Research interests:

Biomathematics, Applied Dynamical Systems, Computational Neuroscience, Coupled Oscillators and Synchronization,  Neural Networks.

Journal papers:

[25] I. Belykh and A. Shilnikov, "When weak inhibition synchronizes strongly desynchronizing networks of bursting neurons", Physical Review Letters, V. 101, 078102 (2008) .  PDF

[24] A. Shilnikov, R. Gordon, and I. Belykh, " "Polyrhythmic synchronization in bursting network motifs", CHAOS, 2008 (accepted).

[23] I. Belykh, C. Piccardi, and S. Rinaldi, "Synchrony in tritrophic food chain metacommunities" (submitted to J. Biological Dynamics) .

 [22]  I. Belykh,  M. Hasler, and V. Belykh, "When symmetrization guarantees synchronization in directed networks," Int. Journal of Bifurcation and Chaos, V. 17, no. 10, pp. 3387-3395 (2007).  PDF

 [21]  I. Belykh,  V. Belykh, and M. Hasler, "Generalized connection graph method for synchronization in asymmetrical networks", Physica D, V. 224, pp. 42–51 (2006) PDF 

 [20]  I. Belykh,  V. Belykh, and M. Hasler, "Synchronization in asymmetrically coupled networks with node balance," CHAOS, V. 16, 16, 015102 (2006) PDF  (invited paper for a Focus issue organized by L. Pecora and S. Boccaletti).

[19] I. Belykh, E. de Lange, and M. Hasler, "Synchronization of bursting neurons: what matters in the network topology",  Physical Review Letters,  V. 94, 188101 (2005).  PDF    This paper has also been selected for the May 15, 2005 issue of Virtual Journal of Biological Physics Research.

 [18] M. Hasler and I. Belykh, "Blinking long-range connections increase the functionality of locally connected networks," IEICE Transactions on Fundamentals (Oxford University Press), V. E88-A, N 10, pp. 2647-2655 (2005). PDF

[16] V. Belykh, I. Belykh, and  E. Mosekilde, "The hyperbolic Plykin attractor can exist in neuron models",  Int. Journal of Bifurcation and Chaos,  Vol. 15, No 11, pp. 3567–3578 (2005).   PDF       Special issue dedicated to Leonid P. Shilnikov on the occasion of his 70th birthday.    

[14]  V. Belykh,  I. Belykh, and M. Hasler,  "Connection graph stability method for synchronized coupled chaotic systems",  Physica D,  V. 195/1-2, pp. 159-187 (2004). PDF

 [12] V. Belykh, I. Belykh, and M. Hasler, "Small-world networks: dynamical models and synchronization",  Journal of  Applied Nonlinear Dynamics, Vol. 11, N  3, pp 67-76 (2003). Abstract

[11]  V. Belykh, I. Belykh, M. Hasler, and  K. Nevidin "Cluster synchronization in three-dimensional lattices of diffusively coupled oscillators",  Int. Journal of Bifurcation and Chaos, 2003, V.13, pp. 755-779  (2003).   PDF  ( the cover  of  Int. Journal of Bifurcation and Chaos representing this article).

[10]  V. Belykh, I. Belykh, and K. Nevidin "Spatiotemporal synchronization in lattices of locally coupled oscillators", Int. Journal Mathematics and Computers in Simulation (NH Elsevier Publishing), Vol. 58, pp. 477-492 (2002).

[8]  V. Belykh, I. Belykh, N. Komrakov, and E. Mosekilde, "Invariant manifolds and cluster synchronization in a family of locally coupled map lattices", Discrete Dynamics in Nature and Society (Gordon and Breach Publishing, New York), V. 4, pp. 245-256 (2000).  PDF

[7]   V. Belykh, I. Belykh, E. Mosekilde, and M. Colding-Joergensen, "Homoclinic bifurcations leading to bursting oscillations in cell models", European Physical Journal   E, V. 3, N 3, pp. 205-219 (2000).  PDF

[6]  I. Belykh, V. Belykh, and M. Hasler, "Hierarchy and stability of partially synchronous oscillations of diffusively coupled  dynamical systems", Physical Review E, V. 62, N 5, pp. 6332-6345 (2000).

[5]  V. Belykh, I.Belykh, and N. Verichev, "Global chaotic synchronization in coupled Josephson junctions", Radiophysics Quantum Electronics (Kluwer Academic Publishing), V. 41, N 7, pp. 912-924 (1997).

[3]  I  Belykh and N.N. Verichev,  "Strange attractors and synchronization in coupled oscillator-pendulum systems", Bulletin of  N. Novgorod University: Nonlinear Dynamics and Chaos, V. 2, pp. 36-48 (1997).

[2]  I. Belykh, "From chaos to synchronization in a coupled system of Josephson junctions", Bulletin of  N. Novgorod University: Nonlinear Dynamics and Chaos (Edited by M.I. Rabinovich), V. 1, pp. 159-164 (1996).

[1]  I. Belykh, "Synchronization of diffusively coupled nonautonomous chaotic pendulums", Radiophysics Quantum Electronics (Kluwer Academic Publishing), V. 37, N 1-2, pp. 69-73 (1995).
 

Papers in refereed proceedings

[20] M. Hasler, I. Belykh, and V. Belykh, ``Classes of stochastically switched (blinking) systems,'' Proceedings of the 2007 International Symposium on Circuits and Systems (ISCAS-2007) , IEEE Press, pp. 1665-1668, 2007. PDF

[19] I. Belykh, V. Belykh, M. Hasler, “Synchronization Stability in Oscillator Networks: Solution for Asymmetrical Configurations”, Proceedings of the 3rd IFAC conference “Periodic Control Systems,” St. Peterburg, Russa, International Federation of Automatic Control Press, pp. 1-6, 2007.

[18] I. Belykh, M. Hasler, and V. Belykh , "Graph-based criteria for synchronization of diffusively coupled oscillators”, Proceedings of the Int. Symposium on Nonlinear Theory and its Applications (NOLTA-2006), Bologna, Italy, pp. 567-570 (2006).

[17] I. Belykh, E. de Lange, and M. Hasler, "Synchronization in pulse-coupled networks of bursting neurons", Proceedings of the Int. Symposium on Nonlinear Theory and its Applications (NOLTA-2005), Bruges, Belgium, 2005, pp. 699-702.

[16] I. Belykh, V. Belykh, and M. Hasler ”Synchronization in complex networks with blinking interactions,” Proceedings of the Int. Conference "Physics and Control 2005", Saint Petersburg, Russia,  2005 , CD: 1-4.

[14] I. Belykh, V. Belykh, and M. Hasler, "Blinking model and small-world networks with a time-varying coupling", Proceedings of the IEEE  Int. Conference on Nonlinear Dynamics of Electronic Systems (NDES'2003), Scuol, Switzerland,   pp. 29-32, 2003.

[12] I. Belykh, V. Belykh, K. Nevidin, and M. Hasler "Cluster synchronization in lattices of diffusively coupled dynamical systems", Proceedings of the Int. Conference "Progress in Nonlinear Science" dedicated to the 100th Anniversary of A.A.Andronov, N. Novgorod, Russia, V.3, pp. 139-143,  2001.

[10] I. Belykh, V. Belykh, K. Nevidin, and M. Hasler "Partial synchronization in two-dimensional lattices of coupled nonlinear systems", Proceedings of the IEEE Conference on Nonlinear Dynamics of Electronic Systems (NDES'2001), (Delft University Press),  pp. 197-200, Delft, 2001.

[8] I.V. Belykh  "Embedded invariant manifolds and ordering of chaotic synchronization of diffusevely coupled systems", Proceedings of the Int. Conference COC-2000, V. 2, pp. 346-350, St.-Petersburg, 2000.

[6] I.V. Belykh, "Neuron model bufurcations leading to bursting oscillations", Proceedings of the Int. Conference NOLTA-98 (Presses Polytechnique et Universitaires Romandes), V. 3, pp. 1177-1181, Crans-Montana, Switzerland, 1998.

[4] I.V. Belykh, and N.N. Verichev, "Global synchronization and strange attractors in coupled superconducting junctions", Proceedings of the Int. Conference NDES-97 (Nonlinear Dynamics of Electronic Systems), pp. 145-149, Moscow, 1997.

 [2] I.V. Belykh and N.N. Verichev, "Strange attractors in systems of coupled superconducting junctions,"  Int. Conference "Contemporary Problems in Theory of Dynamical Systems", Nizhny Novgorod University Press, 1996.

[1] I.V. Belykh "Synchronization in an 1-D chain of diffusively coupled nonautonomous chaotic pendulums,"  Int. Conference "Wave phenomena and oscillations", Nizhny Novgorod-Moscow,  1994.

 

Talks and meetings

• Int. Symposium on Synchronization in Complex Networks (SynCoNet-2007),  Leuven, Belgium , July 2-4 2007. Invited talk: "Patterns of synchrony in bursting neuronal networks." Pictures from the conference.
• Department of Electronics and Information Systems, Politecnico di Milano, Italy, May, 24, 2007. Colloquium talk: “Neuronal synchronization".
• 2007 SIAM Conference on Applications of Dynamical Systems,  Snowbird, USA, May 22-26, 2005 . (Minisymposium "Structure and Dynamics of Complex Networks" . Co-organizer and an invited speaker) .
• Department of Electronics and Information Systems, Politecnico di Milano, Italy, December, 20, 2006. Colloquium talk: “Network topology and synchronization“.
• Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, November 6, 2006. Colloquium talk: “Synchronization in complex networks of dynamical systems.”
• 2006 International Symposium on Nonlinear Theory and its Applications (NOLTA2006) , Bologna, Italy, September 11 - 14, 2006. Talk: "Graph-based Criteria for Synchronization of Diffusively Coupled Oscillators ."
• 6th Crimean School and Workshops Nonlinear Dynamics, Chaos, and Applications. Workshop: Stochastic and Chaotic Dynamics in Action: from Laser to Brain, from Communication to Medicine, Yalta, Crimea, Ukraine 15-26 May, 2006 . Invited talk: Synchrony in networks of bursting neurons.

• Int. Workshop “Origin and Regulation of Bursting Activity in Neurons”, Atlanta , USA , April 7-8, 2006. Invited talk: Synchronized bursting: what matters in the network topology.
• 2005 International Symposium on Nonlinear Theory and its Applications (NOLTA-2005),  Bruges, Belgium,  October 18-21,  2005.
• International Conference "Physics and Control-2005", Saint Petersburg, Russia, August 24-26, 2005.
• 2005 SIAM Conference on Applications of Dynamical Systems,  Snowbird, USA, May 22-26, 2005 . (Minisymposium "Synchronization of Complex Networks", Talk: "Synchronization of bursting neurons: what matters in the network topology "; Minisymposium "Complex Dynamics of Systems with Multiple Time Scales", Talk "The Hyperbolic Plykin Attractor Can Exist in Neuron Models".
• Department of Mathematics and Statstics, Georgia State Universtity, Atlanta, USA, May 10, 2005. Talk: "Synchronization of complex networks".  
• Coupled 60 Workshop, dedicated to M. Golubitsky, J. Guckenheimer, P. Holmes, I. Stewart, and M. Field, on the occasion of their 60th birthdays,  Department of Mathematics, University of Houston, USA, February 2-6, 2005. Talk:  "Synchronization in Complex Networks of Oscillators: Rigorous Results".  
•  Int. Workshop "Nonlinear Dynamics and Complexity in Information and Communication Technology", Bologna, Italy, September 6-8, 2004.  
• SIAM Conference on the Life Sciences,  Portland, USA, July 11-14, 2004  (minisymposium "Synchrony in Neural Networks"). 
• Coupled Map Lattices 2004, Institute Henri Poincaré, Paris, June 21 - July 2, 2004.     
• Laboratory of Computation Neuroscience (headed by W. Gerstner), LCN-I&C-EPFL, June 3, 2004.
• INTAS-Workshop on Synchronization of Biological Oscillators, Center for Dynamics of Complex Systems,  University of Potsdam, Germany, March 29-30, 2004.
• Symmetry and Bifurcation in Biology, Banff International Research Station, Canada, May 31- June 05, 2003.
• 2003 SIAM Conference on Applications of Dynamical Systems,  Snowbird, USA, May 27-31, 2003 (thanks to Oscar de Feo) .
• 11th International IEEE Workshop on Nonlinear Dynamics of Electronic Systems (NDES'2003), Scuol, Switzerland, May 18-21, 2003.
• Reading Group "Distributed Signal Processing and Communiction" (organized by M. Vetterli, LCAV-IC- EPFL ), January 23, 2003.
• Stochastic Dynamical Systems Group,   Institute of  Physics, University of Freiburg, Germany, November 12,  2002.
• International Workshop on Synchronization, Collective Behavior, and Complex Phenomena in Chaotic Systems, Florence,  Italy,  October 15-16, 2002.
• International Workshop on Synchronization of Chaotic and Stochastic Oscillations. Application in Physics, Biology, and Medicine (SYNCHRO-2002), Saratov, Russia, September 22-28, 2002.
• NATO Advance Study Institute School "Synchronization: Theory and Application", May 19-June 1, 2002.
• International Workshop on Control, Communication, and  Synchronization in Chaotic Dynamical Systems, Max Planck Institute for the Physics of  Complex Systems, Dresden, Germany, November 11-16, 2001.
• 2001 International Symposium on Nonlinear Theory and its Applications (NOLTA-2001),  Miyagi,  Japan,  October 28 - November 1,  2001.
•  International Conference Progress in Nonlinear Science, dedicated to the 100th anniversary of A.A.Andronov,  Nizhny Novgorod, Russia, July 2-6, 2001.
• 9th  IEEE Conference on Nonlinear Dynamics of Electronic Systems (NDES'2001),  Delft,  The Netherlands,  June 21-23,  2001.
• Chaos Group,  Department of Physics, The Technical University of Denmark, Denmark, March, 2001. 
• 2nd International Conference "Control of Oscillations and Chaos" (COC- 2000),  St. Petersburg, Russia,   July 5-7,  2000.
• 2000 IEEE  International  Symposium on Circuits and Systems (ISCAS-2000),  Geneva, Switzerland, May 28-31, 2000
• 8th International IEEE Conference on Nonlinear Dynamics of Electronic Systems (NDES-2000),  Catania, Italy,  May 18-20, 2000.

CV:

Education:

• Ph. D. in Applied Mathematics (advisor - Leonid P. Shilnikov), University of Nizhny Novgorod, Nizhny Novgorod (former Gorky), Russia, 1999.
• M.S. in Mathematics and Physics, Division of  Nonlinear Dynamics (Andronov's Chair ), University of Nizhny Novgorod, 1995.

Academic appointments and experience:

• 2006-present, Assistant Professor, Department of Mathematics and Statistics, Georgia State University, Atlanta, USA
• 2001 - 2005  Chargé de cours  (Lecturer)  and Senior Researcher, Laboratory of Nonlinear Systems,  Swiss Federal Institute of  Technology Lausanne (EPFL). Teaching: course "Dynamical System Theory for Engineers" (86 hours)  (2003/2004, 2004/2005).
• 1999 - Present (on leave) Research Scientist II,  Department of Differential Equations (Chair - L.P. Shilnikov), Institute of Applied Mathematics and Cybernetics, N. Novgorod, Russia.
• 1999-2001 Lecturer (half-time position), Department of Radiophysics, University of Nizhny Novgorod,  Course "Global bifurcations."
• 1996-1998 Teaching Assistant, Department of Mathematics, University of Nizhny Novgorod.

Visiting positions held: Visiting Research Scientist, Chaos Group (Chair - E. Mosekilde), Department of Physics, The Technical University of Denmark, Lyngby, Denmark (January-March, 2000; June, 1999; September 1997- January 1998 );  Visiting Research Scientist, CIRC, Department of Electrical Engineering, EPFL (October 1998-July 1999).

Professional service:

Co-organizer of the Int. Workshop “Origin and Regulation of Bursting Activity in Neurons”, Atlanta , USA , 2006, Co-organizer of the Int. Workshop “Nonlinear Dynamics Everywhere”, Swiss Federal Institute of Technology, Lausanne, Switzerland, October 25-26, 2005, Co-organizer of the minisymposium "Synchrony in Neural Networks" at the SIAM conference on the Life Sciences, Portland, OR, USA, 2004. Member of the organizing committee of the Int. Conference "Progress in Nonlinear Science," dedicated to the 100th anniversary of A.A.Andronov,  2000; of the Int. Conference "Contemporary Problems in Nonlinear Dynamics," 1996.

Member of Society for Industrial and Applied Mathematics, American Mathematical Society, IEEE.

Associate member of the Centre for Chaos Control and Synchronization, City University of Hong Kong (governing board: Guarong Chen , Leon Chua, and Steven Smale).

Reviewer for Physical Review Letters, Physical Review E, Physics Letters A, Chaos,  Physica D, Nonlinearity,  Int. Journal of Bifurcation and Chaos, Journal of Computational Neuroscience, IEEE Transactions on Circuits and Systems, IEEE Transactions on Automatic Control, etc.

Associate Edtior of Int. Journal Dynamics of Continuous, Discrete & Impulsive Systems. Series B: Applications and Algorithms

Current Grants

I. Belykh (PI), A. Shilnikov, “Synchronization in networks of bursting neurons,” Brains & Behaviors program, 2007, $23,000.

Grants, Rewards and Fellowships:

• GSU Internal Research 2006- 2007 (Role: Principal Investigator) “Neuronal networks: synchrony and pattern formation.” $10,000
• Fellowship from the Cariplo Foundation and Landau Network-Centro Volta . (2006-2007).
• S. Pallas, A. Shilnikov, S. Prasad, I. Belykh (Co-PI), "Modeling circuits for stimulus velocity tuning in the superior colliculus", Brains & Behaviors program, 2006, $30,000.
• Swiss Confederation fellowship for visiting scientists (1998-1999) .
• The ISSEP grants for Soros students and postgraduates ( 1996, 1997, 1998) .
• The Razuvaev fellowships of Nizhny Novgorod Administration for postgraduate students (1998) .

Languages: Russian (native), English (fluent), French (fluent).