131 research outputs found
Stochastic Resonance in Neuron Models: Endogenous Stimulation Revisited
The paradigm of stochastic resonance (SR)---the idea that signal detection
and transmission may benefit from noise---has met with great interest in both
physics and the neurosciences. We investigate here the consequences of reducing
the dynamics of a periodically driven neuron to a renewal process (stimulation
with reset or endogenous stimulation). This greatly simplifies the mathematical
analysis, but we show that stochastic resonance as reported earlier occurs in
this model only as a consequence of the reduced dynamics.Comment: Some typos fixed, esp. Eq. 15. Results and conclusions are not
affecte
Possible Origin of Stagnation and Variability of Earth's Biodiversity
The magnitude and variability of Earth's biodiversity have puzzled scientists
ever since paleontologic fossil databases became available. We identify and
study a model of interdependent species where both endogenous and exogenous
impacts determine the nonstationary extinction dynamics. The framework provides
an explanation for the qualitative difference of marine and continental
biodiversity growth. In particular, the stagnation of marine biodiversity may
result from a global transition from an imbalanced to a balanced state of the
species dependency network. The predictions of our framework are in agreement
with paleontologic databases.Comment: 5 pages, 6 pages supplemen
Unstable attractors induce perpetual synchronization and desynchronization
Common experience suggests that attracting invariant sets in nonlinear
dynamical systems are generally stable. Contrary to this intuition, we present
a dynamical system, a network of pulse-coupled oscillators, in which
\textit{unstable attractors} arise naturally. From random initial conditions,
groups of synchronized oscillators (clusters) are formed that send pulses
alternately, resulting in a periodic dynamics of the network. Under the
influence of arbitrarily weak noise, this synchronization is followed by a
desynchronization of clusters, a phenomenon induced by attractors that are
unstable. Perpetual synchronization and desynchronization lead to a switching
among attractors. This is explained by the geometrical fact, that these
unstable attractors are surrounded by basins of attraction of other attractors,
whereas the full measure of their own basin is located remote from the
attractor. Unstable attractors do not only exist in these systems, but moreover
dominate the dynamics for large networks and a wide range of parameters.Comment: 14 pages, 12 figure
Correlated microtiming deviations in jazz and rock music
Musical rhythms performed by humans typically show temporal fluctuations.
While they have been characterized in simple rhythmic tasks, it is an open
question what is the nature of temporal fluctuations, when several musicians
perform music jointly in all its natural complexity. To study such fluctuations
in over 100 original jazz and rock/pop recordings played with and without
metronome we developed a semi-automated workflow allowing the extraction of
cymbal beat onsets with millisecond precision. Analyzing the inter-beat
interval (IBI) time series revealed evidence for two long-range correlated
processes characterized by power laws in the IBI power spectral densities. One
process dominates on short timescales ( beats) and reflects microtiming
variability in the generation of single beats. The other dominates on longer
timescales and reflects slow tempo variations. Whereas the latter did not show
differences between musical genres (jazz vs. rock/pop), the process on short
timescales showed higher variability for jazz recordings, indicating that jazz
makes stronger use of microtiming fluctuations within a measure than rock/pop.
Our results elucidate principles of rhythmic performance and can inspire
algorithms for artificial music generation. By studying microtiming
fluctuations in original music recordings, we bridge the gap between
minimalistic tapping paradigms and expressive rhythmic performances
Long Chaotic Transients in Complex Networks
We show that long chaotic transients dominate the dynamics of randomly
diluted networks of pulse-coupled oscillators. This contrasts with the rapid
convergence towards limit cycle attractors found in networks of globally
coupled units. The lengths of the transients strongly depend on the network
connectivity and varies by several orders of magnitude, with maximum transient
lengths at intermediate connectivities. The dynamics of the transient exhibits
a novel form of robust synchronization. An approximation to the largest
Lyapunov exponent characterizing the chaotic nature of the transient dynamics
is calculated analytically.Comment: 4 pages; 5 figure
Quantum Reversibility: Is there an Echo?
We study the possibility to undo the quantum mechanical evolution in a time
reversal experiment. The naive expectation, as reflected in the common
terminology ("Loschmidt echo"), is that maximum compensation results if the
reversed dynamics extends to the same time as the forward evolution. We
challenge this belief, and demonstrate that the time for maximum return
probability is in general shorter. We find that depends on , being the ratio of the error in setting the parameters
(fields) for the time reversed evolution to the perturbation which is involved
in the preparation process. Our results should be observable in spin-echo
experiments where the dynamical irreversibility of quantum phases is measured.Comment: 4 pages, 4 figures, to be published in Phys. Rev. Let
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