425 research outputs found
Aspects of Bifurcation Theory for Piecewise-Smooth, Continuous Systems
Systems that are not smooth can undergo bifurcations that are forbidden in
smooth systems. We review some of the phenomena that can occur for
piecewise-smooth, continuous maps and flows when a fixed point or an
equilibrium collides with a surface on which the system is not smooth. Much of
our understanding of these cases relies on a reduction to piecewise linearity
near the border-collision. We also review a number of codimension-two
bifurcations in which nonlinearity is important.Comment: pdfLaTeX, 9 figure
Delayed feedback control of self-mobile cavity solitons in a wide-aperture laser with a saturable absorber
We investigate the spatiotemporal dynamics of cavity solitons in a broad area
vertical-cavity surface-emitting laser with saturable absorption subjected to
time-delayed optical feedback. Using a combination of analytical, numerical and
path continuation methods we analyze the bifurcation structure of stationary
and moving cavity solitons and identify two different types of traveling
localized solutions, corresponding to slow and fast motion. We show that the
delay impacts both stationary and moving solutions either causing drifting and
wiggling dynamics of initially stationary cavity solitons or leading to
stabilization of intrinsically moving solutions. Finally, we demonstrate that
the fast cavity solitons can be associated with a lateral mode-locking regime
in a broad-area laser with a single longitudinal mode
Bifurcation analysis of a normal form for excitable media: Are stable dynamical alternans on a ring possible?
We present a bifurcation analysis of a normal form for travelling waves in
one-dimensional excitable media. The normal form which has been recently
proposed on phenomenological grounds is given in form of a differential delay
equation. The normal form exhibits a symmetry preserving Hopf bifurcation which
may coalesce with a saddle-node in a Bogdanov-Takens point, and a symmetry
breaking spatially inhomogeneous pitchfork bifurcation. We study here the Hopf
bifurcation for the propagation of a single pulse in a ring by means of a
center manifold reduction, and for a wave train by means of a multiscale
analysis leading to a real Ginzburg-Landau equation as the corresponding
amplitude equation. Both, the center manifold reduction and the multiscale
analysis show that the Hopf bifurcation is always subcritical independent of
the parameters. This may have links to cardiac alternans which have so far been
believed to be stable oscillations emanating from a supercritical bifurcation.
We discuss the implications for cardiac alternans and revisit the instability
in some excitable media where the oscillations had been believed to be stable.
In particular, we show that our condition for the onset of the Hopf bifurcation
coincides with the well known restitution condition for cardiac alternans.Comment: to be published in Chao
Exact period-four solutions of a family of n-dimensional quadratic maps via harmonic balance and Gröbner bases
Analytical solutions of the period-four orbits exhibited by a classical family of n-dimensionalquadratic maps are presented. Exact expressions are obtained by applying harmonic balance and Grobner bases to a single-input single-output representation of the system. A detailed study of a generalized scalar quadratic map and a well-known delayed logistic model is included for illustration. In the former example, conditions for the existence of bistability phenomenon are also introduced.Fil: D'amico, Edith Maria Belen. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico BahÃa Blanca. Instituto de Investigación En IngenierÃa Eléctrica; ArgentinaFil: Calandrini, Guillermo. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico BahÃa Blanca. Instituto de Investigación en IngenierÃa Eléctrica; Argentin
A delay recruitment model of the cardiovascular control system.
Copyright will be owned by Springer. We develop a nonlinear delay-differential equation for the human cardiovascular control system, and use it to explore blood pressure and heart rate variability under short-term baroreflex control. The model incorporates an intrinsically stable heart rate in the absence of nervous control, and features baroreflex influence on both heart rate and peripheral resistance. Analytical simplifications of the model allow a general investigation of the rôles played by gain and delay, and the effects of ageing.
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