Andrey Shilnikov
Andrey Shilnikov
Distinguished University Professor, Georgia State University
Verified email at gsu.edu - Homepage
TitleCited byYear
Methods of qualitative theory in nonlinear dynamics
LP Shilnikov, AL Shilnikov, DV Turaev, LO Chua
World Scientific, 2001
8462001
Методы качественной теории в нелинейной динамике. Часть 1.
ЛП Шильников, АЛ Шильников, ДВ Тураев, Л Чуа
Москва-Ижевск: Институт компьютерных исследований, 2004
212*2004
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
1492005
On bifurcations of the Lorenz attractor in the Shimizu-Morioka model
AL Shil'Nikov
Physica D: Nonlinear Phenomena 62 (1-4), 338-346, 1993
1271993
Mechanism of bistability: tonic spiking and bursting in a neuron model
A Shilnikov, RL Calabrese, G Cymbalyuk
Physical Review E 71 (5), 056214, 2005
1252005
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
1212008
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
1171995
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
1152003
Normal forms and Lorenz attractors
AL Shil'Nikov, LP Shil'Nikov, DV Turaev
International Journal of Bifurcation and Chaos 3, 1123-1123, 1993
1091993
Origin of bursting through homoclinic spike adding in a neuron model
P Channell, G Cymbalyuk, A Shilnikov
Physical Review Letters 98 (13), 134101, 2007
842007
Subthreshold oscillations in a map-based neuron model
AL Shilnikov, NF Rulkov
Physics Letters A 328 (2-3), 177-184, 2004
832004
When weak inhibition synchronizes strongly desynchronizing networks of bursting neurons
I Belykh, A Shilnikov
Physical review letters 101 (7), 078102, 2008
792008
Bifurcations and chaos in the Morioka-Shimizu model: II
AL Shil'nikov
Methods of Qualitative Theory of Differential Equations and Theory of …, 1989
76*1989
Complete dynamical analysis of a neuron model
A Shilnikov
Nonlinear Dynamics 68 (3), 305-328, 2012
742012
Polyrhythmic synchronization in bursting networking motifs
A Shilnikov, R Gordon, I Belykh
Chaos 18 (3), 037120, 2008
742008
Global organization of spiral structures in bi-parameter space of dissipative systems with Shilnikov saddle-foci
R Barrio, F Blesa, S Serrano
Physical Review E 84 (3), 035201, 2011
732011
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
692011
Coexistence of tonic spiking oscillations in a leech neuron model
G Cymbalyuk, A Shilnikov
Journal of computational neuroscience 18 (3), 255-263, 2005
662005
Kneadings, symbolic dynamics and painting Lorenz chaos
R Barrio, A Shilnikov, L Shilnikov
International Journal of Bifurcation and Chaos 22 (04), 1230016, 2012
562012
Six types of multistability in a neuronal model based on slow calcium current
T Malashchenko, A Shilnikov, G Cymbalyuk
PloS One 6 (7), e21782, 2011
522011
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