4,675 research outputs found
Within-burst synchrony changes for coupled elliptic bursters
We study the appearance of a novel phenomenon for linearly coupled identical
bursters: synchronized bursts where there are changes of spike synchrony within
each burst. The examples we study are for normal form elliptic bursters where
there is a periodic slow passage through a Bautin (codimension two degenerate
Andronov-Hopf) bifurcation. This burster has a subcritical Andronov-Hopf
bifurcation at the onset of repetitive spiking while end of burst occurs via a
fold limit cycle bifurcation. We study synchronization behavior of two and
three Bautin-type elliptic bursters for a linear direct coupling scheme. Burst
synchronization is known to be prevalent behavior among such coupled bursters,
while spike synchronization is more dependent on the details of the coupling.
We note that higher order terms in the normal form that do not affect the
behavior of a single burster can be responsible for changes in synchrony
pattern; more precisely, we find within-burst synchrony changes associated with
a turning point in the spiking frequency.Comment: 17 pages, 13 figures, 2 table
Approximation of small-amplitude weakly coupled oscillators with discrete nonlinear Schrodinger equations
Small-amplitude weakly coupled oscillators of the Klein-Gordon lattices are
approximated by equations of the discrete nonlinear Schrodinger type. We show
how to justify this approximation by two methods, which have been very popular
in the recent literature. The first method relies on a priori energy estimates
and multi-scale decompositions. The second method is based on a resonant normal
form theorem. We show that although the two methods are different in the
implementation, they produce equivalent results as the end product. We also
discuss applications of the discrete nonlinear Schrodinger equation in the
context of existence and stability of breathers of the Klein--Gordon lattice
Sufficient Conditions for Fast Switching Synchronization in Time Varying Network Topologies
In previous work, empirical evidence indicated that a time-varying network
could propagate sufficient information to allow synchronization of the
sometimes coupled oscillators, despite an instantaneously disconnected
topology. We prove here that if the network of oscillators synchronizes for the
static time-average of the topology, then the network will synchronize with the
time-varying topology if the time-average is achieved sufficiently fast. Fast
switching, fast on the time-scale of the coupled oscillators, overcomes the
descychnronizing decoherence suggested by disconnected instantaneous networks.
This result agrees in spirit with that of where empirical evidence suggested
that a moving averaged graph Laplacian could be used in the master-stability
function analysis. A new fast switching stability criterion here-in gives
sufficiency of a fast-switching network leading to synchronization. Although
this sufficient condition appears to be very conservative, it provides new
insights about the requirements for synchronization when the network topology
is time-varying. In particular, it can be shown that networks of oscillators
can synchronize even if at every point in time the frozen-time network topology
is insufficiently connected to achieve synchronization.Comment: Submitted to SIAD
A Quantum Non-demolition measurement of Fock states of mesoscopic mechanical oscillators
We investigate a scheme that makes a quantum non-demolition measurement of
the excitation level of a mesoscopic mechanical oscillator by utilizing the
anharmonic coupling between two elastic beam bending modes. The non-linear
coupling between the two modes shifts the resonant frequency of the readout
oscillator proportionate to the excitation of the system oscillator. This
frequency shift may be detected as a phase shift of the readout oscillation
when driven on resonance. We show that in an appropriate regime this
measurement approaches a quantum non-demolition measurement of the phonon
number of the system oscillator. As phonon energies in micromechanical
oscillators become comparable to or greater than the thermal energy, the
individual phonon dynamics within each mode can be resolved. As a result it
should be possible to monitor jumps between Fock states caused by the coupling
of the system to the thermal reservoirs.Comment: revised, 21 pages, 9 figure
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