1,283 research outputs found
Canard-like phenomena in piecewise-smooth Van der Pol systems
We show that a nonlinear, piecewise-smooth, planar dynamical system can
exhibit canard phenomena. Canard solutions and explosion in nonlinear,
piecewise-smooth systems can be qualitatively more similar to the phenomena in
smooth systems than piecewise-linear systems, since the nonlinearity allows for
canards to transition from small cycles to canards ``with heads." The canards
are born of a bifurcation that occurs as the slow-nullcline coincides with the
splitting manifold. However, there are conditions under which this bifurcation
leads to a phenomenon called super-explosion, the instantaneous transition from
a globally attracting periodic orbit to relaxations oscillations. Also, we
demonstrate that the bifurcation---whether leading to canards or
super-explosion---can be subcritical.Comment: 17 pages, 11 figure
On the number of limit cycles of the Lienard equation
In this paper, we study a Lienard system of the form dot{x}=y-F(x),
dot{y}=-x, where F(x) is an odd polynomial. We introduce a method that gives a
sequence of algebraic approximations to the equation of each limit cycle of the
system. This sequence seems to converge to the exact equation of each limit
cycle. We obtain also a sequence of polynomials R_n(x) whose roots of odd
multiplicity are related to the number and location of the limit cycles of the
system.Comment: 10 pages, 5 figures. Submitted to Physical Review
Effects of a localized beam on the dynamics of excitable cavity solitons
We study the dynamical behavior of dissipative solitons in an optical cavity
filled with a Kerr medium when a localized beam is applied on top of the
homogeneous pumping. In particular, we report on the excitability regime that
cavity solitons exhibits which is emergent property since the system is not
locally excitable. The resulting scenario differs in an important way from the
case of a purely homogeneous pump and now two different excitable regimes, both
Class I, are shown. The whole scenario is presented and discussed, showing that
it is organized by three codimension-2 points. Moreover, the localized beam can
be used to control important features, such as the excitable threshold,
improving the possibilities for the experimental observation of this
phenomenon.Comment: 9 Pages, 12 figure
The Evolution of Travelling Waves in a KPP Reaction-Diffusion Model with Cut-off Reaction Rate. I. Permanent Form Travelling Waves
We consider Kolmogorov--Petrovskii--Piscounov (KPP) type models in the
presence of a discontinuous cut-off in reaction rate at concentration .
In Part I we examine permanent form travelling wave solutions (a companion
paper, Part II, is devoted to their evolution in the large time limit). For
each fixed cut-off value , we prove the existence of a unique
permanent form travelling wave with a continuous and monotone decreasing
propagation speed . We extend previous asymptotic results in the
limit of small and present new asymptotic results in the limit of large
which are respectively obtained via the systematic use of matched and
regular asymptotic expansions. The asymptotic results are confirmed against
numerical results obtained for the particular case of a cut-off Fisher reaction
function
A search for pulsations in the HgMn star HD 45975 with CoRoT photometry and ground-based spectroscopy
The existence of pulsations in HgMn stars is still being debated. To provide
the first unambiguous observational detection of pulsations in this class of
chemically peculiar objects, the bright star HD 45975 was monitored for nearly
two months by the CoRoT satellite. Independent analyses of the light curve
provides evidence of monoperiodic variations with a frequency of 0.7572 c/d and
a peak-to-peak amplitude of ~2800 ppm. Multisite, ground-based spectroscopic
observations overlapping the CoRoT observations show the star to be a
long-period, single-lined binary. Furthermore, with the notable exception of
mercury, they reveal the same periodicity as in photometry in the line moments
of chemical species exhibiting strong overabundances (e.g., Mn and Y). In
contrast, lines of other elements do not show significant variations. As found
in other HgMn stars, the pattern of variability consists in an absorption bump
moving redwards across the line profiles. We argue that the photometric and
spectroscopic changes are more consistent with an interpretation in terms of
rotational modulation of spots at the stellar surface. In this framework, the
existence of pulsations producing photometric variations above the ~50 ppm
level is unlikely in HD 45975. This provides strong constraints on the
excitation/damping of pulsation modes in this HgMn star.Comment: Accepted for publication in A&A, 14 pages, 15 colour figures (revised
version after language editing
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