Andrey Shilnikov

Andrey Shilnikov

Associate Professor

Office:  724 COE
Office phone:  404.413.6423
E-mail:  ashilnikov [at] gsu.edu
Personal webpage

Education

M.S.  Physics and Mathematics, University of Nizhny Novgorod, Russia, 1984
Ph.D. Mathematics, University of Nizhny Novgorod, Russia, 1990

Research & Teaching

Dr. Shilnikov's research interests are in the theory of dynamical systems, strange attractors, and computational neuroscience, where the geometric methods of singularly perturbed systems and the advanced technique of the nonlocal bifurcation theory are used to understand the plethora of dynamical regimes observed in real neurons and in their models: continuous and discrete: Atlanta Computational Neuroscience Workshop.
Dr. Shilnikov is a faculty of the Center for Nonlinear Sciences at Georgia Institute of Technology. He is a fellow of the Brains & Behaviors Scientific Committee at GSU.
His favorite teaching courses are ODEs, PDEs, Applied Mathematics and Applied Dynamical Systems.

Selected Publications

° Shilnikov L.P., Shilnikov A., Turaev D. and Chua, L., Methods of Qualitative Theory in Nonlinear Dynamics. Volumes I and II. World Scientific Pub., 1998 and 2001.
° Shilnikov A. L. and Kolomiets M.L., Methods of the qualitative theory for the Hindmarsh-Rose model: a case study. J. Bifircations and Chaos, vol. 18, August, 2008
° Shilnikov A.L., Gordon R. and Belykh I.V., Polyrhythmic synchronization in bursting network motifs, J. Chaos, September, 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, PRL 98, 134101, 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.
° Shilnikov L.P. and Shilnikov A., Shilnikov Bifurcation , Scholarpedia , 2007, 2(8):1891.
° Shilnikov, A.L., Blue Sky Catastrophe, Scholarpedia, 2006.
° Shilnikov A. and Cymbalyuk G., Transition between tonic-spiking and bursting in a neuron model via the blue-sky catastrophe, Phys Rev Letters, 94, 048101, 2005.
° Shilnikov A., Shilnikov L.P. and Turaev D., Blue sky catastrophe in singularly perturbed systems. AMS Moscow Math. J., 5(1), 205-218,2005.
° Shilnikov A., 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.
° Mira, C. and Shilnikov, A.L., Slow and fast dynamics generated by non-invertible plane maps, Bifurcations and Chaos 15(11), 3509-3534, 2005.
° Cymbaluyk G. and Shilnikov A., Co-existent tonic spiking modes in a leech neuron model, J. Computational Neuroscience 18 (3), 269-282, 2005.
° Shilnikov A., Calabrese R. and Cymbalyuk G., How a neuron model can demonstrate coexistence of tonic spiking and bursting? Neurocomputing 65-66, 869-875, 2005.
° Shilnikov A. and Cymbaluyk 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.
° Shilnikov A., Shilnikov L.P. and Turaev D., Mathematical aspects of classical synchronization theory, Tutorial. Bifurcations and Chaos 14(7) 2143-2160, 2004.
° Shilnikov A. and Rulkov N., Subthreshold oscillations in a map-based neuron model, Physics Letters A 328, 177-184, 2004.
° Shilnikov A. and Rulkov N., Origin of chaos in a two-dimensional map modeling spiking-bursting neural activity. Bifurcations and Chaos, 13(11), 3325-3340, 2003.