1,634 research outputs found
Failure of Delayed Feedback Deep Brain Stimulation for Intermittent Pathological Synchronization in Parkinson's Disease
Suppression of excessively synchronous beta-band oscillatory activity in the
brain is believed to suppress hypokinetic motor symptoms of Parkinson's
disease. Recently, a lot of interest has been devoted to desynchronizing
delayed feedback deep brain stimulation (DBS). This type of synchrony control
was shown to destabilize the synchronized state in networks of simple model
oscillators as well as in networks of coupled model neurons. However, the
dynamics of the neural activity in Parkinson's disease exhibits complex
intermittent synchronous patterns, far from the idealized synchronous dynamics
used to study the delayed feedback stimulation. This study explores the action
of delayed feedback stimulation on partially synchronized oscillatory dynamics,
similar to what one observes experimentally in parkinsonian patients. We employ
a model of the basal ganglia networks which reproduces experimentally observed
fine temporal structure of the synchronous dynamics. When the parameters of our
model are such that the synchrony is unphysiologically strong, the feedback
exerts a desynchronizing action. However, when the network is tuned to
reproduce the highly variable temporal patterns observed experimentally, the
same kind of delayed feedback may actually increase the synchrony. As network
parameters are changed from the range which produces complete synchrony to
those favoring less synchronous dynamics, desynchronizing delayed feedback may
gradually turn into synchronizing stimulation. This suggests that delayed
feedback DBS in Parkinson's disease may boost rather than suppress
synchronization and is unlikely to be clinically successful. The study also
indicates that delayed feedback stimulation may not necessarily exhibit a
desynchronization effect when acting on a physiologically realistic partially
synchronous dynamics, and provides an example of how to estimate the
stimulation effect.Comment: 19 pages, 8 figure
Desynchronization of systems of coupled Hindmarsh-Rose oscillators
It is widely assumed that neural activity related to synchronous rhythms of
large portions of neurons in specific locations of the brain is responsible for
the pathology manifested in patients' uncontrolled tremor and other similar
diseases. To model such systems Hindmarsh-Rose (HR) oscillators are considered
as appropriate as they mimic the qualitative behaviour of neuronal firing. Here
we consider a large number of identical HR-oscillators interacting through the
mean field created by the corresponding components of all oscillators.
Introducing additional coupling by feedback of Pyragas type, proportional to
the difference between the current value of the mean-field and its value some
time in the past, Rosenblum and Pikovsky (Phys. Rev. E 70, 041904, 2004)
demonstrated that the desirable desynchronization could be achieved with
appropriate set of parameters for the system. Following our experience with
stabilization of unstable steady states in dynamical systems, we show that by
introducing a variable delay, desynchronization is obtainable for much wider
range of parameters and that at the same time it becomes more pronounced.Comment: 5 pages, 2 figures, RevTe
Synchronization in model networks of class I neurons
We study a modification of the Hoppensteadt-Izhikevich canonical model for networks of class I neurons, in which the 'pulse' emitted by a neuron is smooth rather than a delta-function. We prove two types of results about synchronization and desynchronization of such networks, the first type pertaining to 'pulse' functions which are symmetric, and the other type in the regime in which each neuron is connected to many other neurons
Symmetries, Cluster Synchronization, and Isolated Desynchronization in Complex Networks
Synchronization is of central importance in power distribution,
telecommunication, neuronal, and biological networks. Many networks are
observed to produce patterns of synchronized clusters, but it has been
difficult to predict these clusters or understand the conditions under which
they form, except for in the simplest of networks. In this article, we shed
light on the intimate connection between network symmetry and cluster
synchronization. We introduce general techniques that use network symmetries to
reveal the patterns of synchronized clusters and determine the conditions under
which they persist. The connection between symmetry and cluster synchronization
is experimentally explored using an electro-optic network. We experimentally
observe and theoretically predict a surprising phenomenon in which some
clusters lose synchrony while leaving others synchronized. The results could
guide the design of new power grid systems or lead to new understanding of the
dynamical behavior of networks ranging from neural to social
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