Swarm-Oscillators

Nonlinear coupling between inter- and intra-element dynamics appears as a collective behaviour of elements. The elements in this paper denote symptoms such as a bacterium having an internal network of genes and proteins, a reactive droplet, a neuron in networks, etc. In order to elucidate the capability of such systems, a simple and reasonable model is derived. This model exhibits the rich patterns of systems such as cell membrane, cell fusion, cell growing, cell division, firework, branch, and clustered clusters (self-organized hierarchical structure, modular network). This model is extremely simple yet powerful; therefore, it is expected to impact several disciplines.Comment: 9 pages, 4 figure

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.

Synchronous solutions and their stability in nonlocally coupled phase oscillators with propagation delays

We study the existence and stability of synchronous solutions in a continuum field of non-locally coupled identical phase oscillators with distance-dependent propagation delays. We present a comprehensive stability diagram in the parameter space of the system. From the numerical results a heuristic synchronization condition is suggested, and an analytic relation for the marginal stability curve is obtained. We also provide an expression in the form of a scaling relation that closely follows the marginal stability curve over the complete range of the non-locality parameter.Comment: accepted in Phys. Rev. E (2010

Synchronization Transition in the Kuramoto Model with Colored Noise

We present a linear stability analysis of the incoherent state in a system of globally coupled, identical phase oscillators subject to colored noise. In that we succeed to bridge the extreme time scales between the formerly studied and analytically solvable cases of white noise and quenched random frequencies.Comment: 4 pages, 2 figure

Chimera States for Coupled Oscillators

Arrays of identical oscillators can display a remarkable spatiotemporal pattern in which phase-locked oscillators coexist with drifting ones. Discovered two years ago, such "chimera states" are believed to be impossible for locally or globally coupled systems; they are peculiar to the intermediate case of nonlocal coupling. Here we present an exact solution for this state, for a ring of phase oscillators coupled by a cosine kernel. We show that the stable chimera state bifurcates from a spatially modulated drift state, and dies in a saddle-node bifurcation with an unstable chimera.Comment: 4 pages, 4 figure

Collective phase synchronization in locally-coupled limit-cycle oscillators

We study collective behavior of locally-coupled limit-cycle oscillators with scattered intrinsic frequencies on $d$-dimensional lattices. A linear analysis shows that the system should be always desynchronized up to $d=4$. On the other hand, numerical investigation for $d= 5$ and 6 reveals the emergence of the synchronized (ordered) phase via a continuous transition from the fully random desynchronized phase. This demonstrates that the lower critical dimension for the phase synchronization in this system is $d_{l}=4

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

Oscillatory phase transition and pulse propagation in noisy integrate-and-fire neurons

We study non-locally coupled noisy integrate-and-fire neurons with the Fokker-Planck equation. A propagating pulse state and a wavy state appear as a phase transition from an asynchronous state. We also find a solution in which traveling pulses are emitted periodically from a pacemaker region.Comment: 9 pages, 4 figure

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

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