86 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 relationships—in the driver-responder sense—in 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 that—depending on the degree of intracluster synchrony—certain subsystems can spuriously appear to be driving others, which should be taken into account when analyzing field data with unknown underlying dynamics
Internetwork and intranetwork communications during bursting dynamics: Applications to seizure prediction
We use a simple dynamical model of two interacting networks of integrate-and-fire neurons to explain a seemingly paradoxical result observed in epileptic patients indicating that the level of phase synchrony declines below normal levels during the state preceding seizures (preictal state). We model the transition from the seizure free interval (interictal state) to the seizure (ictal state) as a slow increase in the mean depolarization of neurons in a network corresponding to the epileptic focus. We show that the transition from the interictal to preictal and then to the ictal state may be divided into separate dynamical regimes: the formation of slow oscillatory activity due to resonance between the two interacting networks observed during the interictal period, structureless activity during the preictal period when the two networks have different properties, and bursting dynamics driven by the network corresponding to the epileptic focus. Based on this result, we hypothesize that the beginning of the preictal period marks the beginning of the transition of the epileptic network from normal activity toward seizing
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