667 research outputs found
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 structure of cavity soliton dynamics in a VCSEL with saturable absorber and time-delayed feedback
We consider a wide-aperture surface-emitting laser with a saturable absorber
section subjected to time-delayed feedback. We adopt the mean-field approach
assuming a single longitudinal mode operation of the solitary VCSEL. We
investigate cavity soliton dynamics under the effect of time- delayed feedback
in a self-imaging configuration where diffraction in the external cavity is
negligible. Using bifurcation analysis, direct numerical simulations and
numerical path continuation methods, we identify the possible bifurcations and
map them in a plane of feedback parameters. We show that for both the
homogeneous and localized stationary lasing solutions in one spatial dimension
the time-delayed feedback induces complex spatiotemporal dynamics, in
particular a period doubling route to chaos, quasiperiodic oscillations and
multistability of the stationary solutions
Symmetric bifurcation analysis of synchronous states of time-delayed coupled Phase-Locked Loop oscillators
In recent years there has been an increasing interest in studying
time-delayed coupled networks of oscillators since these occur in many real
life applications. In many cases symmetry patterns can emerge in these
networks, as a consequence a part of the system might repeat itself, and
properties of this subsystem are representative of the dynamics on the whole
phase space. In this paper an analysis of the second order N-node time-delay
fully connected network is presented which is based on previous work by Correa
and Piqueira \cite{Correa2013} for a 2-node network. This study is carried out
using symmetry groups. We show the existence of multiple eigenvalues forced by
symmetry, as well as the existence of Hopf bifurcations. Three different models
are used to analyze the network dynamics, namely, the full-phase, the phase,
and the phase-difference model. We determine a finite set of frequencies
, that might correspond to Hopf bifurcations in each case for critical
values of the delay. The map is used to actually find Hopf bifurcations
along with numerical calculations using the Lambert W function. Numerical
simulations are used in order to confirm the analytical results. Although we
restrict attention to second order nodes, the results could be extended to
higher order networks provided the time-delay in the connections between nodes
remains equal.Comment: 41 pages, 18 figure
The Dynamics of Hybrid Metabolic-Genetic Oscillators
The synthetic construction of intracellular circuits is frequently hindered
by a poor knowledge of appropriate kinetics and precise rate parameters. Here,
we use generalized modeling (GM) to study the dynamical behavior of topological
models of a family of hybrid metabolic-genetic circuits known as
"metabolators." Under mild assumptions on the kinetics, we use GM to
analytically prove that all explicit kinetic models which are topologically
analogous to one such circuit, the "core metabolator," cannot undergo Hopf
bifurcations. Then, we examine more detailed models of the metabolator.
Inspired by the experimental observation of a Hopf bifurcation in a
synthetically constructed circuit related to the core metabolator, we apply GM
to identify the critical components of the synthetically constructed
metabolator which must be reintroduced in order to recover the Hopf
bifurcation. Next, we study the dynamics of a re-wired version of the core
metabolator, dubbed the "reverse" metabolator, and show that it exhibits a
substantially richer set of dynamical behaviors, including both local and
global oscillations. Prompted by the observation of relaxation oscillations in
the reverse metabolator, we study the role that a separation of genetic and
metabolic time scales may play in its dynamics, and find that widely separated
time scales promote stability in the circuit. Our results illustrate a generic
pipeline for vetting the potential success of a potential circuit design,
simply by studying the dynamics of the corresponding generalized model
Coherent Pattern Prediction in Swarms of Delay-Coupled Agents
We consider a general swarm model of self-propelling agents interacting
through a pairwise potential in the presence of noise and communication time
delay. Previous work [Phys. Rev. E 77, 035203(R) (2008)] has shown that a
communication time delay in the swarm induces a pattern bifurcation that
depends on the size of the coupling amplitude. We extend these results by
completely unfolding the bifurcation structure of the mean field approximation.
Our analysis reveals a direct correspondence between the different dynamical
behaviors found in different regions of the coupling-time delay plane with the
different classes of simulated coherent swarm patterns. We derive the
spatio-temporal scales of the swarm structures, and also demonstrate how the
complicated interplay of coupling strength, time delay, noise intensity, and
choice of initial conditions can affect the swarm. In particular, our studies
show that for sufficiently large values of the coupling strength and/or the
time delay, there is a noise intensity threshold that forces a transition of
the swarm from a misaligned state into an aligned state. We show that this
alignment transition exhibits hysteresis when the noise intensity is taken to
be time dependent
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