433 research outputs found
Resonant control of stochastic spatio-temporal dynamics in a tunnel diode by multiple time delayed feedback
We study the control of noise-induced spatio-temporal current density
patterns in a semiconductor nanostructure (double barrier resonant tunnelling
diode) by multiple time-delayed feedback. We find much more pronounced resonant
features of noise-induced oscillations compared to single time feedback,
rendering the system more sensitive to variations in the delay time . The
coherence of noise-induced oscillations measured by the correlation time
exhibits sharp resonances as a function of , and can be strongly
increased by optimal choices of . Similarly, the peaks in the power
spectral density are sharpened. We provide analytical insight into the control
mechanism by relating the correlation times and mean frequencies of
noise-induced breathing oscillations to the stability properties of the
deterministic stationary current density filaments under the influence of the
control loop. Moreover, we demonstrate that the use of multiple time delays
enlarges the regime in which the deterministic dynamical properties of the
system are not changed by delay-induced bifurcations
Adaptive synchronization in delay-coupled networks of Stuart-Landau oscillators
We consider networks of delay-coupled Stuart-Landau oscillators. In these
systems, the coupling phase has been found to be a crucial control parameter.
By proper choice of this parameter one can switch between different synchronous
oscillatory states of the network. Applying the speed-gradient method, we
derive an adaptive algorithm for an automatic adjustment of the coupling phase
such that a desired state can be selected from an otherwise multistable regime.
We propose goal functions based on both the difference of the oscillators and a
generalized order parameter and demonstrate that the speed-gradient method
allows one to find appropriate coupling phases with which different states of
synchronization, e.g., in-phase oscillation, splay or various cluster states,
can be selected.Comment: 8 pages, 7 figure
A hybrid model for chaotic front dynamics: From semiconductors to water tanks
We present a general method for studying front propagation in nonlinear
systems with a global constraint in the language of hybrid tank models. The
method is illustrated in the case of semiconductor superlattices, where the
dynamics of the electron accumulation and depletion fronts shows complex
spatio-temporal patterns, including chaos. We show that this behavior may be
elegantly explained by a tank model, for which analytical results on the
emergence of chaos are available. In particular, for the case of three tanks
the bifurcation scenario is characterized by a modified version of the
one-dimensional iterated tent-map.Comment: 4 pages, 4 figure
Controlling surface morphologies by time-delayed feedback
We propose a new method to control the roughness of a growing surface, via a
time-delayed feedback scheme. As an illustration, we apply this method to the
Kardar-Parisi-Zhang equation in 1+1 dimensions and show that the effective
growth exponent of the surface width can be stabilized at any desired value in
the interval [0.25,0.33], for a significant length of time. The method is quite
general and can be applied to a wide range of growth phenomena. A possible
experimental realization is suggested.Comment: 4 pages, 3 figure
Control of coherence resonance in semiconductor superlattices
We study the effect of time-delayed feedback control and Gaussian white noise
on the spatio-temporal charge dynamics in a semiconductor superlattice. The
system is prepared in a regime where the deterministic dynamics is close to a
global bifurcation, namely a saddle-node bifurcation on a limit cycle ({\it
SNIPER}). In the absence of control, noise can induce electron charge front
motion through the entire device, and coherence resonance is observed. We show
that with appropriate selection of the time-delayed feedback parameters the
effect of coherence resonance can either be enhanced or destroyed, and the
coherence of stochastic domain motion at low noise intensity is dramatically
increased. Additionally, the purely delay-induced dynamics in the system is
investigated, and a homoclinic bifurcation of a limit cycle is found.Comment: 7 pages, 7 figure
Symmetry-breaking transitions in networks of nonlinear circuit elements
We investigate a nonlinear circuit consisting of N tunnel diodes in series,
which shows close similarities to a semiconductor superlattice or to a neural
network. Each tunnel diode is modeled by a three-variable FitzHugh-Nagumo-like
system. The tunnel diodes are coupled globally through a load resistor. We find
complex bifurcation scenarios with symmetry-breaking transitions that generate
multiple fixed points off the synchronization manifold. We show that multiply
degenerate zero-eigenvalue bifurcations occur, which lead to multistable
current branches, and that these bifurcations are also degenerate with a Hopf
bifurcation. These predicted scenarios of multiple branches and degenerate
bifurcations are also found experimentally.Comment: 32 pages, 11 figures, 7 movies available as ancillary file
Feedback control of flow alignment in sheared liquid crystals
Based on a continuum theory, we investigate the manipulation of the
non-equilibrium behavior of a sheared liquid crystal via closed-loop feedback
control. Our goal is to stabilize a specific dynamical state, that is, the
stationary "flow-alignment", under conditions where the uncontrolled system
displays oscillatory director dynamics with in-plane symmetry. To this end we
employ time-delayed feedback control (TDFC), where the equation of motion for
the ith component, q_i(t), of the order parameter tensor is supplemented by a
control term involving the difference q_i(t)-q_i(t-\tau). In this diagonal
scheme, \tau is the delay time. We demonstrate that the TDFC method
successfully stabilizes flow alignment for suitable values of the control
strength, K, and \tau; these values are determined by solving an exact
eigenvalue equation. Moreover, our results show that only small values of K are
needed when the system is sheared from an isotropic equilibrium state, contrary
to the case where the equilibrium state is nematic
Adaptive Tuning of Feedback Gain in Time-Delayed Feedback Control
We demonstrate that time-delayed feedback control can be improved by
adaptively tuning the feedback gain. This adaptive controller is applied to the
stabilization of an unstable fixed point and an unstable periodic orbit
embedded in a chaotic attractor. The adaptation algorithm is constructed using
the speed-gradient method of control theory. Our computer simulations show that
the adaptation algorithm can find an appropriate value of the feedback gain for
single and multiple delays. Furthermore, we show that our method is robust to
noise and different initial conditions.Comment: 7 pages, 6 figure
A proof of Jarzynski's non-equilibrium work theorem for dynamical systems that conserve the canonical distribution
We present a derivation of the Jarzynski identity and the Crooks fluctuation
theorem for systems governed by deterministic dynamics that conserves the
canonical distribution such as Hamiltonian dynamics, Nose-Hoover dynamics,
Nose-Hoover chains and Gaussian isokinetic dynamics. The proof is based on a
relation between the heat absorbed by the system during the non-equilibrium
process and the Jacobian of the phase flow generated by the dynamics.Comment: 12 page
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