Ph.D. Mathematics, University of Nizhny Novgorod, Russia, 1990
M.S. Physics and Mathematics, University of Nizhny Novgorod, Russia, 1984
Dynamical Systems and Bifurcations, Mathematical Neuroscience, Chaos and Machine Learning
I received 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 UC 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 andJ. Discontinuity, Nonlinearity & Complexity.
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.
Deterministic chaotic dynamics, Lorenz and any strange attractors with underlying homo- and heteroclinic puzzles are always on my mind.
To see more of my publications, please visit my Google Scholar page.
- Pusuluri K., Basodi S., and Shilnikov AL. Computational exposition of multistable rhythms in 4-cell neural circuits. J. Communications in Nonlinear Science and Numerical Simulation 2019 (http://dx.doi.org/10.1016/j.cnsns.2015.11.024) [pdf] (https://labs.ni.gsu.edu/ashilnikov/pubs/4CellPaperElsevier_submission.pdf)
- Pusuluri K., and Shilnikov AL. Symbolic representation of neuronal dynamics. in Advances on Nonlinear Dynamics of Electronic Systems. World Scientific Series on Nonlinear Science, Series B. 2019 [pdf] (https://labs.ni.gsu.edu/ashilnikov/pubs/NDSE2018_neuro.pdf)
- Lodi M., Shilnikov AL. and Storace M. Design principles for central pattern generators with preset rhythms. IEEE Transactions on Circuits and Systems I: Regular Paper, 2019 (http://ieeexplore.ieee.org/document/8082521/) [pdf] (https://labs.ni.gsu.edu/ashilnikov/pubs/CPG_gates.pdf)
- Lodi M., Shilnikov AL. and Storace M. Digital architecture to realize programmable center pattern generator producing multiple gaits. 2019 IEEE International Symposium on Circuits and Systems, 2019 [pdf] (https://labs.ni.gsu.edu/ashilnikov/pubs/ISCASCPG2019.pdf)
- Ju H., Neiman AB. and Shilnikov AL. Bottom-up approach to torus bifurcation in neuron models. Chaos 28, 106317, 2018 [ (https://aip.scitation.org/doi/pdf/10.1063/1.5042078?class=pdf) pdf] (https://labs.ni.gsu.edu/ashilnikov/pubs/torus_neuro.pdf)
- Pusuluri K., and Shilnikov AL. Homoclinic chaos and its organization in a nonlinear optics model. Physics Review E - Rapid Communications, 98,040202(R), 2018 (https://journals.aps.org/pre/abstract/10.1103/PhysRevE.98.040202) [pdf] (https://labs.ni.gsu.edu/ashilnikov/pubs/pre_laser_2018.pdf)
- Lodi M., Shilnikov AL. and Storace M. Design of simplified central pattern generators with sensory feedback for quadruped locomotion. 2018 IEEE International Symposium on Circuits and Systems, 2018 [pdf] (https://labs.ni.gsu.edu/ashilnikov/pubs/ISCASCPG2018.pdf)
- Bondorenko V., and Shilnikov AL. Bursting dynamics in normal and failing hearts, Scientific Reports by Nature, 7, 5927, 2017 doi:10.1038/s41598-017-05198-z (https://www.nature.com/articles/s41598-017-05198-z) [pdf] (https://labs.ni.gsu.edu/ashilnikov/pubs/sc-nature.pdf)
- Lodi M., Shilnikov AL, and Storace M. Design of synthetic central pattern generators producing desired quadruped gaits. IEEE Transactions on Circuits and Systems I: Regular Papers, 2017 (http://ieeexplore.ieee.org/document/8082521/) [pdf] (https://labs.ni.gsu.edu/ashilnikov/pubs/08082521.pdf)
- Pusuluri K., Pikovsky A., and Shilnikov AL. Unraveling the Chaos-land and its organization in the Rabinovich System. in Challenges in Complexity: Dynamics, Patterns,
and Cognition, Springer series “Nonlinear Systems and Complexity” 2017 [pdf] (https://labs.ni.gsu.edu/ashilnikov/pubs/pusuluri.pdf)
- Lodi M., Shilnikov AL, and, Storace M. CEPAGE: a toolbox for Central Pattern Generator analysis. 2017 IEEE International Symposium on Circuits and Systems, 2017 [pdf] (https://labs.ni.gsu.edu/ashilnikov/pubs/ISCAS.pdf)
- Knapper D. Schwabedal J. and Shilnikov AL. Qualitative and Quantitative Stability Analysis of Penta-rhythmic Circuits. (http://dx.doi.org/10.1088/0951-7715/29/12/3647) Nonlinearity, 2016 (http://iopscience.iop.org/journal/0951-7715) [pdf] (https://labs.ni.gsu.edu/ashilnikov/pubs/nonlinear_penta.pdf)
- Shilnikov AL, and Maurer AP. The Art of grid fields: Geometry of neuronal time. (http://journal.frontiersin.org/article/10.3389/fncir.2016.00012/full) J. Frontiers in Neural Circuits. 2016 (http://journal.frontiersin.org/journal/neural-circuits) [pdf] (https://labs.ni.gsu.edu/ashilnikov/pubs/neural_time_2016.pdf)
- Nagornov R., Osipov G., Komarov M., Pikovsky A., and Shilnikov AL. Mixed mode synchronization and network bursting of neurons with post-inhibitory rebound. J. Communications in Nonlinear Science and Numerical Simulation 36, 175-191, 2016 (http://dx.doi.org/10.1016/j.cnsns.2015.11.024) [pdf] (https://labs.ni.gsu.edu/ashilnikov/pubs/CNSNS_3709.pdf)
- Barrio R., Rodriguez M. and Shilnikov AL. Mechanism of quasi-periodic lag jitter in bursting rhythms by a neuronal network, European Physics Letters 12(3), 38002, 2015 10.1209/0295-5075/112/38002 (http://iopscience.iop.org/article/10.1209/0295-5075/112/38002) [pdf] (https://labs.ni.gsu.edu/ashilnikov/pubs/epl17485.pdf)
- Krishnan G., Filatov G., Shilnikov AL., and Bazhenov M. Electrogenic properties of the Na+/K+ ATPase controls transitions between normal and pathological brain states. J. Neurophysiology, 113: 3356-3374, 2015, doi:10.1152/jn.00460.2014 (http://jn.physiology.org/content/early/2015/01/09/jn.00460.2014.full-text.pdf+html) [pdf] (https://labs.ni.gsu.edu/ashilnikov/pubs/JN-00460-2014.pdf)
- Alacam D. and Shilnikov AL. Making a swim central pattern generator out of latent parabolic bursters. Bifurcations and Chaos 25(7), 1540003, 2015, doi: 10.1142/s0218127415400039 [pdf] (https://labs.ni.gsu.edu/ashilnikov/pubs/parabolic_swimCPG.pdf)
- Wojcik J. and Shilnikov AL. Voltage interval mappings for an elliptic burster, a referred chapter in "Nonlinear Dynamics: New Directions," Springer. 2015, ISBN 978-3-319-09866-1 (http://www.springer.com/physics/complexity/book/978-3-319-09866-1) [pdf] (https://labs.ni.gsu.edu/ashilnikov/pubs/Chapter_final.pdf)
- Xing T., Wojcik J., Zaks M. and Shilnikov AL. Fractal Parameter Space of Lorenz-like