1,645 research outputs found

### Heating and thermal squeezing in parametrically-driven oscillators with added noise

In this paper we report a theoretical model based on Green functions, Floquet
theory and averaging techniques up to second order that describes the dynamics
of parametrically-driven oscillators with added thermal noise. Quantitative
estimates for heating and quadrature thermal noise squeezing near and below the
transition line of the first parametric instability zone of the oscillator are
given. Furthermore, we give an intuitive explanation as to why heating and
thermal squeezing occur. For small amplitudes of the parametric pump the
Floquet multipliers are complex conjugate of each other with a constant
magnitude. As the pump amplitude is increased past a threshold value in the
stable zone near the first parametric instability, the two Floquet multipliers
become real and have different magnitudes. This creates two different effective
dissipation rates (one smaller and the other larger than the real dissipation
rate) along the stable manifolds of the first-return Poincare map. We also show
that the statistical average of the input power due to thermal noise is
constant and independent of the pump amplitude and frequency. The combination
of these effects cause most of heating and thermal squeezing. Very good
agreement between analytical and numerical estimates of the thermal
fluctuations is achieved.Comment: Submitted to Phys. Rev. E, 29 pages, 12 figures. arXiv admin note:
substantial text overlap with arXiv:1108.484

### Mixed-mode oscillations in a multiple time scale phantom bursting system

In this work we study mixed mode oscillations in a model of secretion of GnRH
(Gonadotropin Releasing Hormone). The model is a phantom burster consisting of
two feedforward coupled FitzHugh-Nagumo systems, with three time scales. The
forcing system (Regulator) evolves on the slowest scale and acts by moving the
slow nullcline of the forced system (Secretor). There are three modes of
dynamics: pulsatility (transient relaxation oscillation), surge (quasi steady
state) and small oscillations related to the passage of the slow nullcline
through a fold point of the fast nullcline. We derive a variety of reductions,
taking advantage of the mentioned features of the system. We obtain two
results; one on the local dynamics near the fold in the parameter regime
corresponding to the presence of small oscillations and the other on the global
dynamics, more specifically on the existence of an attracting limit cycle. Our
local result is a rigorous characterization of small canards and sectors of
rotation in the case of folded node with an additional time scale, a feature
allowing for a clear geometric argument. The global result gives the existence
of an attracting unique limit cycle, which, in some parameter regimes, remains
attracting and unique even during passages through a canard explosion.Comment: 38 pages, 16 figure

### Smoothing tautologies, hidden dynamics, and sigmoid asymptotics for piecewise smooth systems

Switches in real systems take many forms, such as impacts, electronic relays,
mitosis, and the implementation of decisions or control strategies. To
understand what is lost, and what can be retained, when we model a switch as an
instantaneous event, requires a consideration of so-called hidden terms. These
are asymptotically vanishing outside the switch, but can be encoded in the form
of nonlinear switching terms. A general expression for the switch can be
developed in the form of a series of sigmoid functions. We review the key steps
in extending the Filippov's method of sliding modes to such systems. We show
how even slight nonlinear effects can hugely alter the behaviour of an
electronic control circuit, and lead to `hidden' attractors inside the
switching surface.Comment: 12 page

### Time-Scale and Noise Optimality in Self-Organized Critical Adaptive Networks

Recent studies have shown that adaptive networks driven by simple local rules
can organize into "critical" global steady states, providing another framework
for self-organized criticality (SOC). We focus on the important convergence to
criticality and show that noise and time-scale optimality are reached at finite
values. This is in sharp contrast to the previously believed optimal zero noise
and infinite time scale separation case. Furthermore, we discover a noise
induced phase transition for the breakdown of SOC. We also investigate each of
the three new effects separately by developing models. These models reveal
three generically low-dimensional dynamical behaviors: time-scale resonance
(TR), a new simplified version of stochastic resonance - which we call steady
state stochastic resonance (SSR) - as well as noise-induced phase transitions.Comment: 4 pages, 6 figures; several changes in exposition and focus on
applications in revised versio

### The phase-space of generalized Gauss-Bonnet dark energy

The generalized Gauss-Bonnet theory, introduced by Lagrangian F(R,G), has
been considered as a general modified gravity for explanation of the dark
energy. G is the Gauss-Bonnet invariant. For this model, we seek the situations
under which the late-time behavior of the theory is the de-Sitter space-time.
This is done by studying the two dimensional phase space of this theory, i.e.
the R-H plane. By obtaining the conditions under which the de-Sitter space-time
is the stable attractor of this theory, several aspects of this problem have
been investigated. It has been shown that there exist at least two classes of
stable attractors : the singularities of the F(R,G), and the cases in which the
model has a critical curve, instead of critical points. This curve is R=12H^2
in R-H plane. Several examples, including their numerical calculations, have
been discussed.Comment: 19 pages, 11 figures, typos corrected, a reference adde

### Simplification of the tug-of-war model for cellular transport in cells

The transport of organelles and vesicles in living cells can be well
described by a kinetic tug-of-war model advanced by M\"uller, Klumpp and
Lipowsky. In which, the cargo is attached by two motor species, kinesin and
dynein, and the direction of motion is determined by the number of motors which
bind to the track. In recent work [Phys. Rev. E 79, 061918 (2009)], this model
was studied by mean field theory, and it was found that, usually the tug-of-war
model has one, two, or three distinct stable stationary points. However, the
results there are mostly obtained by numerical calculations, since it is hard
to do detailed theoretical studies to a two-dimensional nonlinear system. In
this paper, we will carry out further detailed analysis about this model, and
try to find more properties theoretically. Firstly, the tug-of-war model is
simplified to a one-dimensional equation. Then we claim that the stationary
points of the tug-of-war model correspond to the roots of the simplified
equation, and the stable stationary points correspond to the roots with
positive derivative. Bifurcation occurs at the corresponding parameters, under
which the simplified one-dimensional equation exists root with zero derivative.
Using the simplified equation, not only more properties of the tug-of-war model
can be obtained analytically, the related numerical calculations will become
more accurate and more efficient. This simplification will be helpful to future
studies of the tug-of-war model

### Anomalous exponents at the onset of an instability

Critical exponents are calculated exactly at the onset of an instability,
using asymptotic expansiontechniques. When the unstable mode is subject to
multiplicative noise whose spectrum at zero frequency vanishes, we show that
the critical behavior can be anomalous, i.e. the mode amplitude X scales with
departure from onset \mu as $~ \mu^\beta$ with an exponent $\beta$
different from its deterministic value. This behavior is observed in a direct
numerical simulation of the dynamo instability and our results provide a
possible explanation to recent experimental observations

### Exploring constrained quantum control landscapes

The broad success of optimally controlling quantum systems with external
fields has been attributed to the favorable topology of the underlying control
landscape, where the landscape is the physical observable as a function of the
controls. The control landscape can be shown to contain no suboptimal trapping
extrema upon satisfaction of reasonable physical assumptions, but this
topological analysis does not hold when significant constraints are placed on
the control resources. This work employs simulations to explore the topology
and features of the control landscape for pure-state population transfer with a
constrained class of control fields. The fields are parameterized in terms of a
set of uniformly spaced spectral frequencies, with the associated phases acting
as the controls. Optimization results reveal that the minimum number of phase
controls necessary to assure a high yield in the target state has a special
dependence on the number of accessible energy levels in the quantum system,
revealed from an analysis of the first- and second-order variation of the yield
with respect to the controls. When an insufficient number of controls and/or a
weak control fluence are employed, trapping extrema and saddle points are
observed on the landscape. When the control resources are sufficiently
flexible, solutions producing the globally maximal yield are found to form
connected `level sets' of continuously variable control fields that preserve
the yield. These optimal yield level sets are found to shrink to isolated
points on the top of the landscape as the control field fluence is decreased,
and further reduction of the fluence turns these points into suboptimal
trapping extrema on the landscape. Although constrained control fields can come
in many forms beyond the cases explored here, the behavior found in this paper
is illustrative of the impacts that constraints can introduce.Comment: 10 figure

### Delay-induced multistability near a global bifurcation

We study the effect of a time-delayed feedback within a generic model for a
saddle-node bifurcation on a limit cycle. Without delay the only attractor
below this global bifurcation is a stable node. Delay renders the phase space
infinite-dimensional and creates multistability of periodic orbits and the
fixed point. Homoclinic bifurcations, period-doubling and saddle-node
bifurcations of limit cycles are found in accordance with Shilnikov's theorems.Comment: Int. J. Bif. Chaos (2007), in prin

- â€¦