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Research interests:

Biomathematics, Mathematical Biology, Applied Dynamical Systems, Computational Neuroscience, Population Dynamics, Coupled Oscillators and Synchronization,  Neural Networks, Engineering Networks

 

Referred papers and book chapters: (* indicates students directed)

[41] R. Jeter* and I. Belykh, "Dynamical networks with on-off stochastic connections: beyond fast switching," Proceedings of 2014 IEEE International Symposium on Circuits and Systems, Melbourne, Australia, June 2-5 (2014) (accepted) PDF

[40] R. Reimbayev* and I. Belykh, "When transitions between bursting modes induce neural synchrony," Int. Journal of Bifurcation and Chaos (submitted) PDF.

[39] R. Jeter* and I. Belykh, "Synchronization of metapopulations with on-off stochastic dispersal," Journal of Mathematical Biology (submitted) PDF.

[38] K. Zhao* and I. Belykh, "Augmented graph synchronization method for directed networks", Chaos (submitted) PDF .

[37] I. Belykh, R. Reimbayev*, and K. Zhao*, "Repulsive inhibition promotes synhcrony in excitatory networks: help from the enemy, (submitted to Physical Review Letters) PDF.

[36] I. Belykh, M. di Bernardo, J. Kurths, and M.Porfiri, "Evolving dynamical networks", Physica D, V. 267, pp. 1-6 (2014) PDF (a review paper for a special isssue of Physica D on evolving dynamica networks, Guest Editors: I. Belykh, M. di Bernardo, J. Kurths, and M.Porfiri,)

[35] I. Belykh, V. Belykh, R. Jeter*, and M. Hasler, "Multistable randomly switching oscillators: the odds of meeting a ghost", European Physical Journal Special Topics, V. 222, pp. 2497-2507 (2013). PDF

[34] I. Belykh and M. Hasler, "Patterns of synchrony in neuronal networks: the role of synaptic inputs", Book chapter in "Nonlinear Dynamics: New Directions", Springer 2013 (in press). PDF

[33] M. Hasler, V. Belykh, and I. Belykh, "Dynamics of stochastically blinking systems. Part II: Asymptotic properties", SIAM Journal on Applied Dynamical Systems, Vol. 12, No. 2, pp. 1031–1084 (2013). PDF (54 journal pages!)

[32] M. Hasler, V. Belykh, and I. Belykh, "Dynamics of stochastically blinking systems. Part I: Finite time properties", SIAM Journal on Applied Dynamical Systems, Vol. 12, No. 2, pp. 1007–1030 (2013). PDF (24 journal pages)

[31] S. Jalil*, I. Belykh, and A. Shilnikov, "Spikes matter for phase-locked bursting in inhibitory neurons", Physical Review E 85, 036214 (2012). PDF

[30] I. Belykh and M. Hasler, "Mesoscale and clusters of synchrony in networks of bursting neurons," Chaos, V. 21, 016106 (2011). PDF (invited paper for a Focus issue "Mesoscales in Complex Networks").

[29] I. Belykh and M.Hasler, "Dynamics of networks with stichastically switched connections", Proceedings of the ASME 2011 Dynamic Systems and Control Conference, October 31 - November 2, 2011, Arlington, VA, USA, pages 1-7.  PDF

[28] S. Jalil*, I. Belykh, and A. Shilnikov, "Fast reciprocal inhibition can synchronize bursting neurons," Physical Review E, V. 81, 045201(R) (2010). PDF

[27] I. Belykh, S. Jalil*, and A. Shilnikov, "Burst-duration mechanism of in-phase bursting in inhibitory networks," Regular & Chaotic Dynamics, 15(2-3), pp. 148-160 (2010). (Special issue dedicated to Leonid P. Shilnikov on the occasion of his 75th birthday).

[26] V. Belykh and I. Belykh, "Belykh attractor", Scholarpedia, 6(10): 5545 (2010).

[25] I. Belykh, C. Piccardi, and S. Rinaldi, "Synchrony in tritrophic food chain metacommunities," Journal of Biological Dynamics, V. 3, no. 5, pp. 497 514 (2009) PDF.

[24] I. Belykh and A. Shilnikov, "When weak inhibition synchronizes strongly desynchronizing networks of bursting neurons", Physical Review Letters, V. 101, 078102 (2008) .  PDF . This paper has also been selected for the August 2008 issue of Virtual Journal of Biological Physics Research, V. 16, Issue 4.

[23] A. Shilnikov, R. Gordon*, and I. Belykh, " "Polyrhythmic synchronization in bursting network motifs", Chaos, V. 18, 037120 (2008).  PDF. This paper has also been selected for the October 2008 issue of Virtual Journal of Biological Physics Research.

 [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

[17] I. Belykh, M. Hasler, M. Lauret*, and H. Nijmeijer, "Synchronization and graph topology",  Int. Journal of Bifurcation and Chaos,  Vol. 15, No 11, pp. 3423–3433 (2005) (invited tutorial )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.    

[15] I. Belykh,  V. Belykh, and M. Hasler,  " Blinking model and synchronization in small-world networks with a time-varying coupling", Physica D,  V. 195/1-2, pp 188-206 (2004). PDF (Top 10 cited Physica D paper, published in the last five years: 2004-2009).

[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 (The most cited paper of  Physica D,  published in the last five years: 2004-2009).

[13] I. Belykh, V. Belykh,  K. Nevidin, and M. Hasler, " Persistent clusters in lattices of coupled nonidentical chaotic systems",  Chaos,  V. 13,  pp. 165-178 (2003). 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).

[9] V. Belykh, I. Belykh, and E. Mosekilde "Cluster synchronization modes in an ensemble of coupled chaotic oscillators", Physical Review E, Vol. 63, 036216 (2001).  PDF

[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).

[4]  I. Belykh, "Neuron bifurcations and a way to model electrically coupled neurons by using coupled mappins", Radiophysics Quantum Electronics (Kluwer Academic Publishing), V. 41, N. 12, pp. 1066-1071 (1998).

[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).
 

 

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