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Volumn 8, Issue 6, 2011, Pages

Single input optimal control for globally coupled neuron networks

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL INPUTS; COUPLED NEURONS; COUPLING STRENGTHS; DISCRETE TIME DYNAMICS; HODGKIN-HUXLEY MODELS; HODGKIN-HUXLEY NEURON; KURAMOTO MODELS; NEURAL POPULATIONS; OPTIMAL CONTROLS; PHASE MODEL; SINGLE INPUT; SINGLE NEURON; STATE SPACE;

EID: 81855186895     PISSN: 17412560     EISSN: 17412552     Source Type: Journal    
DOI: 10.1088/1741-2560/8/6/065008     Document Type: Review
Times cited : (42)

References (56)
  • 1
    • 0020069726 scopus 로고
    • The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: A mathematical model
    • Cohen A, Holmes P and Rand R H 1982 The nature of coupling between segmental oscillators of the lamprey spinal generator for locomotion: a model J. Math Biol. 13 345-69 (Pubitemid 12159172)
    • (1982) Journal of Mathematical Biology , vol.13 , Issue.3 , pp. 345-369
    • Cohen, A.H.1    Holmes, P.J.2    Rand, R.H.3
  • 2
    • 0025477416 scopus 로고
    • Phase transitions and other phenomena in chains of coupled oscillators
    • Kopell N and Ermentrout G B 1990 Phase transitions and other phenomena in chains of coupled oscillators SIAM J. Appl. Math. 50 1014-52 (Pubitemid 20710968)
    • (1990) SIAM Journal on Applied Mathematics , vol.50 , Issue.4 , pp. 1014-1052
    • Kopell, N.1    Ermentrout, G.B.2
  • 3
    • 34249831818 scopus 로고
    • The dynamics of N weakly coupled identical oscillators
    • Ashwin P and Swift J 1992 The dynamics of N weakly coupled identical oscillators J. Nonlinear Sci. 2 69-108
    • (1992) J. Nonlinear Sci. , vol.2 , pp. 69-108
    • Ashwin, P.1    Swift, J.2
  • 4
    • 21144476599 scopus 로고
    • Phase dynamics for weakly coupled Hodgkin-Huxley neurons
    • Hansel D, Mato G and Meunier C 1993 Phase dynamics for weakly coupled Hodgkin-Huxley neurons Europhys. Lett. 25 367-72
    • (1993) Europhys. Lett. , vol.25 , pp. 367-372
    • Hansel, D.1    Mato, G.2    Meunier, C.3
  • 7
    • 17744382781 scopus 로고    scopus 로고
    • A minimal model of a central pattern generator and motoneurons for insect locomotion
    • DOI 10.1137/040607563
    • Ghigliazza R M and Holmes P 2004 A minimal model of a central pattern generator and motoneurons for insect locomotion SIAM J. Appl. Dyn. Syst. 3 671-700 (Pubitemid 40578321)
    • (2004) SIAM Journal on Applied Dynamical Systems , vol.3 , Issue.4 , pp. 671-700
    • Ghigliazza, R.M.1    Holmes, P.2
  • 9
    • 1542351229 scopus 로고    scopus 로고
    • On the Phase Reduction and Response Dynamics of Neural Oscillator Populations
    • DOI 10.1162/089976604322860668
    • Brown E, Moehlis J and Holmes P 2004 On the phase reduction and response dynamics of neural oscillator populations Neural Comput. 16 673-715 (Pubitemid 38318129)
    • (2004) Neural Computation , vol.16 , Issue.4 , pp. 673-715
    • Brown, E.1    Moehlis, J.2    Holmes, P.3
  • 13
    • 52449099176 scopus 로고    scopus 로고
    • Spike timing control of oscillatory neuron models using impulsive and quasi-impulsive charge-balanced inputs
    • Danzl P and Moehlis J 2008 Spike timing control of oscillatory neuron models using impulsive and quasi-impulsive charge-balanced inputs Proc. 2008 American Control Conf. (Seattle, WA) pp 171-6
    • (2008) Proc. 2008 American Control Conf. (Seattle, WA) , pp. 171-176
    • Danzl, P.1    Moehlis, J.2
  • 14
    • 65549154476 scopus 로고    scopus 로고
    • Tracking and control of neuronal Hodgkin-Huxley dynamics
    • Ullah G and Schiff S J 2009 Tracking and control of neuronal Hodgkin-Huxley dynamics Phys. Rev. E 79 040901
    • (2009) Phys. Rev. E , vol.79 , pp. 040901
    • Ullah, G.1    Schiff, S.J.2
  • 16
    • 77958031205 scopus 로고    scopus 로고
    • Charge-balanced spike timing control for phase models of spiking neurons Discrete Continuous Dyn
    • Danzl P, Nabi A and Moehlis J 2010 Charge-balanced spike timing control for phase models of spiking neurons Discrete Continuous Dyn. Syst. A 28 1413-35
    • (2010) Syst. A , vol.28 , pp. 1413-1435
    • Danzl, P.1    Nabi, A.2    Moehlis, J.3
  • 19
    • 0035960120 scopus 로고    scopus 로고
    • Deep-brain stimulation of the subthalamic nucleus or the pars interna of the globus pallidus in Parkinson's disease
    • Deep Brain Stimulation for Parkinson's Disease Study Group
    • Deep Brain Stimulation for Parkinson's Disease Study Group 2001 Deep-brain stimulation of the subthalamic nucleus or the pars interna of the globus pallidus in Parkinson's disease N. Engl. J. Med. 345 956-63
    • (2001) N. Engl. J. Med. , vol.345 , pp. 956-963
  • 24
    • 0141923468 scopus 로고    scopus 로고
    • A model of desynchronizing deep brain stimulation with a demand-controlled coordinated reset of neural subpopulations
    • Tass P 2003 A model of desynchronizing deep brain stimulation with a demand-controlled coordinated reset of neural subpopulations Biol. Cybern. 89 81-8
    • (2003) Biol. Cybern. , vol.89 , pp. 81-88
    • Tass, P.1
  • 25
    • 0039592729 scopus 로고    scopus 로고
    • From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators
    • Strogatz S H 2000 From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators Physica D 143 1-20
    • (2000) Physica D , vol.143 , pp. 1-20
    • Strogatz, S.H.1
  • 26
    • 0023204733 scopus 로고
    • Mechanisms of sinoatrial pacemaker synchronization: A new hypothesis
    • Michaels D C, Matyas E P and Jalife J 1987 Mechanisms of sinoatrial pacemaker synchronization: a new hypothesis Circ. Res. 61 704-14 (Pubitemid 17157311)
    • (1987) Circulation Research , vol.61 , Issue.5 , pp. 704-714
    • Michaels, D.C.1    Matyas, E.P.2    Jalife, J.3
  • 27
    • 0024165008 scopus 로고
    • Synchronous rhythmic flashing of fireflies: II
    • Buck J 1988 Synchronous rhythmic flashing of fireflies: II Q. Rev. Biol. 63 265-89
    • (1988) Q. Rev. Biol. , vol.63 , pp. 265-289
    • Buck, J.1
  • 28
    • 0016957851 scopus 로고
    • Synchronous fireflies
    • Buck J and Buck E 1976 Synchronous fireflies Sci.Am. 234 74-85
    • (1976) Sci.Am. , vol.234 , pp. 74-85
    • Buck, J.1    Buck, E.2
  • 29
    • 0000254372 scopus 로고
    • Acoustic synchrony - 2 mechanisms in snowy tree cricket
    • Walker T J 1969 Acoustic synchrony - 2 mechanisms in snowy tree cricket Science 166 891
    • (1969) Science , vol.166 , pp. 891
    • Walker, T.J.1
  • 30
    • 84975645812 scopus 로고
    • Numerical simulation of a large number of coupled lasers
    • Buck J and Buck E 1993 Numerical simulation of a large number of coupled lasers J. Opt. Soc. Am. 10 155-63
    • (1993) J. Opt. Soc. Am. , vol.10 , pp. 155-163
    • Buck, J.1    Buck, E.2
  • 32
    • 0026170890 scopus 로고
    • Quasi-optical power combining using mutually synchronized oscillator arrays
    • York R A and Compton R C 1991 Quasi-optical power combining using mutually synchronized oscillator arrays IEEE Trans. Microw. Theory Tech. 39 1000-9
    • (1991) IEEE Trans. Microw. Theory Tech. , vol.39 , pp. 1000-1009
    • York, R.A.1    Compton, R.C.2
  • 33
    • 0001006240 scopus 로고    scopus 로고
    • Synchronization transitions in a disordered Josephson series array
    • Wiesenfeld K, Colet P and Strogatz S H 1996 Synchronization transitions in a disordered Josephson series array Phys. Rev. Lett. 76 404-7 (Pubitemid 126601867)
    • (1996) Physical Review Letters , vol.76 , Issue.3 , pp. 404-407
    • Wiesenfeld, K.1    Colet, P.2    Strogatz, S.H.3
  • 35
    • 35649001607 scopus 로고
    • A quantitative description of membrane current and its application to conduction and excitation in nerve
    • Hodgkin A L and Huxley A F 1952 A quantitative description of membrane current and its application to conduction and excitation in nerve J. Physiol. 117 500-44
    • (1952) J. Physiol. , vol.117 , pp. 500-544
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 36
    • 31544467353 scopus 로고    scopus 로고
    • Canards for a reduction of the Hodgkin-Huxley equations
    • DOI 10.1007/s00285-005-0347-1
    • Moehlis J 2006 Canards for a reduction of the Hodgkin-Huxley equations J. Math. Biol. 52 141-53 (Pubitemid 43155411)
    • (2006) Journal of Mathematical Biology , vol.52 , Issue.2 , pp. 141-153
    • Moehlis, J.1
  • 38
    • 0016194585 scopus 로고
    • Patterns of phase compromise in biological cycles
    • Winfree A 1974 Patterns of phase compromise in biological cycles J. Math. Biol. 1 73-95
    • (1974) J. Math. Biol. , vol.1 , pp. 73-95
    • Winfree, A.1
  • 41
    • 0016314153 scopus 로고
    • Isochrons and phaseless sets
    • Guckenheimer J 1975 Isochrons and phaseless sets J. Math. Biol. 1 259-73
    • (1975) J. Math. Biol. , vol.1 , pp. 259-273
    • Guckenheimer, J.1
  • 42
    • 84862775256 scopus 로고    scopus 로고
    • Available at
    • Ermentrout G B XPP-AUT. Available at http://www.math.pitt.edu/bard/xpp/ xpp.html
    • Ermentrout G B XPP-AUT
  • 45
    • 0004178386 scopus 로고    scopus 로고
    • Upper Saddle River, NJ: Prentice-Hall
    • Khalil H K 2002 Nonlinear Systems (Upper Saddle River, NJ: Prentice-Hall)
    • (2002) Nonlinear Systems
    • Khalil, H.K.1
  • 48
    • 0026561028 scopus 로고
    • Rhythmogenic effects of weak electrotonic coupling in neuronal models
    • Sherman A and Rinzel J 1992 Rhythmogenic effects of weak electrotonic coupling in neuronal models Proc. Natl Acad. Sci. USA 89 2471-4
    • (1992) Proc. Natl Acad. Sci. USA , vol.89 , pp. 2471-2474
    • Sherman, A.1    Rinzel, J.2
  • 49
    • 0018350623 scopus 로고
    • Electrotonic coupling among neuroendocrine cells in Aplysia
    • Blankenship J E and Haskins J T 1979 Electrotonic coupling among neuroendocrine cells in aplysia J. Neurophysiol. 42 347-55 (Pubitemid 9128387)
    • (1979) Journal of Neurophysiology , vol.42 , Issue.2 , pp. 347-355
    • Blankenship, J.E.1    Haskins, J.T.2
  • 50
    • 0035065832 scopus 로고    scopus 로고
    • Model for olfactory discrimination and learning in Limax procerebrum incorporating oscillatory dynamics and wave propagation
    • Ermentrout G B, Wang J W, Flores J and Gelperin A 2001 Model for olfactory discrimination and learning in limax procerebrum incorporating oscillatory dynamics and wave propagation J. Neurophysiol. 85 1444-52 (Pubitemid 32280585)
    • (2001) Journal of Neurophysiology , vol.85 , Issue.4 , pp. 1444-1452
    • Ermentrout, B.1    Wang, J.W.2    Flores, J.3    Gelperin, A.4
  • 51
    • 4444346831 scopus 로고    scopus 로고
    • Electrotonic coupling between stratum oriens interneurones in the intact in vitro mouse juvenile hippocampus
    • DOI 10.1113/jphysiol.2004.065649
    • Zhang X L, Zhang L and Carlen P L 2004 Electrotonic coupling between stratum oriens interneurons in the intact in vitro mouse juvenile hippocampus J. Physiol. 558 825-39 (Pubitemid 39199107)
    • (2004) Journal of Physiology , vol.558 , Issue.3 , pp. 825-839
    • Zhang, X.-L.1    Zhang, L.2    Carlen, P.L.3
  • 52
    • 0033135299 scopus 로고    scopus 로고
    • Electrotonic coupling interacts with intrinsic properties to generate synchronized activity in cerebellar networks of inhibitory interneurons
    • Mann-Metzer P and Yarom Y 1999 Electrotonic coupling interacts with intrinsic properties to generate synchronized activity in cerebellar networks of inhibitory interneurons J. Neurosci. 19 3298-306 (Pubitemid 29203109)
    • (1999) Journal of Neuroscience , vol.19 , Issue.9 , pp. 3298-3306
    • Mann-Metzer, P.1    Yarom, Y.2
  • 53
    • 14244261263 scopus 로고    scopus 로고
    • Electrotonic coupling in the anterior pituitary of a teleost fish
    • DOI 10.1210/en.2004-1415
    • Levavi-Sivan B, Bloch C L, Gutnick M J and Fleidervish I A 2005 Electrotonic coupling in the anterior pituitary of a teleost fish Endocrinology 146 1048-52 (Pubitemid 40289294)
    • (2005) Endocrinology , vol.146 , Issue.3 , pp. 1048-1052
    • Levavi-Sivan, B.1    Bloch, C.L.2    Gutnick, M.J.3    Fleidervish, I.A.4
  • 56
    • 70349924064 scopus 로고    scopus 로고
    • Collective phase description of coupled oscillators with general network structure
    • Kori H, Kawamura Y, Nakao H, Arai K and Kuramoto Y 2009 Collective phase description of coupled oscillators with general network structure Phys. Rev. E 80 036207
    • (2009) Phys. Rev. E , vol.80 , pp. 036207
    • Kori, H.1    Kawamura, Y.2    Nakao, H.3    Arai, K.4    Kuramoto, Y.5


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