Dr. Andrey Shilnikov
Lab Head
Aaron Keley
PhD student, NI

Tingli Xing,
PhD student, Math

Deniz Alacam,
Ph Student, Math




Dr. Justus Schwabedal,
Posdoctoral Fellow


Joseph Youker BS
B&B Summer Fellowship
NSF REU support
Ana Noriega,
BS student



Dr. Jeremy Wojcik
NSF support

Dr. Sajiya Jaili
Postdoctoral Fellow University of Texas Health Science Center at Houston

Enis Gunay, PhD
Postdoctoral fellow

Kristie Young

Matt Brooks
MS student, 2009
Paul Channell Jr.
MS Student, 1976-2011
Rene Gordon
BS student, 2011
Visiting Scholar, Plymouth UK
Summer Hu
PhD student,
U Maryland
Dane Allen,
BS student
NSF REU support
Emmanuel Thomas
BS student
B&B Fellowship

I seek two outstanding PhD candidates in mathematical/computational neuroscience and/or applied dynamical systems to start in Fall 2014. Apply through Neuroscience or Math graduate programs this 2013 Fall.

Congratulations to Tingli and Jeremy - the SIAM 0213 best poster awards!

Dynamics of individual neurons

Deterministic description of oscillatory activities in neurons is given within the framework of theory of dynamical systems and bifurcations. Mathematically, the corresponding, conductance based model belongs to a class of dynamical systems with several distinct time scales.  Dr. Shilnikov’s research group focuses its research on the origin of complex behavioral dynamics and preceding bifurcation sequences in neuronal models. We develop the geometric tools of slow-fast systems and the advanced, analytical and computational technique of the global bifurcation theory to model and understand in-depth the nonlinear dynamics of single neurons. 

Polyrhythms and Multistability in CPG networks

Bursting is a manifestation of the slow-fast dynamics observed in neuroscience including central pattern generators controlling animal locomotion.  The emergence of synchronous rhythms in neural networks is closely related to temporal characteristics of the coupled neurons due to both their intrinsic properties and types of synaptic coupling, inhibitory and excitatory. When cells are near the transition edge between bursting and tonic spiking, the dynamics of the network become highly sensitive to small perturbations due to changes in the architecture of the network and of strength of synaptic coupling. Research of Dr. Shilnikov’s group focuses on synergetic mechanisms of dynamical designation of pacemakers on a network endowing it with flexible synchronization properties leading to the multistability of coexistent bursting rhythms.

Prospective PhD candidates, MS and BS students in Mathematical and Computational Neuroscience, Dynamical Systems and Applied Math: contact Dr Shilnikov

Congratulations to Sajiya and Jeremy - 2012 PhD graduates!

Lab's publications

Xing T, Wojcik J, Barrio R and Shilnikov A. Symbolic toolkit for chaos exploration. in "Theory and Applications in Nonlinear Dynamics," Springer, 2013 [pdf]
R. Barrio, F. Blesa, S. Serrano, T. Xing and A. Shilnikov, Homoclinic spirals: theory and numeric. “Dynamical Systems: 100 years after Poincaré,” Lecture Notes in Mathematics and Statistics, Springer, 2013 [pdf]
Jalil S., Belykh I and Shilnikov A. Spikes matter in phase-locking of inhibitory bursting networks. Phys Review E 85, 036214, 2012, doi:10.1103/PhysRevE.85.036214 [pdf]
Wojcik J. and Shilnikov A.L. Voltage interval mappings for an elliptic burster, in "Nonlinear Dynamics: New Directions," Springer Series "Nonlinear Physical Science," 2012[pdf]
Wojcik J., Clewley R, and Shilnikov A., Order parameter for bursting polyrhythms in multifunctional central pattern generators.  Physics Review E 83, 056209-6, 2011 [pdf] DOI: 10.1103/PhysRevE.83.056209
Wojcik J. and Shilnikov A.L. Voltage interval mappings for dynamics transitions in elliptic bursters, Physica D 240, 1164-1180, 2011 [pdf]
Hu X, Youker J, Wojcik J, Clewley R and Shilnikov A, Phase and exact models for multifunctional central pattern generators, Proc. the 4th Dynamical Systems and Control Conference, Arlington, VA, Oct 31-Nov 2, 2011 [pdf]
Jalil S., Belykh I and Shilnikov A. Spikes matter in phase-locking of inhibitory bursting networks, submitted to PRE. 2011 [pdf]
Jalil S., Belykh I., and Shilnikov A. Fast reciprocal inhibition can synchronize bursting neurons, Physics Review E 81(4), 045201-4, Rapid Communications, 2010 [pdf] Virtual Journal of Biological Physics Research: biological networks. 19(9), 2010
Belykh I., Jalil S., and Shilnikov A. Burst-duration mechanism of in-phase bursting in inhibitory networks. Regular & Chaotic Dynamics, 15(2-3), 148-160, 2010 [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, 27(3), 527-542, [pdf] DOI 10.1007/s10827-009-0167-1
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.
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] [].      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]