3,048 research outputs found
Adaptive self-organization in a realistic neural network model
Information processing in complex systems is often found to be maximally
efficient close to critical states associated with phase transitions. It is
therefore conceivable that also neural information processing operates close to
criticality. This is further supported by the observation of power-law
distributions, which are a hallmark of phase transitions. An important open
question is how neural networks could remain close to a critical point while
undergoing a continual change in the course of development, adaptation,
learning, and more. An influential contribution was made by Bornholdt and
Rohlf, introducing a generic mechanism of robust self-organized criticality in
adaptive networks. Here, we address the question whether this mechanism is
relevant for real neural networks. We show in a realistic model that
spike-time-dependent synaptic plasticity can self-organize neural networks
robustly toward criticality. Our model reproduces several empirical
observations and makes testable predictions on the distribution of synaptic
strength, relating them to the critical state of the network. These results
suggest that the interplay between dynamics and topology may be essential for
neural information processing.Comment: 6 pages, 4 figure
Transient scaling and resurgence of chimera states in networks of Boolean phase oscillators
We study networks of non-locally coupled electronic oscillators that can be
described approximately by a Kuramoto-like model. The experimental networks
show long complex transients from random initial conditions on the route to
network synchronization. The transients display complex behaviors, including
resurgence of chimera states, which are network dynamics where order and
disorder coexists. The spatial domain of the chimera state moves around the
network and alternates with desynchronized dynamics. The fast timescale of our
oscillators (on the order of ) allows us to study the scaling
of the transient time of large networks of more than a hundred nodes, which has
not yet been confirmed previously in an experiment and could potentially be
important in many natural networks. We find that the average transient time
increases exponentially with the network size and can be modeled as a Poisson
process in experiment and simulation. This exponential scaling is a result of a
synchronization rate that follows a power law of the phase-space volume.Comment: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.03090
Synchronized Dynamics and Nonequilibrium Steady States in a Stochastic Yeast Cell-Cycle Network
Applying the mathematical circulation theory of Markov chains, we investigate
the synchronized stochastic dynamics of a discrete network model of yeast
cell-cycle regulation where stochasticity has been kept rather than being
averaged out. By comparing the network dynamics of the stochastic model with
its corresponding deterministic network counterpart, we show that the
synchronized dynamics can be soundly characterized by a dominant circulation in
the stochastic model, which is the natural generalization of the deterministic
limit cycle in the deterministic system. Moreover, the period of the main peak
in the power spectrum, which is in common use to characterize the synchronized
dynamics, perfectly corresponds to the number of states in the main cycle with
dominant circulation. Such a large separation in the magnitude of the
circulations, between a dominant, main cycle and the rest, gives rise to the
stochastic synchronization phenomenon.Comment: 23 pages,6 figures; in Mathematical Bioscience 200
Synchronization Transition of Identical Phase Oscillators in a Directed Small-World Network
We numerically study a directed small-world network consisting of
attractively coupled, identical phase oscillators. While complete
synchronization is always stable, it is not always reachable from random
initial conditions. Depending on the shortcut density and on the asymmetry of
the phase coupling function, there exists a regime of persistent chaotic
dynamics. By increasing the density of shortcuts or decreasing the asymmetry of
the phase coupling function, we observe a discontinuous transition in the
ability of the system to synchronize. Using a control technique, we identify
the bifurcation scenario of the order parameter. We also discuss the relation
between dynamics and topology and remark on the similarity of the
synchronization transition to directed percolation.Comment: This article has been accepted in AIP, Chaos. After it is published,
it will be found at http://chaos.aip.org/, 12 pages, 9 figures, 1 tabl
Complex and Adaptive Dynamical Systems: A Primer
An thorough introduction is given at an introductory level to the field of
quantitative complex system science, with special emphasis on emergence in
dynamical systems based on network topologies. Subjects treated include graph
theory and small-world networks, a generic introduction to the concepts of
dynamical system theory, random Boolean networks, cellular automata and
self-organized criticality, the statistical modeling of Darwinian evolution,
synchronization phenomena and an introduction to the theory of cognitive
systems.
It inludes chapter on Graph Theory and Small-World Networks, Chaos,
Bifurcations and Diffusion, Complexity and Information Theory, Random Boolean
Networks, Cellular Automata and Self-Organized Criticality, Darwinian
evolution, Hypercycles and Game Theory, Synchronization Phenomena and Elements
of Cognitive System Theory.Comment: unformatted version of the textbook; published in Springer,
Complexity Series (2008, second edition 2010
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