Andrey Shilnikov

I received my PhD in Dynamical Systems from University of Nizhny Novgorod (formerly Gorky) in 1990. The Gorky school had pioneered the qualitative theory of dynamical systems and bifurcations. I was a Royal Society postdoctoral fellow at DAMTP in Cambridge University (UK) and UC Berkeley. Prior to joining GSU in 2000, I held visiting positions at Berkeley, Georgia Institute of Technology, and Cornell University.

I hold a joint appointment at Neuroscience Institute and Department of Mathematics & Statistics. I am a faculty of Center for Nonlinear Science at Gatech, and a member of Center for Behavioral Neuroscience. I currently serve on Editorial board of J. Mathematical Neuroscience and J. Discontinuity, Nonlinearity & Complexity.

Here is my complete CV for reviews.

My original area of expertise is the theory of applied dynamical systems and global bifurcations. I study dynamics and their origin in diversely phenomenological systems and in exact models from life sciences. Of my special interest is a new emergent cross‐disciplinary field known as mathematical neuroscience. Its scopes include nonlinear models of individual neurons and networks. In‐depth analysis of such systems requires development of advanced mathematical tools paired with sophisticated computations. I derive models and create bifurcation toolkits for studying a stunning array of complex activities such as multistability of individual neurons and polyrhythmic bursting patterns discovered in multifunctional central pattern generators governing vital locomotor behaviors of animals and humans.

This research is currently funded through DMS-1009591 Multistability and bifurcations for polyrhythmic Central Pattern Generators from NSF, as well as B&B grants, and a grant 14.740.11.0919 Rhythm formation mechanisms in neuronal networks in application to adaptive bio-robotics from Russian Education and Science Ministry.

Deterministic chaotic dynamics, Lorenz and any strange attractors with underlying homo- and heteroclinic puzzles are always on my mind.

Prospective PhD candidates, MS and BS students interested in Mathematical Neuroscience, Dynamical Systems and Applied Mathematics: contact me. I have research positions funded by NSF and B&B.

The books that I have co-authored are available in English, Russian and Chinese:

Shilnikov L.P., Shilnikov A., Turaev D. and Chua, L., Methods of Qualitative Theory in Nonlinear Dynamics. Part I . World Sci. 1998.
Shilnikov L.P., Shilnikov A., Turaev D. and Chua, L., Methods of Qualitative Theory in Nonlinear Dynamics. Part II. World Sci. 2001. Appendix C [pdf]
Russian edition of Part I. R&C D, 2004 [pdf]
Russian edition of Part II. R&C D, 2009
Chinese Edition of Methods of Qualitative Theory in Nonlinear Dynamics. Part I, 2011 俄罗斯数学教材选译
Chinese Edition of Methods of Qualitative Theory in Nonlinear Dynamics. Part II, 2011 非线性动力学定性理论方法(第二卷)

Professor Neuroscience Institute and Department of Mathematics & Statistics, GSU

Professor
Neuroscience Institute and Department of Mathematics & Statistics, GSU