9,621 research outputs found
Cusp-scaling behavior in fractal dimension of chaotic scattering
A topological bifurcation in chaotic scattering is characterized by a sudden
change in the topology of the infinite set of unstable periodic orbits embedded
in the underlying chaotic invariant set. We uncover a scaling law for the
fractal dimension of the chaotic set for such a bifurcation. Our analysis and
numerical computations in both two- and three-degrees-of-freedom systems
suggest a striking feature associated with these subtle bifurcations: the
dimension typically exhibits a sharp, cusplike local minimum at the
bifurcation.Comment: 4 pages, 4 figures, Revte
Pinned modes in lossy lattices with local gain and nonlinearity
We introduce a discrete linear lossy system with an embedded "hot spot" (HS),
i.e., a site carrying linear gain and complex cubic nonlinearity. The system
can be used to model an array of optical or plasmonic waveguides, where
selective excitation of particular cores is possible. Localized modes pinned to
the HS are constructed in an implicit analytical form, and their stability is
investigated numerically. Stability regions for the modes are obtained in the
parameter space of the linear gain and cubic gain/loss. An essential result is
that the interaction of the unsaturated cubic gain and self-defocusing
nonlinearity can produce stable modes, although they may be destabilized by
finite amplitude perturbations. On the other hand, the interplay of the cubic
loss and self-defocusing gives rise to a bistability.Comment: Phys. Rev. E (in press
Improving Noisy Student Training on Non-target Domain Data for Automatic Speech Recognition
Noisy Student Training (NST) has recently demonstrated extremely strong
performance in Automatic Speech Recognition (ASR). In this paper, we propose a
data selection strategy named LM Filter to improve the performances of NST on
non-target domain data in ASR tasks. Hypothesis with and without Language Model
are generated and CER differences between them are utilized as a filter
threshold. Results reveal that significant improvements of 10.4% compared with
no data filtering baselines. We can achieve 3.31% CER in AISHELL-1 test set,
which is best result from our knowledge without any other supervised data. We
also perform evaluations on supervised 1000 hour AISHELL-2 dataset and
competitive results of 4.72% CER can be achieved
Strange nonchaotic attractors in noise driven systems
Strange nonchaotic attractors (SNAs) in noise driven systems are
investigated. Before the transition to chaos, due to the effect of noise, a
typical trajectory will wander between the periodic attractor and its nearby
chaotic saddle in an intermittent way, forms a strange attractor gradually. The
existence of SNAs is confirmed by simulation results of various critera both in
map and continuous systems. Dimension transition is found and intermittent
behavior is studied by peoperties of local Lyapunov exponent. The universality
and generalization of this kind of SNAs are discussed and common features are
concluded
Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theory
We consider a model of a Hopf bifurcation interacting as a codimension 2 bifurcation with a saddle-node on a limit cycle, motivated by a low-order model for magnetic activity in a stellar dynamo. This model consists of coupled interactions between a saddle-node and two Hopf bifurcations, where the saddle-node bifurcation is assumed to have global reinjection of trajectories. The model can produce chaotic behaviour within each of a pair of invariant subspaces, and also it can show attractors that are stuck-on to both of the invariant subspaces. We investigate the detailed intermittent dynamics for such an attractor, investigating the effect of breaking the symmetry between the two Hopf bifurcations, and observing that it can appear via blowout bifurcations from the invariant subspaces.
We give a simple Markov chain model for the two-state intermittent dynamics that reproduces the time spent close to the invariant subspaces and the switching between the different possible invariant subspaces; this clarifies the observation that the proportion of time spent near the different subspaces depends on the average residence time and also on the probabilities of switching between the possible subspaces
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