6,635 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
Onset of Phase Synchronization in Neurons Conneted via Chemical Synapses
We study the onset of synchronous states in realistic chaotic neurons coupled
by mutually inhibitory chemical synapses. For the realistic parameters, namely
the synaptic strength and the intrinsic current, this synapse introduces
non-coherences in the neuronal dynamics, yet allowing for chaotic phase
synchronization in a large range of parameters. As we increase the synaptic
strength, the neurons undergo to a periodic state, and no chaotic complete
synchronization is found.Comment: to appear in Int. J. Bif. Chao
Collective Almost Synchronization in Complex Networks
This work introduces the phenomenon of Collective Almost Synchronization
(CAS), which describes a universal way of how patterns can appear in complex
networks even for small coupling strengths. The CAS phenomenon appears due to
the existence of an approximately constant local mean field and is
characterized by having nodes with trajectories evolving around periodic stable
orbits. Common notion based on statistical knowledge would lead one to
interpret the appearance of a local constant mean field as a consequence of the
fact that the behavior of each node is not correlated to the behaviors of the
others. Contrary to this common notion, we show that various well known weaker
forms of synchronization (almost, time-lag, phase synchronization, and
generalized synchronization) appear as a result of the onset of an almost
constant local mean field. If the memory is formed in a brain by minimising the
coupling strength among neurons and maximising the number of possible patterns,
then the CAS phenomenon is a plausible explanation for it.Comment: 3 figure
The role of ongoing dendritic oscillations in single-neuron dynamics
The dendritic tree contributes significantly to the elementary computations a neuron performs while converting its synaptic inputs into action potential output. Traditionally, these computations have been characterized as temporally local, near-instantaneous mappings from the current input of the cell to its current output, brought about by somatic summation of dendritic contributions that are generated in spatially localized functional compartments. However, recent evidence about the presence of oscillations in dendrites suggests a qualitatively different mode of operation: the instantaneous phase of such oscillations can depend on a long history of inputs, and under appropriate conditions, even dendritic oscillators that are remote may interact through synchronization. Here, we develop a mathematical framework to analyze the interactions of local dendritic oscillations, and the way these interactions influence single cell computations. Combining weakly coupled oscillator methods with cable theoretic arguments, we derive phase-locking states for multiple oscillating dendritic compartments. We characterize how the phase-locking properties depend on key parameters of the oscillating dendrite: the electrotonic properties of the (active) dendritic segment, and the intrinsic properties of the dendritic oscillators. As a direct consequence, we show how input to the dendrites can modulate phase-locking behavior and hence global dendritic coherence. In turn, dendritic coherence is able to gate the integration and propagation of synaptic signals to the soma, ultimately leading to an effective control of somatic spike generation. Our results suggest that dendritic oscillations enable the dendritic tree to operate on more global temporal and spatial scales than previously thought
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