investigate their effect on dynamical systems, as a first step, we study numerically and theoretically a system of phase oscillators with three-body interaction. As a result, an infinite number of multistable synchronized states appear above a critical coupling strength, while a stable incoherent state always exists for any coupling strength. Owing to the infinite multistability, the degree of synchrony in asymptotic state can vary continuously within some range depending on the initial phase pattern.Comment: 5 pages, 3 figure

Effects of non-resonant interaction in ensembles of phase oscillators

We consider general properties of groups of interacting oscillators, for which the natural frequencies are not in resonance. Such groups interact via non-oscillating collective variables like the amplitudes of the order parameters defined for each group. We treat the phase dynamics of the groups using the Ott-Antonsen ansatz and reduce it to a system of coupled equations for the order parameters. We describe different regimes of co-synchrony in the groups. For a large number of groups, heteroclinic cycles, corresponding to a sequental synchronous activity of groups, and chaotic states, where the order parameters oscillate irregularly, are possible.Comment: 21 pages, 7 fig

Phaselocked patterns and amplitude death in a ring of delay coupled limit cycle oscillators

We study the existence and stability of phaselocked patterns and amplitude death states in a closed chain of delay coupled identical limit cycle oscillators that are near a supercritical Hopf bifurcation. The coupling is limited to nearest neighbors and is linear. We analyze a model set of discrete dynamical equations using the method of plane waves. The resultant dispersion relation, which is valid for any arbitrary number of oscillators, displays important differences from similar relations obtained from continuum models. We discuss the general characteristics of the equilibrium states including their dependencies on various system parameters. We next carry out a detailed linear stability investigation of these states in order to delineate their actual existence regions and to determine their parametric dependence on time delay. Time delay is found to expand the range of possible phaselocked patterns and to contribute favorably toward their stability. The amplitude death state is studied in the parameter space of time delay and coupling strength. It is shown that death island regions can exist for any number of oscillators N in the presence of finite time delay. A particularly interesting result is that the size of an island is independent of N when N is even but is a decreasing function of N when N is odd.Comment: 23 pages, 12 figures (3 of the figures in PNG format, separately from TeX); minor additions; typos correcte

Collective dynamical response of coupled oscillators with any network structure

We formulate a reduction theory that describes the response of an oscillator network as a whole to external forcing applied nonuniformly to its constituent oscillators. The phase description of multiple oscillator networks coupled weakly is also developed. General formulae for the collective phase sensitivity and the effective phase coupling between the oscillator networks are found. Our theory is applicable to a wide variety of oscillator networks undergoing frequency synchronization. Any network structure can systematically be treated. A few examples are given to illustrate our theory.Comment: 4 pages, 2 figure

Interface instability in shear banding flow

We report on the spatio-temporal dynamics of the interface in shear-banding flow of a wormlike micellar system (cetyltrimethylammonium bromide and sodium nitrate in water) during a start-up experiment. Using the scattering properties of the induced structures, we demonstrate the existence of an instability of the interface between bands along the vorticity direction. Different regimes of spatio-temporal dynamics of the interface are indentified along the stress plateau. We build a model based on the flow symetry which qualitatively describes the observed patterns

A power-law distribution of phase-locking intervals does not imply critical interaction

Neural synchronisation plays a critical role in information processing, storage and transmission. Characterising the pattern of synchronisation is therefore of great interest. It has recently been suggested that the brain displays broadband criticality based on two measures of synchronisation - phase locking intervals and global lability of synchronisation - showing power law statistics at the critical threshold in a classical model of synchronisation. In this paper, we provide evidence that, within the limits of the model selection approach used to ascertain the presence of power law statistics, the pooling of pairwise phase-locking intervals from a non-critically interacting system can produce a distribution that is similarly assessed as being power law. In contrast, the global lability of synchronisation measure is shown to better discriminate critical from non critical interaction.Comment: (v3) Fixed error in Figure 1; (v2) Added references. Minor edits throughout. Clarified relationship between theoretical critical coupling for infinite size system and 'effective' critical coupling system for finite size system. Improved presentation and discussion of results; results unchanged. Revised Figure 1 to include error bars on r and N; results unchanged; (v1) 11 pages, 7 figure

Partially Solvable Anisotropic t-J Model with Long-Range Interactions

A new anisotropic t-J model in one dimension is proposed which has long-range hopping and exchange. This t-J model is only partially solvable in contrast to known integrable models with long-range interaction. In the high-density limit the model reduces to the XXZ chain with the long-range exchange. Some exact eigenfunctions are shown to be of Jastrow-type if certain conditions for an anisotropy parameter are satisfied. The ground state as well as the excitation spectrum for various cases of the anisotropy parameter and filling are derived numerically. It is found that the Jastrow-type wave function is an excellent trial function for any value of the anisotropy parameter.Comment: 10 pages, 3 Postscript figure

Multistable behavior above synchronization in a locally coupled Kuramoto model

A system of nearest neighbors Kuramoto-like coupled oscillators placed in a ring is studied above the critical synchronization transition. We find a richness of solutions when the coupling increases, which exists only within a solvability region (SR). We also find that they posses different characteristics, depending on the section of the boundary of the SR where the solutions appear. We study the birth of these solutions and how they evolve when {K} increases, and determine the diagram of solutions in phase space.Comment: 8 pages, 10 figure

Charge gaps and quasiparticle bands of the ionic Hubbard model

The ionic Hubbard model on a cubic lattice is investigated using analytical approximations and Wilson's renormalization group for the charge excitation spectrum. Near the Mott insulating regime, where the Hubbard repulsion starts to dominate all energies, the formation of correlated bands is described. The corresponding partial spectral weights and local densities of states show characteristic features, which compare well with a hybridized-band picture appropriate for the regime at small $U$, which at half-filling is known as a band insulator. In particular, a narrow charge gap is obtained at half-filling, and the distribution of spectral quasi-particle weight reflects the fundamental hybridization mechanism of the model