75 research outputs found
Self-induced switchings between multiple space-time patterns on complex networks of excitable units
We report on self-induced switchings between multiple distinct space--time
patterns in the dynamics of a spatially extended excitable system. These
switchings between low-amplitude oscillations, nonlinear waves, and extreme
events strongly resemble a random process, although the system is
deterministic. We show that a chaotic saddle -- which contains all the patterns
as well as channel-like structures that mediate the transitions between them --
is the backbone of such a pattern switching dynamics. Our analyses indicate
that essential ingredients for the observed phenomena are that the system
behaves like an inhomogeneous oscillatory medium that is capable of
self-generating spatially localized excitations and that is dominated by
short-range connections but also features long-range connections. With our
findings, we present an alternative to the well-known ways to obtain
self-induced pattern switching, namely noise-induced attractor hopping,
heteroclinic orbits, and adaptation to an external signal. This alternative way
can be expected to improve our understanding of pattern switchings in spatially
extended natural dynamical systems like the brain and the heart
Detecting directional coupling in the human epileptic brain: Limitations and potential pitfalls
We study directional relationshipsâin the driver-responder senseâin networks of coupled nonlinear oscillators using a phase modeling approach. Specifically, we focus on the identification of drivers in clusters with varying levels of synchrony, mimicking dynamical interactions between the seizure generating region (epileptic focus) and other brain structures. We demonstrate numerically that such an identification is not always possible in a reliable manner. Using the same analysis techniques as in model systems, we study multichannel electroencephalographic recordings from two patients suffering from focal epilepsy. Our findings demonstrate thatâdepending on the degree of intracluster synchronyâcertain subsystems can spuriously appear to be driving others, which should be taken into account when analyzing field data with unknown underlying dynamics
Unraveling Spurious Properties of Interaction Networks with Tailored Random Networks
We investigate interaction networks that we derive from multivariate time
series with methods frequently employed in diverse scientific fields such as
biology, quantitative finance, physics, earth and climate sciences, and the
neurosciences. Mimicking experimental situations, we generate time series with
finite length and varying frequency content but from independent stochastic
processes. Using the correlation coefficient and the maximum cross-correlation,
we estimate interdependencies between these time series. With clustering
coefficient and average shortest path length, we observe unweighted interaction
networks, derived via thresholding the values of interdependence, to possess
non-trivial topologies as compared to Erd\H{o}s-R\'{e}nyi networks, which would
indicate small-world characteristics. These topologies reflect the mostly
unavoidable finiteness of the data, which limits the reliability of typically
used estimators of signal interdependence. We propose random networks that are
tailored to the way interaction networks are derived from empirical data.
Through an exemplary investigation of multichannel electroencephalographic
recordings of epileptic seizures - known for their complex spatial and temporal
dynamics - we show that such random networks help to distinguish network
properties of interdependence structures related to seizure dynamics from those
spuriously induced by the applied methods of analysis
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