319 research outputs found
Two distinct desynchronization processes caused by lesions in globally coupled neurons
To accomplish a task, the brain works like a synchronized neuronal network
where all the involved neurons work together. When a lesion spreads in the
brain, depending on its evolution, it can reach a significant portion of
relevant area. As a consequence, a phase transition might occur: the neurons
desynchronize and cannot perform a certain task anymore. Lesions are
responsible for either disrupting the neuronal connections or, in some cases,
for killing the neuron. In this work, we will use a simplified model of
neuronal network to show that these two types of lesions cause different types
of desynchronization.Comment: 5 pages, 3 figure
Synchronization of phase oscillators due to nonlocal coupling mediated by the slow diffusion of a substance
Many systems of physical and biological interest are characterized by
assemblies of phase oscillators whose interaction is mediated by a diffusing
chemical. The coupling effect results from the fact that the local
concentration of the mediating chemical affects both its production and
absorption by each oscillator. Since the chemical diffuses through the medium
in which the oscillators are embedded, the coupling among oscillators is
non-local: it considers all the oscillators depending on their relative spatial
distances. We considered a mathematical model for this coupling, when the
diffusion time is arbitrary with respect to the characteristic oscillator
periods, yielding a system of coupled nonlinear integro-differential equations
which can be solved using Green functions for appropriate boundary conditions.
In this paper we show numerical solutions of these equations for three finite
domains: a linear one-dimensional interval, a rectangular, and a circular
region, with absorbing boundary conditions. From the numerical solutions we
investigate phase and frequency synchronization of the oscillators, with
respect to changes in the coupling parameters for the three considered
geometries
Phase synchronization of coupled bursting neurons and the generalized Kuramoto model
Bursting neurons fire rapid sequences of action potential spikes followed by
a quiescent period. The basic dynamical mechanism of bursting is the slow
currents that modulate a fast spiking activity caused by rapid ionic currents.
Minimal models of bursting neurons must include both effects. We considered one
of these models and its relation with a generalized Kuramoto model, thanks to
the definition of a geometrical phase for bursting and a corresponding
frequency. We considered neuronal networks with different connection topologies
and investigated the transition from a non-synchronized to a partially
phase-synchronized state as the coupling strength is varied. The numerically
determined critical coupling strength value for this transition to occur is
compared with theoretical results valid for the generalized Kuramoto model.Comment: 31 pages, 5 figure
Hamiltonian description for magnetic field lines: a tutorial
Under certain circumstances, the equations for the magnetic field lines can
be recast in a canonical form, after defining a suitable field line
Hamiltonian. This analogy is extremely useful for dealing with a variety of
problems involving magnetically confined plasmas, like in tokamaks and other
toroidal devices, where there is usually one symmetric coordinate which plays
the role of time in the canonical equations. In this tutorial paper we review
the basics of the Hamiltonian description for magnetic field lines, emphasizing
the role of a variational principle and gauge invariance. We present
representative applications of the formalism, using cylindrical and magnetic
flux coordinates in tokamak plasmas
Intermingled basins in coupled Lorenz systems
We consider a system of two identical linearly coupled Lorenz oscillators,
presenting synchro- nization of chaotic motion for a specified range of the
coupling strength. We verify the existence of global synchronization and
antisynchronization attractors with intermingled basins of attraction, such
that the basin of one attractor is riddled with holes belonging to the basin of
the other attractor and vice versa. We investigated this phenomenon by
verifying the fulfillment of the mathematical requirements for intermingled
basins, and also obtained scaling laws that characterize quantitatively the
riddling of both basins for this system
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