Andrey Shilnikov
Associate Professor
Office: 724 COE
Office phone: 404.413.6423
E-mail: ashilnikov [at] gsu.edu
Personal webpage
Mirror
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 holds a joint appointment at the newly established Neuroscience Institute and the Department of Mathematics and Statistics at Georgia State University. He is also a faculty of the Center for Nonlinear Sciences at Georgia Institute of Technology, a member of the Brains & Behaviors Scientific Committee at GSU, and of Center for Behavioral Neuroscience.
Dr. Shilnikov does research in computational/mathematical neuroscience, theory of dynamical systems and applied mathematics.
His teaches a whole range of courses including advanced Dynamical Foundations of Neuroscience, Applied Dynamical Systems, Applied Mathematics.
Selected Publications
Books
° 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.
Papers
° 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
° 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;. Virtual Journal of Biological Physics Research: biological networks. 16(4), 2008.
° 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
° Shilnikov L.P. and Shilnikov A., Shilnikov Saddle-Node, Scholarpedia,
3(4):4789, 2008
° 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.
° 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, 2(8):1891, 2007
° Shilnikov, A.L., and
Turaev, D.V., Blue sky catastrophe, Scholarpedia, 2(8):1889, 2007
° 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.