6,122 research outputs found
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
Low dimensional manifolds for exact representation of open quantum systems
Weakly nonlinear degrees of freedom in dissipative quantum systems tend to
localize near manifolds of quasi-classical states. We present a family of
analytical and computational methods for deriving optimal unitary model
transformations based on representations of finite dimensional Lie groups. The
transformations are optimal in that they minimize the quantum relative entropy
distance between a given state and the quasi-classical manifold. This naturally
splits the description of quantum states into quasi-classical coordinates that
specify the nearest quasi-classical state and a transformed quantum state that
can be represented in fewer basis levels. We derive coupled equations of motion
for the coordinates and the transformed state and demonstrate how this can be
exploited for efficient numerical simulation. Our optimization objective
naturally quantifies the non-classicality of states occurring in some given
open system dynamics. This allows us to compare the intrinsic complexity of
different open quantum systems.Comment: Added section on semi-classical SR-latch, added summary of method,
revised structure of manuscrip
Synchronization of coupled stochastic limit cycle oscillators
For a class of coupled limit cycle oscillators, we give a condition on a
linear coupling operator that is necessary and sufficient for exponential
stability of the synchronous solution. We show that with certain modifications
our method of analysis applies to networks with partial, time-dependent, and
nonlinear coupling schemes, as well as to ensembles of local systems with
nonperiodic attractors. We also study robustness of synchrony to noise. To this
end, we analytically estimate the degree of coherence of the network
oscillations in the presence of noise. Our estimate of coherence highlights the
main ingredients of stochastic stability of the synchronous regime. In
particular, it quantifies the contribution of the network topology. The
estimate of coherence for the randomly perturbed network can be used as means
for analytic inference of degree of stability of the synchronous solution of
the unperturbed deterministic network. Furthermore, we show that in large
networks, the effects of noise on the dynamics of each oscillator can be
effectively controlled by varying the strength of coupling, which provides a
powerful mechanism of denoising. This suggests that the organization of
oscillators in a coupled network may play an important role in maintaining
robust oscillations in random environment. The analysis is complemented with
the results of numerical simulations of a neuronal network.
PACS: 05.45.Xt, 05.40.Ca
Keywords: synchronization, coupled oscillators, denoising, robustness to
noise, compartmental modelComment: major revisions; two new section
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