90 research outputs found
Spatial patterns of desynchronization bursts in networks
We adapt a previous model and analysis method (the {\it master stability
function}), extensively used for studying the stability of the synchronous
state of networks of identical chaotic oscillators, to the case of oscillators
that are similar but not exactly identical. We find that bubbling induced
desynchronization bursts occur for some parameter values. These bursts have
spatial patterns, which can be predicted from the network connectivity matrix
and the unstable periodic orbits embedded in the attractor. We test the
analysis of bursts by comparison with numerical experiments. In the case that
no bursting occurs, we discuss the deviations from the exactly synchronous
state caused by the mismatch between oscillators
Stability Analysis of Asynchronous States in Neuronal Networks with Conductance-Based Inhibition
Oscillations in networks of inhibitory interneurons have been reported at various sites of the brain and are thought to play a fundamental role in neuronal processing. This Letter provides a self-contained analytical framework that allows numerically efficient calculations of the population activity of a network of conductance-based integrate-and-fire neurons that are coupled through inhibitory synapses. Based on a normalization equation this Letter introduces a novel stability criterion for a network state of asynchronous activity and discusses its perturbations. The analysis shows that, although often neglected, the reversal potential of synaptic inhibition has a strong influence on the stability as well as the frequency of network oscillations
Breaking Synchrony by Heterogeneity in Complex Networks
For networks of pulse-coupled oscillators with complex connectivity, we
demonstrate that in the presence of coupling heterogeneity precisely timed
periodic firing patterns replace the state of global synchrony that exists in
homogenous networks only. With increasing disorder, these patterns persist
until they reach a critical temporal extent that is of the order of the
interaction delay. For stronger disorder these patterns cease to exist and only
asynchronous, aperiodic states are observed. We derive self-consistency
equations to predict the precise temporal structure of a pattern from the
network heterogeneity. Moreover, we show how to design heterogenous coupling
architectures to create an arbitrary prescribed pattern.Comment: 4 pages, 3 figure
Coupled Oscillators with Chemotaxis
A simple coupled oscillator system with chemotaxis is introduced to study
morphogenesis of cellular slime molds. The model successfuly explains the
migration of pseudoplasmodium which has been experimentally predicted to be
lead by cells with higher intrinsic frequencies. Results obtained predict that
its velocity attains its maximum value in the interface region between total
locking and partial locking and also suggest possible roles played by partial
synchrony during multicellular development.Comment: 4 pages, 5 figures, latex using jpsj.sty and epsf.sty, to appear in
J. Phys. Soc. Jpn. 67 (1998
Topological Speed Limits to Network Synchronization
We study collective synchronization of pulse-coupled oscillators interacting
on asymmetric random networks. We demonstrate that random matrix theory can be
used to accurately predict the speed of synchronization in such networks in
dependence on the dynamical and network parameters. Furthermore, we show that
the speed of synchronization is limited by the network connectivity and stays
finite, even if the coupling strength becomes infinite. In addition, our
results indicate that synchrony is robust under structural perturbations of the
network dynamics.Comment: 5 pages, 3 figure
Solvable model of a phase oscillator network on a circle with infinite-range Mexican-hat-type interaction
We describe a solvable model of a phase oscillator network on a circle with
infinite-range Mexican-hat-type interaction. We derive self-consistent
equations of the order parameters and obtain three non-trivial solutions
characterized by the rotation number. We also derive relevant characteristics
such as the location-dependent distributions of the resultant frequencies of
desynchronized oscillators. Simulation results closely agree with the
theoretical ones
Spectral Properties and Synchronization in Coupled Map Lattices
Spectral properties of Coupled Map Lattices are described. Conditions for the
stability of spatially homogeneous chaotic solutions are derived using linear
stability analysis. Global stability analysis results are also presented. The
analytical results are supplemented with numerical examples. The quadratic map
is used for the site dynamics with different coupling schemes such as global
coupling, nearest neighbor coupling, intermediate range coupling, random
coupling, small world coupling and scale free coupling.Comment: 10 pages with 15 figures (Postscript), REVTEX format. To appear in
PR
Integrate and Fire Neural Networks, Piecewise Contractive Maps and Limit Cycles
We study the global dynamics of integrate and fire neural networks composed
of an arbitrary number of identical neurons interacting by inhibition and
excitation. We prove that if the interactions are strong enough, then the
support of the stable asymptotic dynamics consists of limit cycles. We also
find sufficient conditions for the synchronization of networks containing
excitatory neurons. The proofs are based on the analysis of the equivalent
dynamics of a piecewise continuous Poincar\'e map associated to the system. We
show that for strong interactions the Poincar\'e map is piecewise contractive.
Using this contraction property, we prove that there exist a countable number
of limit cycles attracting all the orbits dropping into the stable subset of
the phase space. This result applies not only to the Poincar\'e map under
study, but also to a wide class of general n-dimensional piecewise contractive
maps.Comment: 46 pages. In this version we added many comments suggested by the
referees all along the paper, we changed the introduction and the section
containing the conclusions. The final version will appear in Journal of
Mathematical Biology of SPRINGER and will be available at
http://www.springerlink.com/content/0303-681
Solvable model for chimera states of coupled oscillators
Networks of identical, symmetrically coupled oscillators can spontaneously
split into synchronized and desynchronized sub-populations. Such chimera states
were discovered in 2002, but are not well understood theoretically. Here we
obtain the first exact results about the stability, dynamics, and bifurcations
of chimera states by analyzing a minimal model consisting of two interacting
populations of oscillators. Along with a completely synchronous state, the
system displays stable chimeras, breathing chimeras, and saddle-node, Hopf and
homoclinic bifurcations of chimeras.Comment: 4 pages, 4 figures. This version corrects a previous error in Figure
3, where the sign of the phase angle psi was inconsistent with Equation 1
Noise Induced Coherence in Neural Networks
We investigate numerically the dynamics of large networks of globally
pulse-coupled integrate and fire neurons in a noise-induced synchronized state.
The powerspectrum of an individual element within the network is shown to
exhibit in the thermodynamic limit () a broadband peak and an
additional delta-function peak that is absent from the powerspectrum of an
isolated element. The powerspectrum of the mean output signal only exhibits the
delta-function peak. These results are explained analytically in an exactly
soluble oscillator model with global phase coupling.Comment: 4 pages ReVTeX and 3 postscript figure
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