86 research outputs found
Period-doubling bifurcations and islets of stability in two-degree-of-freedom Hamiltonian systems
In this paper, we show that the destruction of the main KAM islands in
two-degree-of-freedom Hamiltonian systems occurs through a cascade of
period-doubling bifurcations. We calculate the corresponding Feigenbaum
constant and the accumulation point of the period-doubling sequence. By means
of a systematic grid search on exit basin diagrams, we find the existence of
numerous very small KAM islands ('islets') for values below and above the
aforementioned accumulation point. We study the bifurcations involving the
formation of islets and we classify them in three different types. Finally, we
show that the same types of islets appear in generic two-degree-of-freedom
Hamiltonian systems and in area-preserving maps
Stochastic amplification of fluctuations in cortical up-states
Supporting Information: Appendix S1-S7Cortical neurons are bistable; as a consequence their local field potentials can fluctuate between quiescent and active states, generating slow 0.5-2 Hz oscillations which are widely known as transitions between Up and Down States. Despite a large number of studies on Up-Down transitions, deciphering its nature, mechanisms and function are still today challenging tasks. In this paper we focus on recent experimental evidence, showing that a class of spontaneous oscillations can emerge within the Up states. In particular, a non-trivial peak around 20 Hz appears in their associated power-spectra, what produces an enhancement of the activity power for higher frequencies (in the 30-90 Hz band). Moreover, this rhythm within Ups seems to be an emergent or collective phenomenon given that individual neurons do not lock to it as they remain mostly unsynchronized. Remarkably, similar oscillations (and the concomitant peak in the spectrum) do not appear in the Down states. Here we shed light on these findings by using different computational models for the dynamics of cortical networks in presence of different levels of physiological complexity. Our conclusion, supported by both theory and simulations, is that the collective phenomenon of >stochastic amplification of fluctuations> - previously described in other contexts such as Ecology and Epidemiology - explains in an elegant and parsimonious manner, beyond model-dependent details, this extra-rhythm emerging only in the Up states but not in the Downs. © 2012 Hidalgo et al.Funding provided by Spanish MICINN-FEDER under project FIS2009-08451 and Junta de Andalucia Proyecto de Excelencia P09FQM-4682. L.S. acknowledges the financial support of Fundacion P. Barrie de la Maza and funding grant 01GQ1001A.Peer Reviewe
Energy-based stochastic resetting can avoid noise-enhanced stability
The theory of stochastic resetting asserts that restarting a stochastic
process can expedite its completion. In this paper, we study the escape process
of a Brownian particle in an open Hamiltonian system that suffers
noise-enhanced stability. This phenomenon implies that under specific noise
amplitudes the escape process is delayed. Here, we propose a new protocol for
stochastic resetting that can avoid the noise-enhanced stability effect. In our
approach, instead of resetting the trajectories at certain time intervals, a
trajectory is reset when a predefined energy threshold is reached. The
trajectories that delay the escape process are the ones that lower their energy
due to the stochastic fluctuations. Our resetting approach leverages this fact
and avoids long transients by resetting trajectories before they reach low
energy levels. Finally, we show that the chaotic dynamics (i.e., the sensitive
dependence on initial conditions) catalyzes the effectiveness of the resetting
strategy
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