910 research outputs found
Two Scenarios of Breaking Chaotic Phase Synchronization
Two types of phase synchronization (accordingly, two scenarios of breaking
phase synchronization) between coupled stochastic oscillators are shown to
exist depending on the discrepancy between the control parameters of
interacting oscillators, as in the case of classical synchronization of
periodic oscillators. If interacting stochastic oscillators are weakly detuned,
the phase coherency of the attractors persists when phase synchronization
breaks. Conversely, if the control parameters differ considerably, the chaotic
attractor becomes phase-incoherent under the conditions of phase
synchronization break.Comment: 8 pages, 7 figure
Phase synchronization between collective rhythms of globally coupled oscillator groups: noisy identical case
We theoretically investigate collective phase synchronization between
interacting groups of globally coupled noisy identical phase oscillators
exhibiting macroscopic rhythms. Using the phase reduction method, we derive
coupled collective phase equations describing the macroscopic rhythms of the
groups from microscopic Langevin phase equations of the individual oscillators
via nonlinear Fokker-Planck equations. For sinusoidal microscopic coupling, we
determine the type of the collective phase coupling function, i.e., whether the
groups exhibit in-phase or anti-phase synchronization. We show that the
macroscopic rhythms can exhibit effective anti-phase synchronization even if
the microscopic phase coupling between the groups is in-phase, and vice versa.
Moreover, near the onset of collective oscillations, we analytically obtain the
collective phase coupling function using center-manifold and phase reductions
of the nonlinear Fokker-Planck equations.Comment: 15 pages, 7 figure
Global topological control for synchronized dynamics on networks
A general scheme is proposed and tested to control the symmetry breaking
instability of a homogeneous solution of a spatially extended multispecies
model, defined on a network. The inherent discreteness of the space makes it
possible to act on the topology of the inter-nodes contacts to achieve the
desired degree of stabilization, without altering the dynamical parameters of
the model. Both symmetric and asymmetric couplings are considered. In this
latter setting the web of contacts is assumed to be balanced, for the
homogeneous equilibrium to exist. The performance of the proposed method are
assessed, assuming the Complex Ginzburg-Landau equation as a reference model.
In this case, the implemented control allows one to stabilize the synchronous
limit cycle, hence time-dependent, uniform solution. A system of coupled real
Ginzburg-Landau equations is also investigated to obtain the topological
stabilization of a homogeneous and constant fixed point
Synchronization of organ pipes: experimental observations and modeling
We report measurements on the synchronization properties of organ pipes.
First, we investigate influence of an external acoustical signal from a
loudspeaker on the sound of an organ pipe. Second, the mutual influence of two
pipes with different pitch is analyzed. In analogy to the externally driven, or
mutually coupled self-sustained oscillators, one observes a frequency locking,
which can be explained by synchronization theory. Further, we measure the
dependence of the frequency of the signals emitted by two mutually detuned
pipes with varying distance between the pipes. The spectrum shows a broad
``hump'' structure, not found for coupled oscillators. This indicates a complex
coupling of the two organ pipes leading to nonlinear beat phenomena.Comment: 24 pages, 10 Figures, fully revised, 4 big figures separate in jpeg
format. accepted for Journal of the Acoustical Society of Americ
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