7,232 research outputs found
Switching to nonhyperbolic cycles from codimension two bifurcations of equilibria of delay differential equations
In this paper we perform the parameter-dependent center manifold reduction
near the generalized Hopf (Bautin), fold-Hopf, Hopf-Hopf and transcritical-Hopf
bifurcations in delay differential equations (DDEs). This allows us to
initialize the continuation of codimension one equilibria and cycle
bifurcations emanating from these codimension two bifurcation points. The
normal form coefficients are derived in the functional analytic perturbation
framework for dual semigroups (sun-star calculus) using a normalization
technique based on the Fredholm alternative. The obtained expressions give
explicit formulas which have been implemented in the freely available numerical
software package DDE-BifTool. While our theoretical results are proven to apply
more generally, the software implementation and examples focus on DDEs with
finitely many discrete delays. Together with the continuation capabilities of
DDE-BifTool, this provides a powerful tool to study the dynamics near
equilibria of such DDEs. The effectiveness is demonstrated on various models
Structure and stability of chiral beta-tapes: a computational coarse-grained approach
We present two coarse-grained models of different levels of detail for the
description of beta-sheet tapes obtained from equilibrium self-assembly of
short rationally designed oligopeptides in solution. Here we only consider the
case of the homopolymer oligopeptides with the identical sidegroups attached,
in which the tapes have a helicoid surface with two equivalent sides. The
influence of the chirality parameter on the geometrical characteristics, namely
the diameter, inter-strand distance and pitch, of the tapes have been
investigated. The two models are found to produceequivalent results suggesting
a considerable degree of universality in conformations of the tapes.Comment: 24 pages, 5 PS figures. Accepted to J. Chem. Phy
Dark matter-wave solitons in the dimensionality crossover
We consider the statics and dynamics of dark matter-wave solitons in the
dimensionality crossover regime from 3D to 1D. There, using the nonpolynomial
Schr\"{o}dinger mean-field model, we find that the anomalous mode of the
Bogoliubov spectrum has an eigenfrequency which coincides with the soliton
oscillation frequency obtained by the 3D Gross-Pitaevskii model. We show that
substantial deviations (of order of 10% or more) from the characteristic
frequency ( being the longitudinal trap
frequency) are possible even in the purely 1D regime.Comment: Phys. Rev. A, in pres
Catecholamines and myocardial contractile function during hypodynamia and with an altered thyroid hormone balance
The dynamics of catecholamine content and myocardial contractile function during hypodynamia were studied in 109 white rats whose motor activity was severely restricted for up to 30 days. During the first five days myocardial catecholamine content, contractile function, and physical load tolerance decreased. Small doses of thyroidin counteracted this tendency. After 15 days, noradrenalin content and other indices approached normal levels and, after 30 days, were the same as control levels, although cardiac functional reserve was decreased. Thyroidin administration after 15 days had no noticeable effect. A detailed table shows changes in 17 indices of myocardial contractile function during hypodynamia
Hyperbolic chaos in self-oscillating systems based on mechanical triple linkage: Testing absence of tangencies of stable and unstable manifolds for phase trajectories
Dynamical equations are formulated and a numerical study is provided for
self-oscillatory model systems based on the triple linkage hinge mechanism of
Thurston -- Weeks -- Hunt -- MacKay. We consider systems with holonomic
mechanical constraint of three rotators as well as systems, where three
rotators interact by potential forces. We present and discuss some quantitative
characteristics of the chaotic regimes (Lyapunov exponents, power spectrum).
Chaotic dynamics of the models we consider are associated with hyperbolic
attractors, at least, at relatively small supercriticality of the
self-oscillating modes; that follows from numerical analysis of the
distribution for angles of intersection of stable and unstable manifolds of
phase trajectories on the attractors. In systems based on rotators with
interacting potential the hyperbolicity is violated starting from a certain
level of excitation.Comment: 30 pages, 18 figure
Limitations of PLL simulation: hidden oscillations in MatLab and SPICE
Nonlinear analysis of the phase-locked loop (PLL) based circuits is a
challenging task, thus in modern engineering literature simplified mathematical
models and simulation are widely used for their study. In this work the
limitations of numerical approach is discussed and it is shown that, e.g.
hidden oscillations may not be found by simulation. Corresponding examples in
SPICE and MatLab, which may lead to wrong conclusions concerning the
operability of PLL-based circuits, are presented
Electric double layer effect on observable characteristics of the tunnel current through a bridged electrochemical contact
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