1,642 research outputs found
Geometric Analysis of Synchronization in Neuronal Networks with Global Inhibition and Coupling Delays
We study synaptically coupled neuronal networks to identify the role of
coupling delays in network's synchronized behaviors. We consider a network of
excitable, relaxation oscillator neurons where two distinct populations, one
excitatory and one inhibitory, are coupled and interact with each other. The
excitatory population is uncoupled, while the inhibitory population is tightly
coupled. A geometric singular perturbation analysis yields existence and
stability conditions for synchronization states under different firing patterns
between the two populations, along with formulas for the periods of such
synchronous solutions. Our results demonstrate that the presence of coupling
delays in the network promotes synchronization. Numerical simulations are
conducted to supplement and validate analytical results. We show the results
carry over to a model for spindle sleep rhythms in thalamocortical networks,
one of the biological systems which motivated our study. The analysis helps to
explain how coupling delays in either excitatory or inhibitory synapses
contribute to producing synchronized rhythms.Comment: 43 pages, 12 figure
Collective dynamics of two-mode stochastic oscillators
We study a system of two-mode stochastic oscillators coupled through their
collective output. As a function of a relevant parameter four qualitatively
distinct regimes of collective behavior are observed. In an extended region of
the parameter space the periodicity of the collective output is enhanced by the
considered coupling. This system can be used as a new model to describe
synchronization-like phenomena in systems of units with two or more oscillation
modes. The model can also explain how periodic dynamics can be generated by
coupling largely stochastic units. Similar systems could be responsible for the
emergence of rhythmic behavior in complex biological or sociological systems.Comment: 4 pages, RevTex, 5 figure
The role of intermediaries in the synchronization of pulse-coupled oscillators
The role of intermediaries in the synchronization of small groups of light
controlled oscillators (LCO) is addressed. A single LCO is a two-time-scale
phase oscillator. When pulse-coupling two LCOs, the synchronization time
decreases monotonously as the coupling strength increases, independent of the
initial conditions and frequency detuning. In this work we study numerically
the effects that a third LCO induces to the collective behavior of the system.
We analyze the new system by dealing with directed heterogeneous couplings
among the units. We report a novel and robust phenomenon, absent when coupling
two LCOs, which consists of a discontinuous relationship between the
synchronization time and coupling strength or initial conditions. The mechanism
responsible for the appearance of such discontinuities is discussed.Comment: 11 pages, 8 figure
Zero-lag long-range synchronization via dynamical relaying
We show that simultaneous synchronization between two delay-coupled
oscillators can be achieved by relaying the dynamics via a third mediating
element, which surprisingly lags behind the synchronized outer elements. The
zero-lag synchronization thus obtained is robust over a considerable parameter
range. We substantiate our claims with experimental and numerical evidence of
these synchronization solutions in a chain of three coupled semiconductor
lasers with long inter-element coupling delays. The generality of the mechanism
is validated in a neuronal model with the same coupling architecture. Thus, our
results show that synchronized dynamical states can occur over long distances
through relaying, without restriction by the amount of delay.Comment: 10 pages, 4 figure
Analysis of self-oscillating DC-DC resonant power converters using a hysteretic relay
The paper presents a technique for exciting resonant DC-DC converters in a self-oscillating manner. The analysis necessary to predict the behaviour of such converters is also given. The oscillation is based on the behaviour of a hysteretic relay with a negative hysteresis transition. Self-oscillating converters benefit from higher efficiency/higher power density than their non-self-oscillating counterparts as they can be operated closer to the tank resonant frequency. The self-oscillating mechanism presented here is also simple and cost effective to implement. A prototype converter is presented in order to verify the theoretical claims
The role of inhibitory feedback for information processing in thalamocortical circuits
The information transfer in the thalamus is blocked dynamically during sleep,
in conjunction with the occurence of spindle waves. As the theoretical
understanding of the mechanism remains incomplete, we analyze two modeling
approaches for a recent experiment by Le Masson {\sl et al}. on the
thalamocortical loop. In a first step, we use a conductance-based neuron model
to reproduce the experiment computationally. In a second step, we model the
same system by using an extended Hindmarsh-Rose model, and compare the results
with the conductance-based model. In the framework of both models, we
investigate the influence of inhibitory feedback on the information transfer in
a typical thalamocortical oscillator. We find that our extended Hindmarsh-Rose
neuron model, which is computationally less costly and thus siutable for
large-scale simulations, reproduces the experiment better than the
conductance-based model. Further, in agreement with the experiment of Le Masson
{\sl et al}., inhibitory feedback leads to stable self-sustained oscillations
which mask the incoming input, and thereby reduce the information transfer
significantly.Comment: 16 pages, 15eps figures included. To appear in Physical Review
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