Deep brain stimulation; Kuramoto oscillators; Mean-field feedback; Phase-locking; All to alls; Hyperbolicity; Mean field; Neurological disease; Output feedback; Control and Systems Engineering; General Economics, Econometrics and Finance
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Franci, Alessio ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Brain-Inspired Computing ; Univ. Paris Sud 11, L2S, Supélec, Gif sur Yvette, 91192, France
Chaillet, A.; L2S, EECI, Supélec, France
Bezzaoucha, S.; L2S, Ecole Polytechnique, LIX, France
Language :
English
Title :
Toward oscillations inhibition by mean-field feedback in Kuramoto oscillators
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
Aeyels, D. and Rogge, J.A. (2004). Existence of partial entrainment and stability of phase locking behavior of coupled oscillators. Progress of Theoretical Physics,112(6), 921-942.
Alberts, W.W., Wright, E.J., and Feistein, B. (1969). Cortical potentials and Parkinsonian tremor. Nature, 221, 670-672.
Benabid, A., Pollack, P., Gao, D., Hoffman, D., Limousin, P., Gay, E., Payen, I., and Benazzouz, A. (1996). Chronic electrical stimulation of the ventralis intermedium nucleus of the thalamus as a treatment of movement disorders. J Neurosurg, 84, 203-214.
Carlson, J., Cleary, D., Cetas, J., Heinricher, M., and Burchiel, K. (2010). Deep brain stimulation does not silence neurons in subthalamic nucleus in Parkinson's patients. Journal of Neurophysiology, 103, 962-967.
Dörer, F. and Bullo, F. (2010). Transient stability analysis in power networks and synchronization of nonuniform Kuramoto oscillators. In Proc. American Control Conference, 930-937. Baltimore, MD.
Filali, M., Hutchison, W.D., Palter, V.N., Lozano, A.M., and Dostrovsky, J.O. (2004). Stimulation-induced inhibition of neuronal firing in human subthalamic nucleus.Exp. Brain Res., 156, 274-278.
Franci, A., Chaillet, A., and Pasillas-Lépine, W. (2010). Existence and robustness of phase-locking in coupled Kuramoto oscillators under mean-field feedback. To appear in: Automatica - Special Issue on Biology Systems. Extended version available at: http://hal.archives-ouvertes.fr/hal- 00526066/.
Guckenheimer, J. and Holmes, P. (1983). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, volume 42 of Applied Mathematical Sciences. Springer, New-York.
Hammond, C., Ammari, R., Bioulac, B., and Garcia, L. (2008). Latest view on the mechanism of action of deep brain stimulation. Movement Disorders, 23(15), 2111-2121.
Hauptmann, C., Popovych, O., and Tass, P.A. (2005). Delayed feedback control of synchronization in locally coupled neuronal networks. Neurocomputing, 65, 759-767.
Hirsch, M.W. and Smale, S. (1974). Differential equations, dynamical systems, and linear algebra. Pure and applied mathematics. Harcourt Brace Jovanovich, Accademic Press, Inc., San Diego - New York - Boston - London - Sydney - Tokio - Toronto.
Hirsh, M., Pugh, C., and Shub, M. (1977). Invariant Manifolds. Lecture Notes in Mathematics. Springer- Verlag, Berlin, Germany.
Hodgkin, A. and Huxley, A. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol, 117, 500-544.
Horn, R.A. and Johnson, C.R. (1985). Matrix Analysis. Cambridge University Press.
Jadbabaie, A., Motee, N., and Barahona, M. (2004). On the stability of the Kuramoto model of coupled nonlinear oscillators. Proc. American Control Conf., 4296-4301.
Kuramoto, Y. (1984). Chemical Oscillations, Waves, and Turbulence. Springer, Berlin.
McIntyre, C., Savasta, M., Kerkerian-Le Goff, L., and Vitek, J.L. (2004). Uncovering the mechanism(s) of action of deep brain stimulation: activation, inhibition, or both. Clinical Neurophysiology, 115, 1239-1248.
Nini, A., Feingold, A., Slovin, H., and Bergman, H. (1995). Neurons in the globus pallidus do not show correlated activity in the normal monkey, but phase-locked oscillationsappear in the MPTP model of Parkinsonism. J Neurophysiol., 74(4), 1800-1805.
Popovych, O.V., Hauptmann, C., and Tass, P.A. (2006). Desynchronization and decoupling of interacting oscillators by nonlinear delayed feedback. Internat. J. Bifur. Chaos, 16(7), 1977-1987. doi: 10.1142/S0218127406015830.
Pyragas, K., Popovych, O., and Tass, P.A. (2007). Controlling synchrony in oscillatory networks with a separate stimulation-registration setup. EPL, 80, 40002.
Rosenblum, M. and Pikovsky, A. (2004). Delayed feedback control of collective synchrony: an approach to suppression of pathological brain rhythms. Phys. Rev. E, 70(4), 041904. doi:10.1103/PhysRevE.70.041904.
Sarlette, A. (2009). Geometry and Symmetries in Coordination Control. Ph.D. thesis, University of Liège, (B).
Sarma, S.V., Cheng, M., Williams, Z., Hu, R., Eskandar, E., and Brown, E.N. (2010). Comparing healthy and Parkinsonian neuronal activity in sub-thalamic nucleus using point process models. IEEE Trans Biomed Eng., 57(6), 1297-1305.
Sepulchre, R., Paley, D.A., and Leonard, N.E. (2007). Stabilization of planar collective motion: All-to-all communication. IEEE Trans. on Automat. Contr., 52(5), 811-824.
Sijbrand, J. (1985). Properties of center manifolds. Transaction of the American Mathematical Society, 289(2), 431-469.
Tarsy, D., Vitek, J.L., Starr, P., and Okun, M. (2008). Deep Brain Stimulation in Neurological and Psychiatric Disorders. Humana Press.
Tass, P.A. (2003). A model of desynchronizing deep brain stimulation with a demand-controlled coordinated reset of neural subpopulations. Biol. Cybern., 89, 81-88.
Tukhlina, N., Rosenblum, M., Pikovsky, A., and Kurths, J. (2007). Feedback suppression of neural synchrony by vanishing stimulation. Physical Review E, 75(1), 011918.
Volkmann, J., Joliot, M., Mogilner, A., Ioannides, A.A., Lado, F., Fazzini, E., Ribary, U., and Llinás, R. (1996). Central motor loop oscillations in Parkinsonian resting tremor revealed by magnetoencephalography. Neurology, 46, 1359-1370.
Winfree, A.T. (1980). The Geometry of Biological Times. Springer, New-York.
Similar publications
Sorry the service is unavailable at the moment. Please try again later.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.