{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T23:46:17Z","timestamp":1768347977477,"version":"3.49.0"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,4,3]],"date-time":"2018-04-03T00:00:00Z","timestamp":1522713600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2018,4,3]],"date-time":"2018-04-03T00:00:00Z","timestamp":1522713600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["NSF-1264535\/1631170"],"award-info":[{"award-number":["NSF-1264535\/1631170"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["NSF-1635542"],"award-info":[{"award-number":["NSF-1635542"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Comput Neurosci"],"published-print":{"date-parts":[[2018,6]]},"DOI":"10.1007\/s10827-018-0683-y","type":"journal-article","created":{"date-parts":[[2018,4,3]],"date-time":"2018-04-03T04:27:53Z","timestamp":1522729673000},"page":"363-378","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Phase model-based neuron stabilization into arbitrary clusters"],"prefix":"10.1007","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9512-8864","authenticated-orcid":false,"given":"Timothy D.","family":"Matchen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jeff","family":"Moehlis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,4,3]]},"reference":[{"issue":"13","key":"683_CR1","doi-asserted-by":"publisher","first-page":"1679","DOI":"10.1002\/mds.25923","volume":"29","author":"I Adamchic","year":"2014","unstructured":"Adamchic, I., Hauptmann, C., Barnikol, U.B., Pawelczyk, N., Popovych, O., Barnikol, T.T., Silchenko, A., Volkmann, J., Deuschl, G., Meissner, W.G., Maarouf, M., Sturm, V., Freund, H.-J., Tass, P.A. (2014). Coordinated reset neuromodulation for Parkinson\u2019s disease: proof-of-concept study. Movement Disorders, 29(13), 1679\u20131684.","journal-title":"Movement Disorders"},{"issue":"SUPPL. 3","key":"683_CR2","first-page":"19","volume":"17","author":"AL Benabid","year":"2002","unstructured":"Benabid, A.L., Benazzous, A., Pollak, P. (2002). Mechanisms of deep brain stimulation. Movement Disorders, 17(SUPPL. 3), 19\u201338.","journal-title":"Movement Disorders"},{"issue":"1\u20134","key":"683_CR3","first-page":"73","volume":"77","author":"A Beric","year":"2002","unstructured":"Beric, A., Kelly, P.J., Rezai, A., Sterio, D., Mogilner, A., Zonenshayn, M., Kopell, B. (2002). Complications of deep brain stimulation surgery. Stereotactic and Functional Neurosurgery, 77(1\u20134), 73\u201378.","journal-title":"Stereotactic and Functional Neurosurgery"},{"issue":"4","key":"683_CR4","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1162\/089976604322860668","volume":"16","author":"E Brown","year":"2004","unstructured":"Brown, E., Moehlis, J., Holmes, P. (2004). On the phase reduction and response dynamics of neural oscillator populations. Neural Computation, 16(4), 673\u2013715.","journal-title":"Neural Computation"},{"issue":"10","key":"683_CR5","doi-asserted-by":"publisher","first-page":"3062","DOI":"10.1093\/brain\/awt239","volume":"136","author":"H Cagnan","year":"2013","unstructured":"Cagnan, H., Brittain, J.S., Little, S., Foltynie, T., Limousin, P., Zrinzo, L., Hariz, M., Joint, C., Fitzgerald, J., Green, A.L., Aziz, T., Brown, P. (2013). Phase dependent modulation of tremor amplitude in essential tremor through thalamic stimulation. Brain: A Journal of Neurology, 136(10), 3062\u20133075.","journal-title":"Brain: A Journal of Neurology"},{"issue":"1","key":"683_CR6","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1016\/j.expneurol.2007.01.027","volume":"205","author":"CC Chen","year":"2007","unstructured":"Chen, C.C., Litvak, V., Gilbertson, T., Ku\u0307hn, A., Lu, C.S., Lee, S.T., Tsai, C.H., Tisch, S., Limousin, P., Hariz, M., Brown, P. (2007). Excessive synchronization of basal ganglia neurons at 20 Hz slows movement in Parkinson\u2019s disease. Experimental Neurology, 205(1), 214\u2013221.","journal-title":"Experimental Neurology"},{"issue":"5-6","key":"683_CR7","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1007\/s00422-009-0344-3","volume":"101","author":"P Danzl","year":"2009","unstructured":"Danzl, P., Hespanha, J., Moehlis, J. (2009). Event-based minimum-time control of oscillatory neuron models: Phase randomization, maximal spike rate increase, and desynchronization. Biological Cybernetics, 101(5-6), 387\u2013399.","journal-title":"Biological Cybernetics"},{"key":"683_CR8","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718195","volume-title":"Simulating, analyzing, and animating dynamical systems","author":"B Ermentrout","year":"2002","unstructured":"Ermentrout, B. (2002). Simulating, analyzing, and animating dynamical systems. Philadelphia: Society for Industrial and Applied Mathematics."},{"key":"683_CR9","volume-title":"Mathematical foundations of neuroscience, volume 35 of interdisciplinary applied mathematics","author":"GB Ermentrout","year":"2010","unstructured":"Ermentrout, G.B., & Terman, D.H. (2010). Mathematical foundations of neuroscience, volume 35 of interdisciplinary applied mathematics. New York: Springer."},{"issue":"15","key":"683_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1103\/PhysRevLett.94.158101","volume":"94","author":"RF Galan","year":"2005","unstructured":"Galan, R.F., Ermentrout, G.B., Urban, N.N. (2005). Efficient estimation of phase-resetting curves in real neurons and its significance for neural-network modeling. Physical Review Letters, 94(15), 1\u20134.","journal-title":"Physical Review Letters"},{"issue":"5","key":"683_CR11","doi-asserted-by":"publisher","first-page":"1095","DOI":"10.1162\/089976600300015529","volume":"12","author":"D Golomb","year":"2000","unstructured":"Golomb, D., & Hansel, D. (2000). The number of synaptic inputs and the synchrony of large, sparse neuronal networks. Neural Computation, 12(5), 1095\u20131139.","journal-title":"Neural Computation"},{"issue":"7","key":"683_CR12","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1016\/j.tins.2007.05.004","volume":"30","author":"C Hammond","year":"2007","unstructured":"Hammond, C., Bergman, H., Brown, P. (2007). Pathological synchronization in Parkinson\u2019s disease: networks, models and treatments. Trends in Neurosciences, 30(7), 357\u2013364.","journal-title":"Trends in Neurosciences"},{"key":"683_CR13","doi-asserted-by":"publisher","first-page":"500","DOI":"10.1113\/jphysiol.1952.sp004764","volume":"117","author":"A Hodgkin","year":"1952","unstructured":"Hodgkin, A., & Huxley, A. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology, 117, 500\u2013544.","journal-title":"Journal of Physiology"},{"issue":"2","key":"683_CR14","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1136\/jnnp.64.2.273","volume":"64","author":"SE Hua","year":"1998","unstructured":"Hua, S.E., Lenz, F. a., Zirh, T. a., Reich, S.G., Dougherty, P.M. (1998). Thalamic neuronal activity correlated with essential tremor. Journal of Neurology, Neurosurgery, and Psychiatry, 64(2), 273\u2013276.","journal-title":"Journal of Neurology, Neurosurgery, and Psychiatry"},{"key":"683_CR15","volume-title":"Foundations of cellular neurophysiology","author":"D Johnston","year":"1995","unstructured":"Johnston, D., & Wu, S. M.-S. (1995). Foundations of cellular neurophysiology, 1st edn. Cambridge: MIT Press.","edition":"1st edn."},{"key":"683_CR16","volume-title":"Mathematical physiology. Interdisciplinary applied mathematics","author":"J Keener","year":"2009","unstructured":"Keener, J., & Sneyd, J. (2009). Mathematical physiology. Interdisciplinary applied mathematics. New York: Springer."},{"key":"683_CR17","volume-title":"Nonlinear control","author":"H Khalil","year":"2015","unstructured":"Khalil, H. (2015). Nonlinear control, 1st edn. New York: Pearson.","edition":"1st edn."},{"key":"683_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-69689-3","volume-title":"Chemical oscillations, waves, and turbulence, volume 19 of springer series in synergetics","author":"Y Kuramoto","year":"1984","unstructured":"Kuramoto, Y. (1984). Chemical oscillations, waves, and turbulence, volume 19 of springer series in synergetics. Springer: Berlin."},{"issue":"20","key":"683_CR19","doi-asserted-by":"publisher","first-page":"7766","DOI":"10.1523\/JNEUROSCI.20-20-07766.2000","volume":"20","author":"R Levy","year":"2000","unstructured":"Levy, R., Hutchison, W., Lozano, A., Dostrovsky, J. (2000). High-frequency synchronization of neuronal activity in the subthalamic nucleus of Parkinsonian patients with limb tremor. The Journal of Neuroscience, 20(20), 7766\u20137775.","journal-title":"The Journal of Neuroscience"},{"issue":"8","key":"683_CR20","doi-asserted-by":"publisher","first-page":"1919","DOI":"10.1109\/TAC.2013.2250112","volume":"58","author":"J-S Li","year":"2013","unstructured":"Li, J.-S., Dasanayake, I., Ruths, J. (2013). Control and synchronization of neuron ensembles. IEEE Transactions on Automatic Control, 58(8), 1919\u20131930.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"683_CR21","doi-asserted-by":"publisher","first-page":"63","DOI":"10.3389\/fncom.2013.00063","volume":"7","author":"L Lu\u0307cken","year":"2013","unstructured":"Lu\u0307cken, L., Yanchuk, S., Popovych, O.V., Tass, P.A. (2013). Desynchronization boost by non-uniform coordinated reset stimulation in ensembles of pulse-coupled neurons. Frontiers in Computational Neuroscience, 7, 63.","journal-title":"Frontiers in Computational Neuroscience"},{"issue":"3","key":"683_CR22","doi-asserted-by":"publisher","first-page":"036019","DOI":"10.1088\/1741-2560\/8\/3\/036019","volume":"8","author":"B Lysyansky","year":"2011","unstructured":"Lysyansky, B., Popovych, O.V., Tass, P.A. (2011). Desynchronizing anti-resonance effect of m: n ON-OFF coordinated reset stimulation. Journal of Neural Engineering, 8(3), 036019.","journal-title":"Journal of Neural Engineering"},{"issue":"July","key":"683_CR23","first-page":"5","volume":"6","author":"B Lysyansky","year":"2013","unstructured":"Lysyansky, B., Popovych, O.V., Tass, P.A. (2013). Optimal number of stimulation contacts for coordinated reset neuromodulation. Frontiers in Neuroengineering, 6(July), 5.","journal-title":"Frontiers in Neuroengineering"},{"key":"683_CR24","doi-asserted-by":"crossref","unstructured":"Matchen, T., & Moehlis, J. (2017). Real-time stabilization of neurons into clusters. In American controls conference (pp. 2805\u20132810). Seattle.","DOI":"10.23919\/ACC.2017.7963376"},{"issue":"10","key":"683_CR25","doi-asserted-by":"publisher","first-page":"2240","DOI":"10.1093\/brain\/awh571","volume":"128","author":"MC Rodriguez-Oroz","year":"2005","unstructured":"Rodriguez-Oroz, M.C., Obeso, J.A., Lang, A.E., Houeto, J.L., Pollak, P., Rehncrona, S., Kulisevsky, J., Albanese, A., Volkmann, J., Hariz, M.I., Quinn, N.P., Speelman, J.D., Guridi, J., Zamarbide, I., Gironell, A., Molet, J., Pascual-Sedano, B., Pidoux, B., Bonnet, A.M., Agid, Y., Xie, J., Benabid, A.L., Lozano, A.M., Saint-Cyr, J., Romito, L., Contarino, M.F., Scerrati, M., Fraix, V., Van Blercom, N. (2005). Bilateral deep brain stimulation in Parkinson\u2019s disease: a multicentre study with 4 years follow-up. Brain: A Journal of Neurology, 128(10), 2240\u20132249.","journal-title":"Brain: A Journal of Neurology"},{"issue":"4","key":"683_CR26","doi-asserted-by":"publisher","first-page":"041904","DOI":"10.1103\/PhysRevE.70.041904","volume":"70","author":"M Rosenblum","year":"2004","unstructured":"Rosenblum, M., & Pikovsky, A. (2004). Delayed feedback control of collective synchrony: an approach to suppression of pathological brain rhythms. Physical Review E, 70(4), 041904.","journal-title":"Physical Review E"},{"issue":"3","key":"683_CR27","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1023\/B:JCNS.0000025686.47117.67","volume":"16","author":"JE Rubin","year":"2004","unstructured":"Rubin, J.E., & Terman, D. (2004). High frequency stimulation of the subthalamic nucleus eliminates pathological thalamic rhythmicity in a computational model. Journal of Computational Neuroscience, 16(3), 211\u2013235.","journal-title":"Journal of Computational Neuroscience"},{"issue":"2","key":"683_CR28","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1109\/MCS.2013.2295710","volume":"34","author":"P Sacr\u0117","year":"2014","unstructured":"Sacr\u0117, P., & Sepulchre, R. (2014). Sensitivity analysis of oscillator models in the space of phase-response curves: oscillators as open systems. IEEE Control Systems, 34(2), 50\u201374.","journal-title":"IEEE Control Systems"},{"issue":"1","key":"683_CR29","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/j.mayocp.2011.08.005","volume":"87","author":"R Savica","year":"2012","unstructured":"Savica, R., Stead, M., Mack, K.J., Lee, K.H., Klassen, B.T. (2012). Deep brain stimulation in Tourette syndrome: a description of 3 patients with excellent outcome. Mayo Clinic Proceedings, 87(1), 59\u201362.","journal-title":"Mayo Clinic Proceedings"},{"issue":"4","key":"683_CR30","doi-asserted-by":"publisher","first-page":"424","DOI":"10.1587\/nolta.5.424","volume":"5","author":"GS Schmidt","year":"2014","unstructured":"Schmidt, G.S., Wilson, D., Allgower, F., Moehlis, J. (2014). Selective averaging with application to phase reduction and neural controls. Nonlinear Theory and Its Application IEICE, 5(4), 424\u2013435.","journal-title":"Nonlinear Theory and Its Application IEICE"},{"issue":"4","key":"683_CR31","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1038\/nrn1650","volume":"6","author":"A Schnitzler","year":"2005","unstructured":"Schnitzler, A., & Gross, J. (2005). Normal and pathological oscillatory communication in the brain. Nature Reviews Neuroscience, 6(4), 285\u201396.","journal-title":"Nature Reviews Neuroscience"},{"issue":"2","key":"683_CR32","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1007\/s00422-003-0425-7","volume":"89","author":"PA Tass","year":"2003","unstructured":"Tass, P.A. (2003a). A model of desynchronizing deep brain stimulation with a demand-controlled coordinated reset of neural subpopulations. Biological Cybernetics, 89(2), 81\u201388.","journal-title":"Biological Cybernetics"},{"issue":"150","key":"683_CR33","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1143\/PTPS.150.281","volume":"150","author":"PA Tass","year":"2003","unstructured":"Tass, P.A. (2003b). Desynchronization by means of a coordinated reset of neural sub-populations - a novel technique for demand-controlled deep brain stimulation. Progress of Theoretical Physics Supplement, 150(150), 281\u2013296.","journal-title":"Progress of Theoretical Physics Supplement"},{"issue":"13","key":"683_CR34","doi-asserted-by":"publisher","first-page":"956","DOI":"10.1056\/NEJMoa000827","volume":"345","author":"The Deep-Brain Stimulation for Parkinson\u2019s Disease Study Group","year":"2001","unstructured":"The Deep-Brain Stimulation for Parkinson\u2019s Disease Study Group. (2001). Deep-brain stimulation of the subthalamic nucleus or the pars interna of the globus pallidus in Parkinson\u2019s disease. New England Journal of Medicine, 345(13), 956\u2013963.","journal-title":"New England Journal of Medicine"},{"issue":"1","key":"683_CR35","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/j.neuron.2006.09.020","volume":"52","author":"PJ Uhlhaas","year":"2006","unstructured":"Uhlhaas, P.J., & Singer, W. (2006). Neural synchrony in brain disorders: relevance for cognitive dysfunctions and pathophysiology. Neuron, 52(1), 155\u2013168.","journal-title":"Neuron"},{"issue":"1","key":"683_CR36","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1137\/120901702","volume":"13","author":"D Wilson","year":"2014","unstructured":"Wilson, D., & Moehlis, J. (2014). Optimal chaotic desynchronization for neural populations. SIAM Journal on Applied Dynamical Systems, 13(1), 276\u2013305.","journal-title":"SIAM Journal on Applied Dynamical Systems"},{"issue":"12","key":"683_CR37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1371\/journal.pcbi.1004673","volume":"11","author":"D Wilson","year":"2015","unstructured":"Wilson, D., & Moehlis, J. (2015). Clustered desynchronization from high-frequency deep brain stimulation. PLoS Computational Biology, 11(12), 1\u201326.","journal-title":"PLoS Computational Biology"},{"key":"683_CR38","doi-asserted-by":"publisher","first-page":"50","DOI":"10.3389\/fnsys.2011.00050","volume":"5","author":"CJ Wilson","year":"2011","unstructured":"Wilson, C.J., Beverlin, B., Netoff, T. (2011). Chaotic desynchronization as the therapeutic mechanism of deep brain stimulation. Frontiers in Systems Neuroscience, 5, 50.","journal-title":"Frontiers in Systems Neuroscience"},{"issue":"3","key":"683_CR39","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1002\/hipo.20748","volume":"21","author":"C Zhao","year":"2011","unstructured":"Zhao, C., Wang, L., Netoff, T., Yuan, L.L. (2011). Dendritic mechanisms controlling the threshold and timing requirement of synaptic plasticity. Hippocampus, 21(3), 288\u2013297.","journal-title":"Hippocampus"},{"issue":"4","key":"683_CR40","doi-asserted-by":"publisher","first-page":"1654","DOI":"10.1137\/140952211","volume":"13","author":"A Zlotnik","year":"2014","unstructured":"Zlotnik, A., & Li, J.-S. (2014). Optimal subharmonic entrainment of weakly forced nonlinear oscillators. SIAM Journal on Applied Dynamical Systems, 13(4), 1654\u20131693.","journal-title":"SIAM Journal on Applied Dynamical Systems"},{"key":"683_CR41","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/ncomms10788","volume":"7","author":"A Zlotnik","year":"2016","unstructured":"Zlotnik, A., Nagao, R., Kiss, I.Z., Li, J.-S. (2016). Phase-selective entrainment of nonlinear oscillator ensembles. Nature Communications, 7, 1\u20137.","journal-title":"Nature Communications"}],"container-title":["Journal of Computational Neuroscience"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10827-018-0683-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10827-018-0683-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10827-018-0683-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T10:29:02Z","timestamp":1589711342000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10827-018-0683-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,3]]},"references-count":41,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,6]]}},"alternative-id":["683"],"URL":"https:\/\/doi.org\/10.1007\/s10827-018-0683-y","relation":{},"ISSN":["0929-5313","1573-6873"],"issn-type":[{"value":"0929-5313","type":"print"},{"value":"1573-6873","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4,3]]},"assertion":[{"value":"8 June 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 March 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 March 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 April 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with Ethical Standards"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Conflict of interests"}}]}}