Professor
My research interests are in the area of mathematical and computational neuroscience, in particular, applications of dynamical systems to the problems of biology and medicine. I am using mathematical and computational methods to study the dynamics of the nervous system to get insights into its function. My current research is concentrated on the dynamics of basal ganglia - brain nuclei, which, among other things, control motor programs and are impacted in Parkinson's disease. Despite the large amount of factual knowledge about basal ganglia at all levels - from cells to behavior, the principles of function of basal ganglia in Parkinson's disease (and other diseases involving basal ganglia) and even in normal conditions are far from being fully understood. There is mounting experimental evidence that complex collective dynamics of interaction of various ionic channels and various cells are responsible for normal basal ganglia operation and pathological variations of these dynamics are responsible for its pathophysiology. Mathematical models help to bridge the gap between different levels of biological knowledge, provide insights about the principles of the function of neuronal system and be effective tool for the development of practical applications (such as treatment strategies). What is no less important, theoretical approach to basal ganglia function can help us to elucidate general principles of human brain function.
S. Ahn, L.L. Rubchinsky. Short desynchronization episodes prevail in synchronous dynamics of human brain rhythms. Chaos, accepted, 2013. (also available as arXiv:1302.5866)
A. Dovzhenok, C. Park, R.M. Worth, L.L. Rubchinsky (2013) Failure of Delayed Feedback Deep Brain Stimulation for Intermittent Pathological Synchronization in Parkinson's Disease. PLoS ONE 8(3): e58264. (also available as arXiv:1302.1758)
C Park, LL Rubchinsky (2012) Potential mechanisms for imperfect synchronization in parkinsonian basal ganglia. PLoS ONE, 7(12):e51530. (also available as arXiv:1211.1990)
A. Dovzhenok, L.L. Rubchinsky (2012) On the Origin of Tremor in Parkinson's Disease. PLoS ONE 7(7): e41598. (also available as arXiv:1206.5811)
A. Dovzhenok, C. Park, R.M. Worth, L.L. Rubchinsky (2012) Synchronizing and desynchronizing effects of nonlinear delayed feedback deep brain stimulation in Parkinson's disease. BMC Neuroscience 13 (Suppl 1): P53.
C. Park, L.L. Rubchinsky (2012) Mechanisms of pathological synchrony in Parkinson's disease induced by changes in synaptic and cellular properties due to dopamine. BMC Neuroscience 13 (Suppl 1): P54.
L.L. Rubchinsky, C. Park, R.M. Worth. Intermittent neural synchronization in Parkinson's disease. Nonlinear Dynamics, 68: 329-346, 2012.
C. Park, L.L. Rubchinsky. Intermittent synchronization in a network of bursting neurons. Chaos, 21, 033125, 2011. (available as arXiv:1109.2556, profiled in Physics News Highlights by American Institute of Physics)
S. Ahn, C. Park, L.L. Rubchinsky. Detecting the temporal structure of intermittent phase locking.Physical Review E, 84, 016201, 2011. (available as arXiv:1106.1120)
Y. Guo, C. Park, M. Rong, R. M. Worth, L. L. Rubchinsky. Modulation of thalamocortical relay by basal ganglia in Parkinson's disease and dystonia. BMC Neuroscience 12(Suppl 1): P275, 2011.
C. Park, L.L. Rubchinsky. Possible mechanisms underlying intermittent synchronous activity in the networks of excitatory and inhibitory bursting neurons. BMC Neuroscience 12(Suppl 1): P276, 2011.
C. Park, R.M. Worth, L.L. Rubchinsky. Neural dynamics in parkinsonian brain: the boundary between synchronized and nonsynchronized dynamics. Physical Review E. 83, 042901, 2011. (available as arXiv:1103.0182, profiled in New Scientist)
L.L. Rubchinsky, C. Park, R.M. Worth. Fine temporal structure of beta-band synchronization in Parkinson's disease: experiments, models and mechanisms. BMC Neuroscience 11(Suppl 1): O6, 2010.
A. Dovzhenok, L.L. Rubchinsky. Modeling the origin of parkinsonian tremor. BMC Neuroscience 11(Suppl 1): P34, 2010
C. Park, R.M. Worth, L.L. Rubchinsky. Fine temporal structure of beta oscillations synchronization in subthalamic nucleus in Parkinson's disease. J. Neurophysiol. 103:2707-2716, 2010.
C. Park, R.M. Worth, L.L. Rubchinsky. Intermittent patterns of synchronous activity in human basal ganglia. BMC Neuroscience 9(Suppl 1): 150, 2008.
L.L. Rubchinsky, A.S. Kuznetsov, V.L. Wheelock, K.A. Sigvardt. Tremor. Scholarpedia, 2(10): 1379, 2007.
A.S. Kuznetsov, L.L. Rubchinsky, N. Kopell, C. Wilson. Models of Midbrain Dopaminergic Neurons. Scholarpedia, 2(10): 1812, 2007.
L.L. Rubchinsky, N. Kopell, K.A. Sigvardt. Conductance-based models of STN-GPe-GPi circuits: from biophysics to behavior. In Recent Breakthroughs in Basal Ganglia Research, ed. E. Bezard. Nova Publishers, 17-25, 2006.
J.M. Hurtado, L.L. Rubchinsky, K.A. Sigvardt. The dynamics of tremor networks in Parkinson's disease. In Recent Breakthroughs in Basal Ganglia Research, ed. E Bezard. Nova Publishers, 249-266, 2006.
J.M. Hurtado, L.L. Rubchinsky, K.A. Sigvardt, V.L. Wheelock, C.T.E. Pappas. Temporal evolution of oscillations and synchrony in GPi/muscle pairs in Parkinson's disease. J. Neurophysiol. 93: 1569-1584, 2005.
J.M. Hurtado, L.L. Rubchinsky, K.A. Sigvardt. Statistical method for detection of phase locking episodes in neural oscillations. J. Neurophysiol. 91:1883-1898, 2004
L.L. Rubchinsky, N. Kopell, K.A. Sigvardt. Modeling facilitation and inhibition of competing motor programs in basal ganglia subthalamic nucleus - pallidal circuits. Proc. Nat. Acad. Sci. USA 100: 14427-14432, 2003.
L.L. Rubchinsky, M.M. Sushchik, G.V. Osipov. Patterns in networks of oscillators formed via synchronization and oscillator death. Mathematics and Computers in Simulation 58: 443-467, 2002.
L. Rubchinsky, M. Sushchik. Disorder can eliminate oscillator death. Physical Review E 62: 6440-6446, 2000.
L.L. Rubchinsky, G.V. Osipov, M.M. Sushchik. Intermittent front propagation in arrays of bistable oscillators. In Proc. Int. Symposium on Nonlinear Theory and Its Applications. Dresden, Germany, v. 1, 273-276, 2000.
L. Rubchinsky, M. Sushchik. The action of disorder on oscillator death. In Proc. 2nd IEEE - IUTAM Int. Conference "Control of Oscillations and Chaos". Ed. by F.L. Chernousko and A.L. Fradkov. Piscataway, NJ: IEEE, v. 1, 181-182, 2000.
M.M. Sushchik, G.V. Osipov, L.L. Rubchinsky. Intermittency in transitions from non-propagation to propagation in bistable active media. In Proc. VII School-Seminar "Wave Phenomena in Inhomogeneous Media". Krasnovidovo, Russia, v. 1, 19-20, 2000.
L.L. Rubchinsky, M.M. Sushchik. The influence of disorder on oscillator death in inhomogeneous arrays of self-oscillators. In Proc. VII School-Seminar "Wave Phenomena in Inhomogeneous Media". Krasnovidovo, Russia, v. 1, 20-22, 2000.
L. Rubchinsky, M. Sushchik. The influence of disorder on oscillator death in smoothly inhomogeneous arrays of oscillators. In Stochaos: Stochastic and Chaotic Dynamics in the Lakes. Ed. by D.S. Broomhead, E.A. Luchinskaya, P.V.E. McClintock., T. Mullin. Woodbury, NY: American Institute of Physics, 567-572, 2000.
L. Rubchinsky, M. Sushchik. Anomalous relationship between spatial and temporal patterns of dynamical behavior. Int. J. Bifurcation and Chaos 9: 2329-2334, 1999.
L.L. Rubchinskii, M.M. Sushchik. Direct and reverse relationship between disordered spatial and temporal patterns in arrays of chaotic oscillators. Izv. VUZov Prikladnaya Nelineinaya Dinamika 7: 81-87, 1999. In Russian.
G. Osipov, L. Rubchinsky, M. Sushchik. Controlled formation of synchronized clusters in arrays of diffusively coupled Van der Pol oscillators. In Proc. Int. Symposium on Nonlinear Theory and Its Applications. Crans-Montana, Switzerland, v. 2, 531-534, 1998.
L. Rubchinsky, M. Sushchik, Anomalous relationship between spatial and temporal patterns of behavior in homogeneous nonlinear nonequilibrium media. In Proc. Int. Symposium on Nonlinear Theory and Its Applications. Crans-Montana, Switzerland, v. 1, 307-310, 1998.
L.L. Rubchinsky, M.M. Sushchik. Synchronized clusters and their control in the chains of self-oscillators with inhomogeneous distribution of natural frequencies. In Proc. VI School-Seminar "Wave Phenomena in Inhomogeneous Media". Krasnovidovo, Russia, 62, 1998.
H.D.I. Abarbanel, M.I. Rabinovich, A. Selverston, M.V. Bazhenov, R. Huerta, M.M. Sushchik, L.L. Rubchinskii. Synchronization in neural networks. Uspekhi Fizicheskih Nauk 166: 363-390 (translated to English in Physics-Uspekhi 39: 337-362), 1996.
M. Rabinovich, A. Selverston, L. Rubchinsky, R. Huerta. Dynamics and kinematics of simple neural systems. Chaos 6: 288-296, 1996.
M. Bazhenov, M. Rabinovich, L. Rubchinsky. Time-periodic spatial chaos in the complex Ginzburg-Landau equation. J. Stat. Phys. 83: 1165-1181, 1996.
M.V. Bazhenov, M.I. Rabinovich, L.L. Rubchinsky. Simple neuronal model with complex oscillatory activity. Izv. VUZov Prikladnaya Nelineinaya Dinamika 4: 33-39, 1996. In Russian.
M. Bazhenov, M. Rabinovich, L. Rubchinsky. An oscillatory neural network unit model. In Chaotic, Fractal, and Nonlinear Signal Processing. Ed. R.A. Katz. American Institute of Physics, 726-733, 1996.
M. Bazhenov, M. Rabinovich, L. Rubchinsky. Time periodic spatial disorder in a complex Ginzburg-Landau equation. In Chaotic, Fractal, and Nonlinear Signal Processing. Ed. R.A. Katz. American Institute of Physics, 533-540, 1996.
M. Bazhenov, M. Rabinovich, L. Rubchinsky. A model for neural network with complex oscillatory activity. In Proc. 1995 Int. Symposium on Nonlinear Theory and Its Applications. Las Vegas, NV, v. 2, 1045-1048, 1995.
M.V. Bazhenov, M.I. Rabinovich, L.L. Rubchinskii. Periodic evolution of space chaos in the one-dimensional complex Ginzburg-Landau equation. Izv. VUZov. Radiofizika 38: 37-43 (translated to English in Radiophysics and Quantum Electronics 38: 25-29), 1995.