Research and Publications

Research Interests

My research interests include: Mathematical Biology and Neuroscience, Biomechanics, Applied Mathematics, Applied Dynamical Systems, Control, Applications in Biological, Ecological, Social, and Engineering Networks

Referred Papers and Book Chapters

(* indicates students/postdocs/visiting faculty directed)
   
2017-2023
R. Greenfield*, R. Jeter, S. N. Housley, and I. Belykh, "Rehabiliation Robotics and Machine Learning for Stroke Residual Severity Classification," Journal of Neuroenginering and Rehabilitation (submitted) (2023). PDF
M. Honari-Latifpour, J. Ding, I. Belykh, and M.-A. Miri, "Spectral network principle for frequency synchronization in repulsive laser networks," (2023) (submitted). PDF, Supplementary Material
V.O. Munyayev, M.I. Bolotov, L.A. Smirnov, G.V. Osipov, and I. Belykh, "Cyclops states in repulsive Kuramoto networks: the role of higher-order coupling," Physical Review Letters, 130, 107201 (2023). PDF, Supplementary Material
I. Belykh, R. Kuske, M. Porfiri, and D.J.W. Simpson, "Beyond the Bristol book: advances and perspectives in non-smooth dynamics and applications," Chaos, 33, 010402 (2023) PDF
V.N. Belykh, N. Barabash, and I. Belykh, "The hidden complexity of a double-scroll attractor: Analytic proofs from a piecewise-smooth system," Chaos, 33, 043119 (2023). PDF
L. Tang*, K. Smith*, K. Daley*, and I. Belykh, "When multilayer links exchange their roles in synchronization," Physical Review E, V. 106, 024214 (2022). PDF
I. Belykh, M. Bocian, A. Champneys, K. Daley*, R. Jeter*, J. Macdonald, and A. McRobie, "The London Millennium Bridge revisited: Emergent instability without synchronisation," SIAM News, V. 55, Issue 3, 1-2, (2022) PDF
I. Belykh, K. Daley*, and V. Belykh, "Pedestrian-induced instability: the role of frequency ratios," Radiophysics Quantum Electronics, Vol. 64, No 10, 700-708 (2022). PDF
V.O. Munyayev, M.I. Bolotov, L.A. Smirnov, G.V. Osipov, and I. Belykh, "Stability of rotatory solitary states in Kuramoto networks with inertia," Physical Review E, V. 105, 024203 (2022). PDF
I. Belykh, M. Bocian, A. Champneys, K. Daley*, R. Jeter*, J. Macdonald, and A. McRobie, "Emergence of the London Millennium Bridge instability without synchronisation," Nature Communications, V. 12, 7223 (2021) PDF, Supplementary Information, and Supplementary Video . This paper was featured in Nature.
N.V. Barabash, V.N. Belykh, G.V. Osipov, and I. Belykh, "Partial synchronization in the second-order Kuramoto model: an auxiliary system approach," Chaos, V. 31, 113113 (2021). PDF
V. Belykh, N. Barabash, and I. Belykh, "Sliding homoclinic bifurcations in a Lorenz-type system: analytic proofs," Chaos, V. 31, 043117 (2021). PDF
M. Porfiri, R. Jeter*, and I. Belykh, "Antiresonance in switched systems with only unstable modes," Physical Review Research, V. 3, L022001 (2021). PDF
B. Brister*, V. Belykh, and I. Belykh, "When three is a crowd: chaos from clusters of Kuramoto oscillators with inertia," Physical Review E, V. 101, 062206 (2020). PDF
K. Daley*, K. Zhao*, and I. Belykh, "Synchronizability of directed networks: the power of non-existent ties," Chaos, V. 30, 043102 (2020). PDF
V. Belykh, N. Barabash, and I. Belykh, "Bifurcations of chaotic attractors in a piecewise-smooth Lorenz-type system," Journal of Automation and Remote Control, V. 81, No 8, 1385-1393 (2020).
I. Belykh, D. Carter*, and R. Jeter*, "Synchronization in multilayer networks: when good links go bad," SIAM Journal on Applied Dynamical Systems, V. 18, No. 4, pp. 2267-2302 (2019) PDF
V. Belykh, N. Barabash, and I. Belykh, "A Lorenz-type attractor in a piecewise-smooth system: rigorous results," Chaos, V. 29, 103108 (2019). PDF (this paper was chosen as an Editor's Pick. )
R. Jeter*, M. Porfiri, and I. Belykh, "Dynamics and control of stochastically switching networks: beyond fast switching," Book chapter in "Temporal Network Theory," Eds. P. Holme and J. Saramaki, Computational Social Sciences Series, Springer, pp. 269-304 (2019). PDF
J. Ding, I. Belykh, A. Marandi, and M.-A. Miri, "Dispersive versus dissipative coupling for frequency synchronization in lasers," Physical Review Applied, V. 12, 054039 (2019). PDF
M. Porfiri, R. Jeter*, and I. Belykh, "Windows of opportunity for the stability of jump linear systems: almost sure versus moment convergence," Automatica, 100, 323-329 (2019). PDF
B. Brister*, V. Belykh, and I. Belykh, "Multistable cluster rhythms in networks of coupled rotators," Proceedings of the 9th International Conference "Physics and Control" (PhysCon-2019), Innopolis, Russia, September 8-11, IPACS Press, pp. 1-6 (2019).
R. Jeter*, M. Porfiri, and I. Belykh, " Overcoming network resilience to synchronization through non-fast stochastic broadcasting," Chaos, V. 28, 071104 (2018). PDF (this paper was chosen as an Editor's Pick. )
R. Jeter*, M. Porfiri, and I. Belykh, "Network synchronization through stochastic broadcasting," IEEE Control Systems Letters, V. 2, No 1, pp. 103-108 (2018). PDF
I. Belykh, R. Jeter*, and V. Belykh, "Foot force models of crowd dynamics on a wobbly bridge," Science Advances, V. 3, No 11, e1701512 (2017). PDF Media coverage: New York Times, Popular Science, Physics World, New Scientist, Science News, Russia News Today, Welt der Physik (in German).
R. Reimbayev*, K. Daley*, and I. Belykh, "When two wrongs make a right: synchronized bursting from combined electrical and inhibitory coupling," Philosophical Transactions of the Royal Society A, V. 375, 20160282 (2017) (invited paper to a special issue "Mathematical methods in medicine, neuroscience, cardiology and pathology") . PDF
M. Porfiri and I. Belykh, "Memory matters in synchronization of stochastically coupled maps," SIAM Journal on Applied Dynamical Systems, V. 16, No. 3, pp. 1372-1396 (2017). PDF
R. Reimbayev*, K. Zhao*, and I. Belykh , "When repulsive inhibition promotes synchrony of bursting neurons: Help from the enemy," Book chapter in " Advances in Dynamics, Patterns, Cognition,"  Nonlinear Systems and Complexity Series, Springer, 2017, pp. 161-185.
O. Golovneva*, R. Jeter*, I. Belykh, and M. Porfiri, "Windows of opportunity for synchronization in coupled stochastic maps," Physica D, V. 340, pp. 1-13 (2017). PDF
2016
I. Belykh, R. Jeter*, and V. Belykh, "Bistable gaits and wobbling induced by pedestrian-bridge interactions," Chaos, V. 26, 116314 (2016). PDF
I. Belykh and M. Porfiri, "Introduction: Collective dynamics of mechanical oscillators and beyond," Chaos, V. 26, 116101 (2016). PDF
I. Belykh, B. Brister*, and V. Belykh, "Bistability of patterns of synchrony in Kuramoto oscillators with inertia," Chaos, V. 26, 094822 (2016). PDF (invited paper to a Focus Issue on Pattern Synchronization) .
2015
I. Belykh, R. Reimbayev*, and K. Zhao*, "Synergistic effect of repulsive inhibition in synchronization of excitatory networks," Physical Review E, V. 91, 062919 (2015). PDF
R. Jeter* and I. Belykh, "Synchronization in on-off stochastic networks: windows of opportunity," IEEE Transactions on Circuits and Systems I: Regular Papers, V. 62, No 5, pp. 1260-1269 (2015). PDF
R. Jeter* and I. Belykh, "Synchronization of metapopulations with sporadic dispersal," Int. Journal of Bifurcation and Chaos, Vol. 25, No 7, 1540002 (2015). PDF
I. Belykh and M. Hasler, "Patterns of synchrony in neuronal networks: the role of synaptic inputs", Book chapter in "Nonlinear Dynamics: New Directions", Eds. H. Gonzalez-Aguilar and E. Ugalde, Nonlinear Systems and Complexity Series, V. 12, Springer, pp. 1-28 (2015). PDF (ISBN 978-3-319-09863-0).
2014
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), pp. 1-4 PDF
R. Reimbayev* and I. Belykh, "When transitions between bursting modes induce neural synchrony," Int. Journal of Bifurcation and Chaos, V. 24, No. 8, 1440013 (2014) PDF.
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 dynamical networks, Guest Editors: I. Belykh, M. di Bernardo, J. Kurths, and M.Porfiri,)
2013
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
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!)
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).
2012 and eariler
S. Jalil*, I. Belykh, and A. Shilnikov, "Spikes matter for phase-locked bursting in inhibitory neurons", Physical Review E 85, 036214 (2012). PDF
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").
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
S. Jalil*, I. Belykh, and A. Shilnikov, "Fast reciprocal inhibition can synchronize bursting neurons," Physical Review E, V. 81, 045201(R) (2010). PDF
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).
V. Belykh and I. Belykh, "Belykh attractor", Scholarpedia, 6(10): 5545 (2010).
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.
I. Belykh and A. Shilnikov, "When weak inhibition synchronizes strongly desynchronizing networks of bursting neurons", Physical Review Letters, V. 101, 078102 (2008) .  PDF
A. Shilnikov, R. Gordon*, and I. Belykh, "Polyrhythmic synchronization in bursting network motifs", Chaos, V. 18, 037120 (2008).  PDF.
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
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 
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).
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
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
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
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.    
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).
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).
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
  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
  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).
  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).
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
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
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
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).
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).
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).
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).
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).
I. Belykh, "Synchronization of diffusively coupled nonautonomous chaotic pendulums", Radiophysics Quantum Electronics (Kluwer Academic Publishing), V. 37, N 1-2, pp. 69-73 (1995).