Andrey Shilnikov
Andrey Shilnikov
Distinguished University Professor, Georgia State University
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Cited by
Cited by
Methods of qualitative theory in nonlinear dynamics
LP Shilnikov, AL Shilnikov, DV Turaev, LO Chua
World Scientific, 2001
Методы качественной теории в нелинейной динамике. Часть 1.
ЛП Шильников, АЛ Шильников, ДВ Тураев, Л Чуа
Москва-Ижевск: Институт компьютерных исследований, 2004
Methods of the qualitative theory for the Hindmarsh-Rose model: A case study. A tutorial
A Shilnikov, M Kolomiets
International Journal of Bifurcation and chaos 18 (7), 1-32, 2008
Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe
A Shilnikov, G Cymbalyuk
Physical review letters 94 (4), 048101, 2005
On bifurcations of the Lorenz attractor in the Shimizu-Morioka model
AL Shil'Nikov
Physica D: Nonlinear Phenomena 62 (1-4), 338-346, 1993
Mechanism of bistability: tonic spiking and bursting in a neuron model
A Shilnikov, RL Calabrese, G Cymbalyuk
Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 71 (5 …, 2005
Normal forms and Lorenz attractors
AL Shil'Nikov, LP Shil'Nikov, DV Turaev
International Journal of Bifurcation and Chaos 3 (05), 1123-1139, 1993
Origin of chaos in a two-dimensional map modeling spiking-bursting neural activity
AL Shilnikov, NF Rulkov
International Journal of Bifurcation and Chaos 13 (11), 3325-3340, 2003
Bifurcation and chaos in the Morioka-Shimizu system
AL Shilnikov
Methods in Qualitative Theory and Bifurcation Theory, 1986
Bifurcation and predictability analysis of a low-order atmospheric circulation model
A SHIL'NIKOV, G Nicolis, C Nicolis
International Journal of Bifurcation and Chaos 5 (06), 1701-1711, 1995
Origin of bursting through homoclinic spike adding in a neuron model
P Channell, G Cymbalyuk, A Shilnikov
Physical Review Letters 98 (13), 134101, 2007
When weak inhibition synchronizes strongly desynchronizing networks of bursting neurons
I Belykh, A Shilnikov
Physical review letters 101 (7), 078102, 2008
Subthreshold oscillations in a map-based neuron model
AL Shilnikov, NF Rulkov
Physics Letters A 328 (2-3), 177-184, 2004
Parameter-sweeping techniques for temporal dynamics of neuronal systems: case study of Hindmarsh-Rose model
R Barrio, A Shilnikov
The Journal of Mathematical Neuroscience 1 (1), 6, 2011
Complete dynamical analysis of a neuron model
A Shilnikov
Nonlinear Dynamics 68, 305-328, 2012
Kneadings, symbolic dynamics and painting Lorenz chaos
R Barrio, A Shilnikov, L Shilnikov
International Journal of Bifurcation and Chaos 22 (04), 1230016, 2012
Global organization of spiral structures in bi-parameter space of dissipative systems with Shilnikov saddle-foci
R Barrio, F Blesa, S Serrano, AL Shilnikov
Physical Review E 84 (3), 035201, 2011
Polyrhythmic synchronization in bursting networking motifs
A Shilnikov, R Gordon, I Belykh
Chaos 18 (3), 037120, 2008
Coexistence of tonic spiking oscillations in a leech neuron model
G Cymbalyuk, A Shilnikov
Journal of computational neuroscience 18, 255-263, 2005
Key bifurcations of bursting polyrhythms in 3-cell central pattern generators
J Wojcik, J Schwabedal, R Clewley, AL Shilnikov
PloS one 9 (4), e92918, 2014
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