Mathematical frameworks for oscillatory network dynamics in neuroscience

P Ashwin, S Coombes, R Nicks - The Journal of Mathematical …, 2016‏ - Springer
The tools of weakly coupled phase oscillator theory have had a profound impact on the
neuroscience community, providing insight into a variety of network behaviours ranging from …

[كتاب][B] Dynamical systems in neuroscience

EM Izhikevich - 2007‏ - books.google.com
In order to model neuronal behavior or to interpret the results of modeling studies,
neuroscientists must call upon methods of nonlinear dynamics. This book offers an …

Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model

XJ Wang, G Buzsáki - Journal of neuroscience, 1996‏ - Soc Neuroscience
Fast neuronal oscillations (gamma, 20–80 Hz) have been observed in the neocortex and
hippocampus during behavioral arousal. Using computer simulations, we investigated the …

[كتاب][B] Synchronization in oscillatory networks

GV Osipov, J Kurths, C Zhou - 2007‏ - books.google.com
This work systematically investigates a large number of oscillatory network configurations
that are able to describe many real systems such as electric power grids, lasers or even the …

Modeling a synthetic multicellular clock: repressilators coupled by quorum sensing

J Garcia-Ojalvo, MB Elowitz… - Proceedings of the …, 2004‏ - National Acad Sciences
Diverse biochemical rhythms are generated by thousands of cellular oscillators that
somehow manage to operate synchronously. In fields ranging from circadian biology to …

On partial contraction analysis for coupled nonlinear oscillators

W Wang, JJE Slotine - Biological cybernetics, 2005‏ - Springer
We describe a simple yet general method to analyze networks of coupled identical nonlinear
oscillators and study applications to fast synchronization, locomotion, and schooling …

Connection graph stability method for synchronized coupled chaotic systems

VN Belykh, IV Belykh, M Hasler - Physica D: nonlinear phenomena, 2004‏ - Elsevier
This paper elucidates the relation between network dynamics and graph theory. A new
general method to determine global stability of total synchronization in networks with …

Synchronizing genetic relaxation oscillators by intercell signaling

D McMillen, N Kopell, J Hasty… - Proceedings of the …, 2002‏ - National Acad Sciences
The ability to design and construct synthetic gene regulatory networks offers the prospect of
studying issues related to cellular function in a simplified context; such networks also have …

Image segmentation based on oscillatory correlation

DL Wang, D Terman - Neural Computation, 1997‏ - ieeexplore.ieee.org
We study image segmentation on the basis of locally excitatory, globally inhibitory oscillator
networks (LEGION), whereby the phases of oscillators encode the binding of pixels. We …

Synchronization of elliptic bursters

EM Izhikevich - SIAM review, 2001‏ - SIAM
Periodic bursting behavior in neurons is a recurrent transition between a quiescent state and
repetitive spiking. When the transition to repetitive spiking occurs via a subcritical Andronov …