Andrey Shilnikov - chaos, bifurcations, nonlinear dynamics, mathematical computational neuroscience, neuron and network modeling

Comp Neuroscience
Workshop in Atlanta

Current Students
PhD Sajiya Jalil, Jeremy Wojcik and Tatiana Malaschenko
MS: Matt Brooks and
Paul Channell;
BS: Rene Gordon

· LP Special Issue

· Bursting Workshop

I received my PhD in Dynamical Systems from University of Nizhny Novgorod (formerly Gorky) in 1990. The Gorky school has pioneered the theory of dynamical systems and bifurcations. I was a postdoc at Berkeley and Cambridge (UK). Prior joining GSU in 2000 I had held visiting positions at Cornell University, Gatech, UC Berkeley. Here is my complete CV.
I hold a joint appointment at the newly established Neuroscience Institute and at Department of Mathematics & Statistics. I am also a faculty of Center for Nonlinear Science at GaTech, and a member of Center for Behavioral Neuroscience.
My research interests are in mathematical and computational neuroscience viewed through the prism of dynamical systems, bifurcation theory and nonlinear phenomena. I develop the geometric tools of singularly perturbed systems and advanced technique of the global bifurcation theory to understand the plethora of dynamical regimes observed in neurons and neuronal networks like CPGs.
Chaotic dynamics, Lorenz attractors and underlying homoclinic puzzles remain always on my mind.
Prospective PhD candidates, MS and BS students in Mathematical and Computational Neuroscience, Dynamical Systems and Applied Math: please contact me

Books I have co-authored:
Shilnikov L.P., Shilnikov A., Turaev D. and Chua, L., Methods of Qualitative Theory in Nonlinear Dynamics. Part I . World Scientific Pub., 1998.
Shilnikov L.P., Shilnikov A., Turaev D. and Chua, L., Methods of Qualitative Theory in Nonlinear Dynamics. Part II. World Scientific Pub., 2001.
Russian edition of Volume I , 2004

Russian edition of Volume II , 2009

My recent publications

Russian Edition of Shilnikov L.P., Shilnikov A., Turaev D. and Chua, L., Methods of Qualitative Theory in Nonlinear Dynamics. Part II. World Scientific Pub., 2009 [pdf]
Channell P., Fuwape I., Neiman A., and Shilnikov A.L., Variability of bursting patterns in a neuronal model in the presence of noise, 2009, J. Computational Neuroscience [pdf] DOI 10.1007/s10827-009-0167-1

Shilnikov A. L. and Kolomiets M.L., Methods of the qualitative theory for the Hindmarsh-Rose model: a case study. Tutorial. J. Bifurcations and Chaos, 18 (8), 1-27, 2008 [pdf]
Shilnikov A.L., Gordon R. and Belykh I.V., Polyrhythmic synchronization in bursting network motifs, J. Chaos, 18, 037120, 2008, DOI: 10.1063/1.2959850 [pdf] Virtual Journal of Biological Physics Research: biological networks. 16(7), 2008.
Belykh I.V. and Shilnikov, A.L., David vs. Goliath: when weak inhibition synchronizes strongly desynchronizing networks of bursting neurons, Phys. Rev. Letters 101, 078102, 2008 [original_pdf] [published_pdf] DOI: 10.1103/PhysRevLett.101.078102. Virtual Journal of Biological Physics Research: biological networks. 16(4), 2008.
Shilnikov L.P. and Shilnikov A., Shilnikov Saddle-Node, Scholarpedia, 2008, 3(4):4789.

Channell P., Cymbalyuk G. and Shilnikov A. L., Origin of bursting through homoclinic spike adding in a neuron model, Phys. Rev. Letters 98, 134101, 2007; doi: 10.1103/PhysRevLett.98.134101 [pdf] [gzip.ps]. Virtual Journal of Biological Physics, 3(7), 2007.
Channell P., Cymbalyuk, G. and Shilnikov, A. L., Applications of the Poincare mapping technique to analysis of neuronal dynamics, Neurocomputing, 70 (10-12), 2007; doi:10.1016/j.neucom.2006.10.091 [pdf]
Shilnikov L.P. and Shilnikov A., Shilnikov Bifurcation, Scholarpedia, 2007, 2(8):1891.

Shilnikov A.L. and Turaev D., Blue Sky Catastrophe, Scholarpedia, 2006, 2(8):1889.

Shilnikov A.L. and Cymbalyuk G., Transition between tonic-spiking and bursting in a neuron model via the blue-sky catastrophe, Phys Rev Letters, 94, 048101, 2005 [pdf]
Shilnikov A.L., Shilnikov L.P. and Turaev D., Blue sky catastrophe in singularly perturbed systems. AMS Moscow Math. J., 5(1), 205-218,2005 [pdf]
Shilnikov A.L., Calabrese R. and Cymbalyuk G., Mechanism of bi-stability: tonic spiking and bursting in a neuron model, Phys Review E 71(5), 056214-046221, 2005 [pdf]
Chua, L.O, Turaev, D.V. and Shilnikov, A.L., Editorial, Bifurcations and Chaos 15(11), 3509-3534, 2005 [pdf]

Mira, C. and Shilnikov, A.L., Slow and fast dynamics generated by non-invertible plane maps, Bifurcations and Chaos 15(11), 3509-3534, 2005 [pdf]
Cymbaluyk G. and Shilnikov A.L., Co-existent tonic spiking modes in a leech neuron model, J. Computational Neuroscience 18 (3), 269-282, 2005 [pdf]
Shilnikov A.L, Calabrese R. and Cymbalyuk G., How a neuron model can demonstrate coexistence of tonic spiking and bursting? Neurocomputing 65-66, 869-875, 2005 [pdf]
Shilnikov A.L. and Cymbalyuk G., Homoclinic saddle-node orbit bifurcations en a route between tonic spiking and bursting in neuron models, Invited review. Regular & Chaotic Dynamics, 3(9), 281-297, 2004 [pdf]
Shilnikov A.L., Shilnikov L.P. and Turaev D., Mathematical aspects of classical synchronization theory, Tutorial. Bifurcations and Chaos 14(7) 2143-2160, 2004 [pdf]
Shilnikov A.L. and Rulkov N., Subthreshold oscillations in a map-based neuron model, Physics Letters A 328, 177-184, 2004 [pdf]

Shilnikov A.L. and Rulkov N., Origin of chaos in a two-dimensional map modeling spiking-bursting neural activity. Bifurcations and Chaos, 13(11), 3325-3340, 2003 [pdf]