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Andrey Shilnikov
Andrey Shilnikov
Distinguished University Professor, Georgia State University
Verified email at gsu.edu - Homepage
Title
Cited by
Cited by
Year
Methods of qualitative theory in nonlinear dynamics
LP Shilnikov, AL Shilnikov, DV Turaev, LO Chua
World Scientific, 2001
12142001
Методы качественной теории в нелинейной динамике. Часть 1.
ЛП Шильников, АЛ Шильников, ДВ Тураев, Л Чуа
Москва-Ижевск: Институт компьютерных исследований, 2004
315*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
2102008
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
1962005
On bifurcations of the Lorenz attractor in the Shimizu-Morioka model
AL Shil'Nikov
Physica D: Nonlinear Phenomena 62 (1-4), 338-346, 1993
1861993
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
1662005
Normal forms and Lorenz attractors
AL Shil'Nikov, LP Shil'Nikov, DV Turaev
International Journal of Bifurcation and Chaos 3 (05), 1123-1139, 1993
1531993
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
1492003
Bifurcation and chaos in the Morioka-Shimizu system
AL Shilnikov
Methods in Qualitative Theory and Bifurcation Theory, 1986
134*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
1331995
Origin of bursting through homoclinic spike adding in a neuron model
P Channell, G Cymbalyuk, A Shilnikov
Physical Review Letters 98 (13), 134101, 2007
1172007
When weak inhibition synchronizes strongly desynchronizing networks of bursting neurons
I Belykh, A Shilnikov
Physical review letters 101 (7), 078102, 2008
1162008
Subthreshold oscillations in a map-based neuron model
AL Shilnikov, NF Rulkov
Physics Letters A 328 (2-3), 177-184, 2004
1142004
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
1112011
Complete dynamical analysis of a neuron model
A Shilnikov
Nonlinear Dynamics 68, 305-328, 2012
1082012
Kneadings, symbolic dynamics and painting Lorenz chaos
R Barrio, A Shilnikov, L Shilnikov
International Journal of Bifurcation and Chaos 22 (04), 1230016, 2012
1062012
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
1052011
Polyrhythmic synchronization in bursting networking motifs
A Shilnikov, R Gordon, I Belykh
Chaos 18 (3), 037120, 2008
932008
Coexistence of tonic spiking oscillations in a leech neuron model
G Cymbalyuk, A Shilnikov
Journal of computational neuroscience 18, 255-263, 2005
892005
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
822014
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