565 research outputs found
Ducks on the torus: existence and uniqueness
We show that there exist generic slow-fast systems with only one
(time-scaling) parameter on the two-torus, which have canard cycles for
arbitrary small values of this parameter. This is in drastic contrast with the
planar case, where canards usually occur in two-parametric families. Here we
treat systems with a convex slow curve. In this case there is a set of
parameter values accumulating to zero for which the system has exactly one
attracting and one repelling canard cycle. The basin of the attracting cycle is
almost the whole torus.Comment: To appear in Journal of Dynamical and Control Systems, presumably
Vol. 16 (2010), No. 2; The final publication is available at
www.springerlink.co
SYNTHESIS AND APPLICATION OF CROWN ETHERS
Mono- and bis-benzo-15-crown-5-ether derivatives have been synthesized and determined
their potentiometric K+ selectivity factors. Of bis-crown ether urethanes highly selective Iigands
were found some of which was used as active ingredient in potassium selective membrane
electrode.
Sugar based crown ethers, aza-crowns and cryptands were also prepared and applied as
chiral catalyst in enantioselective reactions
Memory Effects and Scaling Laws in Slowly Driven Systems
This article deals with dynamical systems depending on a slowly varying
parameter. We present several physical examples illustrating memory effects,
such as metastability and hysteresis, which frequently appear in these systems.
A mathematical theory is outlined, which allows to show existence of hysteresis
cycles, and determine related scaling laws.Comment: 28 pages (AMS-LaTeX), 18 PS figure
ANALYSIS OF SODIUM TRANSPORT IN THE AMPHIBIAN OOCYTE BY EXTRACTIVE AND RADIOAUTOGRAPHIC TECHNIQUES
Shilnikov Lemma for a nondegenerate critical manifold of a Hamiltonian system
We prove an analog of Shilnikov Lemma for a normally hyperbolic symplectic
critical manifold of a Hamiltonian system. Using this
result, trajectories with small energy shadowing chains of homoclinic
orbits to are represented as extremals of a discrete variational problem,
and their existence is proved. This paper is motivated by applications to the
Poincar\'e second species solutions of the 3 body problem with 2 masses small
of order . As , double collisions of small bodies correspond to
a symplectic critical manifold of the regularized Hamiltonian system
Global Production Increased by Spatial Heterogeneity in a Population Dynamics Model
Spatial and temporal heterogeneity are often described as important factors having a strong impact on biodiversity. The effect of heterogeneity is in most cases analyzed by the response of biotic interactions such as competition of predation. It may also modify intrinsic population properties such as growth rate. Most of the studies are theoretic since it is often difficult to manipulate spatial heterogeneity in practice. Despite the large number of studies dealing with this topics, it is still difficult to understand how the heterogeneity affects populations dynamics. On the basis of a very simple model, this paper aims to explicitly provide a simple mechanism which can explain why spatial heterogeneity may be a favorable factor for production.We consider a two patch model and a logistic growth is assumed on each patch. A general condition on the migration rates and the local subpopulation growth rates is provided under which the total carrying capacity is higher than the sum of the local carrying capacities, which is not intuitive. As we illustrate, this result is robust under stochastic perturbations
The regularized visible fold revisited
The planar visible fold is a simple singularity in piecewise smooth systems.
In this paper, we consider singularly perturbed systems that limit to this
piecewise smooth bifurcation as the singular perturbation parameter
. Alternatively, these singularly perturbed systems can
be thought of as regularizations of their piecewise counterparts. The main
contribution of the paper is to demonstrate the use of consecutive blowup
transformations in this setting, allowing us to obtain detailed information
about a transition map near the fold under very general assumptions. We apply
this information to prove, for the first time, the existence of a locally
unique saddle-node bifurcation in the case where a limit cycle, in the singular
limit , grazes the discontinuity set. We apply this
result to a mass-spring system on a moving belt described by a Stribeck-type
friction law
Resolvent estimates for normally hyperbolic trapped sets
We give pole free strips and estimates for resolvents of semiclassical
operators which, on the level of the classical flow, have normally hyperbolic
smooth trapped sets of codimension two in phase space. Such trapped sets are
structurally stable and our motivation comes partly from considering the wave
equation for Kerr black holes and their perturbations, whose trapped sets have
precisely this structure. We give applications including local smoothing
effects with epsilon derivative loss for the Schr\"odinger propagator as well
as local energy decay results for the wave equation.Comment: Further changes to erratum correcting small problems with Section 3.5
and Lemma 4.1; this now also corrects hypotheses, explicitly requiring
trapped set to be symplectic. Erratum follows references in this versio
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