-
2
-
-
0004242420
-
-
2nd edn. Cambridge University Press
-
Biggs N (1993) Algebraic graph theory, 2nd edn. Cambridge University Press
-
(1993)
Algebraic Graph Theory
-
-
Biggs, N.1
-
4
-
-
0344848562
-
Models of respiratory rhythm generation in the pre-Botzinger complex. I. Bursting pacemaker neurons
-
Butera RJ, Rinzel J, Smith JC (1999) Models of respiratory rhythm generation in the pre-Botzinger complex: I. Bursting pacemaker neurons. J Neurophysiol 82:382-397 (Pubitemid 29330092)
-
(1999)
Journal of Neurophysiology
, vol.82
, Issue.1
, pp. 382-397
-
-
Butera Jr., R.J.1
Rinzel, J.2
Smith, J.C.3
-
5
-
-
46549093797
-
Chaos in a three-variable model of an excitable cell
-
Chay TR (1985) Chaos in a three-variable model of an excitable cell. Phys D 16:233-242
-
(1985)
Phys D
, vol.16
, pp. 233-242
-
-
Chay, T.R.1
-
6
-
-
0020957719
-
Minimal model for membrane oscillations in the pancreatic β-cell
-
Chay TR, Keizer J (1983) Minimal model for membrane oscillations in the pancreatic β-cell. Biophys J 42:181-190
-
(1983)
Biophys J
, vol.42
, pp. 181-190
-
-
Chay, T.R.1
Keizer, J.2
-
8
-
-
0034223131
-
Dynamics of spiking neurons with electrical coupling
-
Chow CC, Kopell N (2000) Dynamics of spiking neurons with electrical coupling. Neural Comp 12:1643-1679
-
(2000)
Neural Comp
, vol.12
, pp. 1643-1679
-
-
Chow, C.C.1
Kopell, N.2
-
10
-
-
5544221875
-
Aperiodic stochastic resonance in excitable systems
-
Collins JJ, Chow CC, Imhoff TT (1995) Aperiodic stochastic resonance in excitable systems. Phys Rev E 52(4):R3321-R3324
-
(1995)
Phys Rev e
, vol.52
, Issue.4
-
-
Collins, J.J.1
Chow, C.C.2
Imhoff, T.T.3
-
11
-
-
3943074508
-
Electrical synapses in the mammalian brain
-
DOI 10.1146/annurev.neuro.26.041002.131128
-
Connors BW, Long MA (2004) Electrical synapses in the mammalian brain. Ann Rev Neurosci 27:393-418 (Pubitemid 39050408)
-
(2004)
Annual Review of Neuroscience
, vol.27
, pp. 393-418
-
-
Connors, B.W.1
Long, M.A.2
-
12
-
-
55849138986
-
Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models
-
Coombes S (2008) Neuronal networks with gap junctions: a study of piece-wise linear planar neuron models. SIAM J Appl Dyn Syst 7:1101-1129
-
(2008)
SIAM J Appl Dyn Syst
, vol.7
, pp. 1101-1129
-
-
Coombes, S.1
-
13
-
-
0020500503
-
On the exponential exit law in the small parameter exit problem
-
Day MV (1983) On the exponential exit law in the small parameter exit problem. Stochastics 8:297-323
-
(1983)
Stochastics
, vol.8
, pp. 297-323
-
-
Day, M.V.1
-
14
-
-
28844486373
-
Twodistinct mechanisms of coherence in randomly perturbed dynamical systems
-
DeVille REL, MuratovC,Vanden-EijndenE (2005) Twodistinct mechanisms of coherence in randomly perturbed dynamical systems. Phys Rev E 72:031105
-
(2005)
Phys Rev e
, vol.72
, pp. 031105
-
-
Deville, R.E.L.1
Muratov, C.2
Vanden-Eijnden, E.3
-
15
-
-
0034700423
-
Channel sharing in pancreatic β-cells revisited: Enhancement of emergent bursting by noise
-
De Vries G, Sherman A (2000) Channel sharing in pancreatic β-cells revisited: enhancement of emergent bursting by noise. J Theor Biol 207:513-530
-
(2000)
J Theor Biol
, vol.207
, pp. 513-530
-
-
De Vries, G.1
Sherman, A.2
-
16
-
-
0001350119
-
Algebraic connectivity of graphs
-
Fiedler M (1973) Algebraic connectivity of graphs. Czech Math J 23(98):298-305
-
(1973)
Czech Math J
, vol.23
, Issue.98
, pp. 298-305
-
-
Fiedler, M.1
-
17
-
-
0035532611
-
On stable oscillations and equilibriums induced by small noise
-
Freidlin MI (2001) On stable oscillations and equilibriums induced by small noise. J Stat Phys 103(1-2):283-300
-
(2001)
J Stat Phys
, vol.103
, Issue.1-2
, pp. 283-300
-
-
Freidlin, M.I.1
-
19
-
-
67949093089
-
A proof of Alon's second eigenvalue conjecture and related problems
-
Friedman J (2008) A proof of Alon's second eigenvalue conjecture and related problems. Memoirs of the American Mathematical Society, vol 195
-
(2008)
Memoirs of the American Mathematical Society
, vol.195
-
-
Friedman, J.1
-
21
-
-
40749116553
-
Minimizing effective resistance of a graph
-
DOI 10.1137/050645452
-
Ghosh A, Boyd S, Saberi A (2008) Minimizing effective resistance of a graph. SIAM Rev 50(1):37-66 (Pubitemid 351386903)
-
(2008)
SIAM Review
, vol.50
, Issue.1
, pp. 37-66
-
-
Ghosh, A.1
Boyd, S.2
Saberi, A.3
-
22
-
-
33745053321
-
Antireliability of noise-driven neurons
-
Goldobin DS, Pikovsky A (2006) Antireliability of noise-driven neurons. Phys Rev E 73:061906
-
(2006)
Phys Rev e
, vol.73
, pp. 061906
-
-
Goldobin, D.S.1
Pikovsky, A.2
-
23
-
-
0021714346
-
The control of firing pattern in nigral dopamine neurons: Single spike firing
-
Grace AA, Bunney BS (1984) The control of firing pattern in nigral dopamine neuron: single spike firing. J Neurosci 4:2866-2876 (Pubitemid 15224431)
-
(1984)
Journal of Neuroscience
, vol.4
, Issue.11
, pp. 2866-2876
-
-
Grace, A.A.1
Bunney, B.S.2
-
26
-
-
62249174825
-
Bursting oscillations induced by small noise
-
Hitczenko P, Medvedev GS (2009) Bursting oscillations induced by small noise. SIAM J Appl Math 69(5):1359-1392
-
(2009)
SIAM J Appl Math
, vol.69
, Issue.5
, pp. 1359-1392
-
-
Hitczenko, P.1
Medvedev, G.S.2
-
29
-
-
0000303940
-
Neural excitability, spiking, and bursting
-
Izhikevich EM (2000) Neural excitability, spiking, and bursting,. Int J Bifurcation Chaos 10:1171-1266
-
(2000)
Int J Bifurcation Chaos
, vol.10
, pp. 1171-1266
-
-
Izhikevich, E.M.1
-
30
-
-
0002316532
-
Geometric singular perturbation theory
-
Springer, Berlin
-
Jones CKRT (1995) Geometric singular perturbation theory, Lecture Notes in Mathematics, vol 1609. Springer, Berlin, pp 44-118
-
(1995)
Lecture Notes in Mathematics
, vol.1609
, pp. 44-118
-
-
Jones, C.K.R.T.1
-
31
-
-
34249656076
-
Dynamical networks
-
Feng J, Jost J, Qian M (eds) Springer
-
Jost J (2007) Dynamical networks. In: Feng J, Jost J, Qian M (eds) Networks: from biology to theory. Springer
-
(2007)
Networks: From Biology to Theory
-
-
Jost, J.1
-
32
-
-
33845884817
-
On the dynamics of electrically-coupled neurons with inhibitory synapses
-
DOI 10.1007/s10827-006-9676-3
-
Juan Gao, Philip Holmes (2007) On the dynamics of electrically-coupled neurons with inhibitory synapses. J Comput Neurosci 22:39-61 (Pubitemid 46017838)
-
(2007)
Journal of Computational Neuroscience
, vol.22
, Issue.1
, pp. 39-61
-
-
Gao, J.1
Holmes, P.2
-
34
-
-
21144484097
-
Resistance distance
-
Klein D, Randic M (1993) Resistance distance. J Math Chem 12:81-95
-
(1993)
J Math Chem
, vol.12
, pp. 81-95
-
-
Klein, D.1
Randic, M.2
-
35
-
-
40749096575
-
Coupled oscillators and the design of central pattern generators
-
Kopell N, Ermentrout GB (1988) Coupled oscillators and the design of central pattern generators. Math Biosci 90(1-2):87-109
-
(1988)
Math Biosci
, vol.90
, Issue.1-2
, pp. 87-109
-
-
Kopell, N.1
Ermentrout, G.B.2
-
36
-
-
78650706645
-
Survival of subthreshold oscillations: The interplay of noise, bifurcation structure, and return mechanism
-
Kuske R, Borowski P (2099) Survival of subthreshold oscillations: the interplay of noise, bifurcation structure, and return mechanism. Discrete Contin Dynam Syst S 2(4):873-895
-
(2099)
Discrete Contin Dynam Syst S
, vol.2
, Issue.4
, pp. 873-895
-
-
Kuske, R.1
Borowski, P.2
-
38
-
-
21944438553
-
Uniqueness and stability of periodic bursting solutions
-
Lee E, Terman D (1999) Uniqueness and stability of periodic bursting solutions. J Differ Equ 158:48-78
-
(1999)
J Differ Equ
, vol.158
, pp. 48-78
-
-
Lee, E.1
Terman, D.2
-
39
-
-
0038701723
-
Dynamics of spiking neurons connected by both inhibitory and electrical coupling
-
DOI 10.1023/A:1023265027714
-
Lewis T, Rinzel J (2003) Dynamics of spiking neurons connected by both inhibitory and electrical coupling. J Comput Neurosci 14:283-309 (Pubitemid 36596481)
-
(2003)
Journal of Computational Neuroscience
, vol.14
, Issue.3
, pp. 283-309
-
-
Lewis, T.J.1
Rinzel, J.2
-
40
-
-
77549088163
-
Noise-induced transitions in slow wave neuronal dynamics
-
Lim S, Rinzel J (2010) Noise-induced transitions in slow wave neuronal dynamics. J Comput Neurosci 28(1):1-17
-
(2010)
J Comput Neurosci
, vol.28
, Issue.1
, pp. 1-17
-
-
Lim, S.1
Rinzel, J.2
-
43
-
-
0029030249
-
Reliability of spike timing in neocor-tical neurons
-
Mainen ZF, Sejnowski TJ (1995) Reliability of spike timing in neocor-tical neurons. Science 268:1503-1506
-
(1995)
Science
, vol.268
, pp. 1503-1506
-
-
Mainen, Z.F.1
Sejnowski, T.J.2
-
44
-
-
77955555364
-
First return maps for the dynamics of synaptically coupled conditional bursters
-
Manica E, Medvedev GS, Rubin JE (2010) First return maps for the dynamics of synaptically coupled conditional bursters. Biol Cybern 103:87-104
-
(2010)
Biol Cybern
, vol.103
, pp. 87-104
-
-
Manica, E.1
Medvedev, G.S.2
Rubin, J.E.3
-
45
-
-
0003059022
-
Explicit group-theoretic constructions of combinatorial schemes and their applications in the construction of expanders and concentrators
-
(English translation in Probl Inform Transm 24 (1988), no. 1, 39-46)
-
Margulis G (1988) Explicit group-theoretic constructions of combinatorial schemes and their applications in the construction of expanders and concentrators. (Russian) Problemy Peredachi Informatsii 24 (1988), no. 1, 51-60; (English translation in Probl Inform Transm 24 (1988), no. 1, 39-46)
-
(1988)
(Russian) Problemy Peredachi Informatsii
, vol.24
, Issue.1
, pp. 51-60
-
-
Margulis, G.1
-
47
-
-
14944346854
-
Reduction of a model of an excitable cell to a one-dimensional map
-
DOI 10.1016/j.physd.2005.01.021, PII S0167278905000564
-
Medvedev GS (2005) Reduction of a model of an excitable cell to a one-dimensional map. Phys D 202(1-2):37-59 (Pubitemid 40371041)
-
(2005)
Physica D: Nonlinear Phenomena
, vol.202
, Issue.1-2
, pp. 37-59
-
-
Medvedev, G.S.1
-
48
-
-
33746613350
-
Transition to bursting via deterministic chaos
-
Medvedev GS (2006) Transition to bursting via deterministic chaos. Phys Rev Lett 97:048102
-
(2006)
Phys Rev Lett
, vol.97
, pp. 048102
-
-
Medvedev, G.S.1
-
49
-
-
77949293395
-
Electrical coupling promotes fidelity of responses in the networks of model neurons
-
Medvedev GS (2009) Electrical coupling promotes fidelity of responses in the networks of model neurons. Neural Comput 21(11):3057-3078
-
(2009)
Neural Comput
, vol.21
, Issue.11
, pp. 3057-3078
-
-
Medvedev, G.S.1
-
50
-
-
77949276956
-
Synchronization of coupled stochastic limit cycle oscillators
-
Medvedev GS (2010) Synchronization of coupled stochastic limit cycle oscillators. Phys Lett A (374):1712-1720
-
(2010)
Phys Lett A
, vol.374
, pp. 1712-1720
-
-
Medvedev, G.S.1
-
51
-
-
80053385555
-
Synchronization of coupled limit cycles
-
Medvedev GS (2011) Synchronization of coupled limit cycles. J Nonlin Sci 21(3):441-464
-
(2011)
J Nonlin Sci
, vol.21
, Issue.3
, pp. 441-464
-
-
Medvedev, G.S.1
-
52
-
-
2942560675
-
Multimodal regimes in a compart-mental model of the dopamine neuron
-
Medvedev GS, Cisternas JE (2004) Multimodal regimes in a compart-mental model of the dopamine neuron. Phys D 194(3-4):333-356
-
(2004)
Phys D
, vol.194
, Issue.3-4
, pp. 333-356
-
-
Medvedev, G.S.1
Cisternas, J.E.2
-
53
-
-
0035181503
-
Synchronization and transient dynamics in the chains of electrically coupled Fitzhugh-Nagumo oscillators
-
DOI 10.1137/S0036139900368807, PII S0036139900368807
-
Medvedev GS, Kopell N (2001) Synchronization and transient dynamics in the chains of electrically coupled FitzHugh-Nagumo oscillators. SIAM J Appl Math 61(5):1762-1801 (Pubitemid 33099622)
-
(2001)
SIAM Journal on Applied Mathematics
, vol.61
, Issue.5
, pp. 1762-1801
-
-
Medvedev, G.S.1
Kopell, N.2
-
54
-
-
84869885675
-
The geometry of spontaneous spiking in neuronal networks
-
doi:10.1007/s00332-012-9125-6
-
Medvedev GS, Zhuravytska S (2012) The geometry of spontaneous spiking in neuronal networks. J Nonlin Sci. doi:10.1007/s00332-012-9125-6.
-
(2012)
J Nonlin Sci.
-
-
Medvedev, G.S.1
Zhuravytska, S.2
-
56
-
-
25144460267
-
Self-induced stochastic resonance in excitable systems
-
DOI 10.1016/j.physd.2005.07.014, PII S0167278905003155
-
Muratov CB, Vanden Eijnden E, Weinan E (2005) Self-induced stochastic resonance in excitable systems. Phys D 210:227-240 (Pubitemid 41348619)
-
(2005)
Physica D: Nonlinear Phenomena
, vol.210
, Issue.3-4
, pp. 227-240
-
-
Muratov, C.B.1
Vanden-Eijnden, E.2
Weinan, E.3
-
57
-
-
34247628855
-
The effect of noise on β-cell burst period
-
Pedersen MG, Sorensen MP (2007) The effect of noise on β-cell burst period. SIAM J Appl Math 67:530-542
-
(2007)
SIAM J Appl Math
, vol.67
, pp. 530-542
-
-
Pedersen, M.G.1
Sorensen, M.P.2
-
58
-
-
0037706084
-
Electrical synapses and synchrony: The role of intrinsic currents
-
Pfeuty B, Mato G, Golomb D, Hansel D (2003) Electrical synapses and synchrony: the role of intrinsic currents. J Neurosci 23:6280-6294 (Pubitemid 36875630)
-
(2003)
Journal of Neuroscience
, vol.23
, Issue.15
, pp. 6280-6294
-
-
Pfeuty, B.1
Mato, G.2
Golomb, D.3
Hansel, D.4
-
60
-
-
0002453062
-
Analysis of neural excitability and oscillations
-
Koch C, Segev I (eds) MIT Press, Cambridge
-
Rinzel J, Ermentrout GB (1989) Analysis of neural excitability and oscillations. In: Koch C, Segev I (eds) Methods in neuronal modeling. MIT Press, Cambridge
-
(1989)
Methods in Neuronal Modeling
-
-
Rinzel, J.1
Ermentrout, G.B.2
-
61
-
-
0034150797
-
Geometric analysis of population rhythms in synaptically coupled neuronal networks
-
Rubin J, Terman D (2000) Geometric analysis of population rhythms in synaptically coupled neuronal networks. Neural Comp 12:597-645
-
(2000)
Neural Comp
, vol.12
, pp. 597-645
-
-
Rubin, J.1
Terman, D.2
-
62
-
-
23444458006
-
What is an expander?
-
Sarnak P (2004) What is an expander?. Notices Am Math Soc 51:762-763
-
(2004)
Notices Am Math Soc
, vol.51
, pp. 762-763
-
-
Sarnak, P.1
-
63
-
-
0025979886
-
Model for synchronization of pancreatic β-cells by gap junction coupling
-
Sherman A, Rinzel J (1991) Model for synchronization of pancreatic β-cells by gap junction coupling. Biophys J 59:547-559
-
(1991)
Biophys J
, vol.59
, pp. 547-559
-
-
Sherman, A.1
Rinzel, J.2
-
64
-
-
0023791327
-
Emergence of organized bursting in clusters of pancreatic β-cells by channel sharing
-
Sherman A, Rinzel J, Keizer J (1988) Emergence of organized bursting in clusters of pancreatic β-cells by channel sharing. Biophys J 54:411-425
-
(1988)
Biophys J
, vol.54
, pp. 411-425
-
-
Sherman, A.1
Rinzel, J.2
Keizer, J.3
-
65
-
-
16344379385
-
Modeling of the stochastic gating of ion channels
-
Fall CP et al (eds) Springer, New York
-
Smith GD (2002) Modeling of the stochastic gating of ion channels. In: Fall CP et al (eds) Computational cell biology. Springer, New York
-
(2002)
Computational Cell Biology
-
-
Smith, G.D.1
-
66
-
-
0347931871
-
Effects of noise on elliptic bursters
-
DOI 10.1088/0951-7715/17/1/009, PII S0951771504583500
-
Su J, Rubin J, Terman D (2004) Effects of noise on elliptic bursters. Nonlinearity 17:133-157 (Pubitemid 38085739)
-
(2004)
Nonlinearity
, vol.17
, Issue.1
, pp. 133-157
-
-
Su, J.1
Rubin, J.2
Terman, D.3
-
68
-
-
34249839599
-
The transition from bursting to continuous spiking in excitable membrane models
-
Terman D (1992) The transition from bursting to continuous spiking in excitable membrane models. J Nonl Sci 2:135-182
-
(1992)
J Nonl Sci
, vol.2
, pp. 135-182
-
-
Terman, D.1
-
69
-
-
0033593588
-
The role of locus coeruleus in the regulation of cognitive performance
-
Usher M, Cohen JD, Servan-Schreiber D, Rajkowski J, Aston-Jones G (1999) The role of locus coeruleus in the regulation of cognitive performance. Science 283:549-554
-
(1999)
Science
, vol.283
, pp. 549-554
-
-
Usher, M.1
Cohen, J.D.2
Servan-Schreiber, D.3
Rajkowski, J.4
Aston-Jones, G.5
-
70
-
-
0001736010
-
Oscillatory and bursting properties of neurons
-
Arbib MA (ed) MIT Press, Cambridge
-
Wang XJ, Rinzel J (1995) Oscillatory and bursting properties of neurons. In: Arbib MA (ed) Handbook of brain theory and neural networks. MIT Press, Cambridge pp 686-691
-
(1995)
Handbook of Brain Theory and Neural Networks
, pp. 686-691
-
-
Wang, X.J.1
Rinzel, J.2
-
71
-
-
0034159903
-
Channel noise in neurons
-
DOI 10.1016/S0166-2236(99)01521-0, PII S0166223699015210
-
White J, Rubenstein J, Kay A (2000) Channel noise in neurons. Trends Neurosci 23(3):131-137 (Pubitemid 30110629)
-
(2000)
Trends in Neurosciences
, vol.23
, Issue.3
, pp. 131-137
-
-
White, J.A.1
Rubinstein, J.T.2
Kay, A.R.3
-
72
-
-
0346220170
-
Resistance distance and Laplacian spectrum
-
DOI 10.1007/s00214-003-0460-4
-
Xiao W, Gutman I (2003) Resistance distance and Laplacian spectrum. Theor Chem Acc 110:284-289 (Pubitemid 37524165)
-
(2003)
Theoretical Chemistry Accounts
, vol.110
, Issue.4
, pp. 284-289
-
-
Xiao, W.1
Gutman, I.2
|