-
2
-
-
0017713690
-
Dynamics of pattern formation in lateral inhibition type neural fields
-
S. Amari, Dynamics of pattern formation in lateral inhibition type neural fields, Biol. Cybern., 27 (1977), pp. 77-87.
-
(1977)
Biol. Cybern.
, vol.27
, pp. 77-87
-
-
Amari, S.1
-
3
-
-
0000364015
-
Ballistic and diffusive corrections to front propagation in the presence of multiplicative noise
-
J. Armero, J. Casademunt, L. Ramirez-Piscina, and J. M. Sancho, Ballistic and diffusive corrections to front propagation in the presence of multiplicative noise, Phys. Rev. E, 58 (1998), pp. 5494- 5500.
-
(1998)
Phys. Rev. e
, vol.58
, pp. 5494-5500
-
-
Armero, J.1
Casademunt, J.2
Ramirez-Piscina, L.3
Sancho, J.M.4
-
4
-
-
84861832463
-
-
preprint, arXiv:1110.4294
-
J. Baladron, D. Fasoli, O. Faugeras, and J. Touboul, Mean Field Description of and Propagation of Chaos in Recurrent Multipopulation Networks of Hodgkin-Huxley and FitzHugh-Nagumo Neurons, preprint, arXiv:1110.4294.
-
Mean Field Description of and Propagation of Chaos in Recurrent Multipopulation Networks of Hodgkin-Huxley and FitzHugh-Nagumo Neurons
-
-
Baladron, J.1
Fasoli, D.2
Faugeras, O.3
Touboul, J.4
-
5
-
-
2642572763
-
Neuronal avalanches are diverse and precise activity patterns that are stable for many hours in cortical slice cultures
-
J. M. Beggs and D. Plenz, Neuronal avalanches are diverse and precise activity patterns that are stable for many hours in cortical slice cultures, J. Neurosci., 24 (2004), pp. 5216-5229.
-
(2004)
J. Neurosci.
, vol.24
, pp. 5216-5229
-
-
Beggs, J.M.1
Plenz, D.2
-
6
-
-
70450225745
-
The non-local Fisher-KPP equation: Traveling waves and steady states
-
H. Berestycki, G. Nadin, B. Perthame, and L. Ryzhik, The non-local Fisher-KPP equation: Traveling waves and steady states, Nonlinearity, 22 (2009), pp. 2813-2844.
-
(2009)
Nonlinearity
, vol.22
, pp. 2813-2844
-
-
Berestycki, H.1
Nadin, G.2
Perthame, B.3
Ryzhik, L.4
-
8
-
-
34247485515
-
Random fluctuations of the firing rate function in a continuum neural field model
-
C. A. Brackley and M. S. Turner, Random fluctuations of the firing rate function in a continuum neural field model, Phys. Rev. E, 75 (2007), 041913.
-
(2007)
Phys. Rev. e
, vol.75
, pp. 041913
-
-
Brackley, C.A.1
Turner, M.S.2
-
9
-
-
0035400302
-
Traveling fronts and wave propagation failure in an inhomogeneous neural network
-
P. C. Bressloff, Traveling fronts and wave propagation failure in an inhomogeneous neural network, Phys. D, 155 (2001), pp. 83-100.
-
(2001)
Phys. D
, vol.155
, pp. 83-100
-
-
Bressloff, P.C.1
-
10
-
-
73949151166
-
Stochastic neural field theory and the system-size expansion
-
P. C. Bressloff, Stochastic neural field theory and the system-size expansion, SIAM J. Appl. Math., 70 (2009), pp. 1488-1521.
-
(2009)
SIAM J. Appl. Math.
, vol.70
, pp. 1488-1521
-
-
Bressloff, P.C.1
-
11
-
-
78651317616
-
Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics
-
P. C. Bressloff, Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics, Phys. Rev. E, 85 (2010), 051903.
-
(2010)
Phys. Rev. e
, vol.85
, pp. 051903
-
-
Bressloff, P.C.1
-
12
-
-
84863866591
-
Neural field model of binocular rivalry waves
-
P. C. Bressloff and M. Webber, Neural field model of binocular rivalry waves, J. Comput. Neurosci., 32 (2012), pp. 2951-2970.
-
(2012)
J. Comput. Neurosci.
, vol.32
, pp. 2951-2970
-
-
Bressloff, P.C.1
Webber, M.2
-
13
-
-
84555218593
-
Spatiotemporal dynamics of continuum neural fields. Invited topical review
-
P. C. Bressloff, Spatiotemporal dynamics of continuum neural fields. Invited topical review, J. Phys. A, 45 (2012), 033001.
-
(2012)
J. Phys. A
, vol.45
, pp. 033001
-
-
Bressloff, P.C.1
-
14
-
-
0001425072
-
Shift in the velocity of a front due to a cutoff
-
E. Brunet and B. Derrida, Shift in the velocity of a front due to a cutoff, Phys. Rev. E, 56 (1997), pp. 2597-2604.
-
(1997)
Phys. Rev. e
, vol.56
, pp. 2597-2604
-
-
Brunet, E.1
Derrida, B.2
-
15
-
-
34547276719
-
Field-theoretic approach to fluctuation effects in neural networks
-
M. Buice and J. D. Cowan, Field-theoretic approach to fluctuation effects in neural networks, Phys. Rev. E, 75 (2007), 051919.
-
(2007)
Phys. Rev. e
, vol.75
, pp. 051919
-
-
Buice, M.1
Cowan, J.D.2
-
16
-
-
77649304853
-
Systematic fluctuation expansion for neural network activity equations
-
M. Buice, J. D. Cowan, and C. C. Chow, Systematic fluctuation expansion for neural network activity equations, Neural Comp., 22 (2010), pp. 377-426.
-
(2010)
Neural Comp.
, vol.22
, pp. 377-426
-
-
Buice, M.1
Cowan, J.D.2
Chow, C.C.3
-
17
-
-
2442679125
-
An effective kinetic representation of fluctuation-driven neuronal networks with application to simple and complex cells in visual cortex
-
D. Cai, L. Tao, M. Shelley, and D. W. McLaughlin, An effective kinetic representation of fluctuation-driven neuronal networks with application to simple and complex cells in visual cortex, Proc. Natl. Acad. Sci. USA, 101 (2004), pp. 7757-7762.
-
(2004)
Proc. Natl. Acad. Sci. USA
, vol.101
, pp. 7757-7762
-
-
Cai, D.1
Tao, L.2
Shelley, M.3
McLaughlin, D.W.4
-
18
-
-
17744400704
-
Evans functions for integral neural field equations with Heaviside firing rate function
-
S. Coombes and M. R. Owen, Evans functions for integral neural field equations with Heaviside firing rate function, SIAM J. Appl. Dyn. Syst., 3 (2004), pp. 574-600.
-
(2004)
SIAM J. Appl. Dyn. Syst.
, vol.3
, pp. 574-600
-
-
Coombes, S.1
Owen, M.R.2
-
19
-
-
23944441267
-
Waves, bumps and patterns in neural field theories
-
S. Coombes, Waves, bumps and patterns in neural field theories, Biol. Cybern., 93 (2005), pp. 91-108.
-
(2005)
Biol. Cybern.
, vol.93
, pp. 91-108
-
-
Coombes, S.1
-
20
-
-
35949003696
-
Modeling electrocortical activity through improved local approximations of integral neural field equations
-
S. Coombes, N. A. Venkov, I. Bojak, D. T. J. Liley, and C. R. Laing, Modeling electrocortical activity through improved local approximations of integral neural field equations, Phys. Rev. E, 76 (2007), 051901.
-
(2007)
Phys. Rev. e
, vol.76
, pp. 051901
-
-
Coombes, S.1
Venkov, N.A.2
Bojak, I.3
Liley, D.T.J.4
Laing, C.R.5
-
21
-
-
79951700180
-
Pulsating fronts in periodically modulated neural field models
-
S. Coombes and C. R. Laing, Pulsating fronts in periodically modulated neural field models, Phys. Rev. E, 83 (2011), 011912.
-
(2011)
Phys. Rev. e
, vol.83
, pp. 011912
-
-
Coombes, S.1
Laing, C.R.2
-
22
-
-
84555183838
-
Waves in random neural media
-
S. Coombes, C. R. Laing, H. Schmidt, N. Svanstedt, and J. A. Wyller, Waves in random neural media, Discrete Contin. Dyn. Syst. Ser. A, 32 (2012), pp. 2951-2970.
-
(2012)
Discrete Contin. Dyn. Syst. Ser. A
, vol.32
, pp. 2951-2970
-
-
Coombes, S.1
Laing, C.R.2
Schmidt, H.3
Svanstedt, N.4
Wyller, J.A.5
-
24
-
-
0039149429
-
Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts
-
U. Ebert and W. van Saarloos, Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts, Phys. D, 146 (2000), pp. 1-99.
-
(2000)
Phys. D
, vol.146
, pp. 1-99
-
-
Ebert, U.1
Van Saarloos, W.2
-
25
-
-
84971116294
-
Existence and uniqueness of travelling waves for a neural network
-
G. B. Ermentrout and J. B. McLeod, Existence and uniqueness of travelling waves for a neural network, Proc. Roy. Soc. Edinburgh Sect. A, 123 (1993), pp. 461-478.
-
(1993)
Proc. Roy. Soc. Edinburgh Sect. A
, vol.123
, pp. 461-478
-
-
Ermentrout, G.B.1
McLeod, J.B.2
-
26
-
-
0001104658
-
Neural networks as spatio-temporal pattern-forming systems
-
G. B. Ermentrout, Neural networks as spatio-temporal pattern-forming systems, Rep. Progr. Phys., 61 (1998), pp. 353-430.
-
(1998)
Rep. Progr. Phys.
, vol.61
, pp. 353-430
-
-
Ermentrout, G.B.1
-
27
-
-
78751496276
-
Stimulus-driven traveling solutions in continuum neuronal models with a general smooth firing rate function
-
G. B. Ermentrout, J. Z. Jalics, and J. E. Rubin, Stimulus-driven traveling solutions in continuum neuronal models with a general smooth firing rate function, SIAM J. Appl. Math., 70 (2010), pp. 3039- 3054.
-
(2010)
SIAM J. Appl. Math.
, vol.70
, pp. 3039-3054
-
-
Ermentrout, G.B.1
Jalics, J.Z.2
Rubin, J.E.3
-
28
-
-
77958032223
-
A constructive mean-field analysis of multi-population neural networks with random synaptic weights and stochastic inputs
-
O. Faugeras, J. Touboul, and B. Cessac, A constructive mean-field analysis of multi-population neural networks with random synaptic weights and stochastic inputs, Frontiers Comput. Neurosci., 3 (2009), pp. 1-28.
-
(2009)
Frontiers Comput. Neurosci.
, vol.3
, pp. 1-28
-
-
Faugeras, O.1
Touboul, J.2
Cessac, B.3
-
29
-
-
0000268135
-
The wave of advance of advantageous genes
-
R. A. Fisher, The wave of advance of advantageous genes, Ann. Eugenics, 7 (1937), pp. 355-369.
-
(1937)
Ann. Eugenics
, vol.7
, pp. 355-369
-
-
Fisher, R.A.1
-
30
-
-
29144530269
-
Stimulus-locked traveling waves and breathers in an excitatory neural network
-
S. E. Folias and P. C. Bressloff, Stimulus-locked traveling waves and breathers in an excitatory neural network, SIAM J. Appl. Math., 65 (2005), pp. 2067-2092.
-
(2005)
SIAM J. Appl. Math.
, vol.65
, pp. 2067-2092
-
-
Folias, S.E.1
Bressloff, P.C.2
-
31
-
-
0040851897
-
External fluctuations in a pattern-forming instability
-
J. Garcia-Ojalvo and J. M. Sancho, External fluctuations in a pattern-forming instability, Phys. Rev. E, 53 (1996), pp. 5680-5689.
-
(1996)
Phys. Rev. e
, vol.53
, pp. 5680-5689
-
-
Garcia-Ojalvo, J.1
Sancho, J.M.2
-
33
-
-
0034277973
-
Travelling front solutions of a nonlocal Fisher equation
-
S. A. Gourley, Travelling front solutions of a nonlocal Fisher equation, J. Math. Biol., 41 (2000), pp. 272-284.
-
(2000)
J. Math. Biol.
, vol.41
, pp. 272-284
-
-
Gourley, S.A.1
-
34
-
-
7744238736
-
Spiral waves in disinhibited mammalian neocortex
-
X. Huang, W. C. Troy, Q. Yang, H. Ma, C. R. Laing, S. J. Schiff, and J. Wu, Spiral waves in disinhibited mammalian neocortex, J. Neurosci., 24 (2004), pp. 9897-9902.
-
(2004)
J. Neurosci.
, vol.24
, pp. 9897-9902
-
-
Huang, X.1
Troy, W.C.2
Yang, Q.3
Ma, H.4
Laing, C.R.5
Schiff, S.J.6
Wu, J.7
-
35
-
-
33847254397
-
Generalization of the reaction-diffusion, Swift-Hohenberg, and Kuramoto-Sivashinsky equations and effects of finite propagation speeds
-
A. Hutt, Generalization of the reaction-diffusion, Swift-Hohenberg, and Kuramoto-Sivashinsky equations and effects of finite propagation speeds, Phys. Rev. E, 75 (2007), 026214.
-
(2007)
Phys. Rev. e
, vol.75
, pp. 026214
-
-
Hutt, A.1
-
36
-
-
42149167934
-
Additive noise-induced Turing transitions in spatial systems with application to neural fields and the Swift-Hohenberg equation
-
A. Hutt, A. Longtin, and L. Schimansky-Geier, Additive noise-induced Turing transitions in spatial systems with application to neural fields and the Swift-Hohenberg equation, Phys. D, 237 (2008), pp. 755-773.
-
(2008)
Phys. D
, vol.237
, pp. 755-773
-
-
Hutt, A.1
Longtin, A.2
Schimansky-Geier, L.3
-
37
-
-
0030786828
-
A derivation of a macroscopic field theory of the brain from the quasimicroscopic neural dynamics
-
V. K. Jirsa and H. Haken, A derivation of a macroscopic field theory of the brain from the quasimicroscopic neural dynamics, Phys. D, 99 (1997), pp. 503-526.
-
(1997)
Phys. D
, vol.99
, pp. 503-526
-
-
Jirsa, V.K.1
Haken, H.2
-
38
-
-
60749130222
-
Periodic perturbations producing phase-locked fluctuations in visual perception
-
M. Kang, D. J. Heeger, and R. Blake, Periodic perturbations producing phase-locked fluctuations in visual perception, J. Vision, 9 (2009), pp. 1-12.
-
(2009)
J. Vision
, vol.9
, pp. 1-12
-
-
Kang, M.1
Heeger, D.J.2
Blake, R.3
-
39
-
-
0002722044
-
Study of the diffusion equation with growth of the quantity of matter and its application to a biology problem
-
article 8
-
A. Kolmogorov, I. Petrovsky, and N. Piscunov, Study of the diffusion equation with growth of the quantity of matter and its application to a biology problem, Bull. Univ. Moskou Ser. Int. Se. A, 1 (1937), article 8.
-
(1937)
Bull. Univ. Moskou Ser. Int. Se. A
, vol.1
-
-
Kolmogorov, A.1
Petrovsky, I.2
Piscunov, N.3
-
41
-
-
16644369689
-
Traveling waves of activity in primary visual cortex during binocular rivalry
-
S. H. Lee, R. Blake, and D. J. Heeger, Traveling waves of activity in primary visual cortex during binocular rivalry, Nature Neurosci., 8 (2005), pp. 22-23.
-
(2005)
Nature Neurosci.
, vol.8
, pp. 22-23
-
-
Lee, S.H.1
Blake, R.2
Heeger, D.J.3
-
43
-
-
29444438812
-
Stochastic motion of the propagating front in bistable media
-
A. S. Mikhailov, L. Schimansky-Geier, and W. Ebeling, Stochastic motion of the propagating front in bistable media, Phys. Lett. A, 96 (1983), pp. 453-456.
-
(1983)
Phys. Lett. A
, vol.96
, pp. 453-456
-
-
Mikhailov, A.S.1
Schimansky-Geier, L.2
Ebeling, W.3
-
45
-
-
0000667247
-
Functionals and the random-force method in turbulence theory
-
E. A. Novikov, Functionals and the random-force method in turbulence theory, Sov. Phys. JETP, 20 (1965), pp. 1290-1294.
-
(1965)
Sov. Phys. JETP
, vol.20
, pp. 1290-1294
-
-
Novikov, E.A.1
-
46
-
-
1342308281
-
Effects of fluctuations on propagating fronts
-
D. Panja, Effects of fluctuations on propagating fronts, Phys. Rep., 393 (2004), pp. 87-174.
-
(2004)
Phys. Rep.
, vol.393
, pp. 87-174
-
-
Panja, D.1
-
47
-
-
0004608843
-
On the stochastic correlations in a randomly perturbed chemical front
-
F. de Pasquale, J. Gorecki, and J. Poielawski, On the stochastic correlations in a randomly perturbed chemical front, J. Phys. A, 25 (1992), pp. 433-446.
-
(1992)
J. Phys. A
, vol.25
, pp. 433-446
-
-
De Pasquale, F.1
Gorecki, J.2
Poielawski, J.3
-
48
-
-
0036226617
-
Spatially structured activity in synaptically coupled neuronal networks: I. Traveling fronts and pulses
-
D. J. Pinto and G. B. Ermentrout, Spatially structured activity in synaptically coupled neuronal networks: I. Traveling fronts and pulses, SIAM J. Appl. Math., 62 (2001), pp. 206-225.
-
(2001)
SIAM J. Appl. Math.
, vol.62
, pp. 206-225
-
-
Pinto, D.J.1
Ermentrout, G.B.2
-
49
-
-
24744449310
-
Initiation, propagation, and termination of epileptiform activity in rodent neocortex in vitro involve distinct mechanisms
-
D. Pinto, S. L. Patrick, W. C. Huang, and B. W. Connors, Initiation, propagation, and termination of epileptiform activity in rodent neocortex in vitro involve distinct mechanisms, J. Neurosci., 25 (2005), pp. 8131-8140.
-
(2005)
J. Neurosci.
, vol.25
, pp. 8131-8140
-
-
Pinto, D.1
Patrick, S.L.2
Huang, W.C.3
Connors, B.W.4
-
50
-
-
33847236188
-
The organizing principles of neuronal avalanches: Cell assemblies in the cortex?
-
D. Plenz and T. C. Thiagarajan, The organizing principles of neuronal avalanches: Cell assemblies in the cortex?, Trends Neurosci., 30 (2007), pp. 101-110.
-
(2007)
Trends Neurosci.
, vol.30
, pp. 101-110
-
-
Plenz, D.1
Thiagarajan, T.C.2
-
51
-
-
18144371247
-
Control of traveling waves in the mammalian cortex
-
K. A. Richardson, S. J. Schiff, and B. J. Gluckman, Control of traveling waves in the mammalian cortex, Phys. Rev. Lett., 94 (2005), 028103.
-
(2005)
Phys. Rev. Lett.
, vol.94
, pp. 028103
-
-
Richardson, K.A.1
Schiff, S.J.2
Gluckman, B.J.3
-
52
-
-
18344397152
-
Prediction of electroencephalographic spectra from neurophysiology
-
P. A. Robinson, C. J. Rennie, J. J. Wright, H. Bahramali, E. Gordon, and D. I. Rowe, Prediction of electroencephalographic spectra from neurophysiology, Phys. Rev. E, 63 (2001), 021903.
-
(2001)
Phys. Rev. e
, vol.63
, pp. 021903
-
-
Robinson, P.A.1
Rennie, C.J.2
Wright, J.J.3
Bahramali, H.4
Gordon, E.5
Rowe, D.I.6
-
53
-
-
0034228944
-
Subdiffusive fluctuations of "pulled" fronts with multiplicative noise
-
A. Rocco, U. Ebert, and W. van Saarloos, Subdiffusive fluctuations of "pulled" fronts with multiplicative noise, Phys. Rev. E, 65 (2000), pp. R13-R16.
-
(2000)
Phys. Rev. e
, vol.65
-
-
Rocco, A.1
Ebert, U.2
Van Saarloos, W.3
-
54
-
-
34547221045
-
Spatiotemporal order out of noise
-
F. Sagues, J. M. Sancho, and J. Garcia-Ojalvo, Spatiotemporal order out of noise, Rev. Modern Phys., 79 (2007), pp. 829-882.
-
(2007)
Rev. Modern Phys.
, vol.79
, pp. 829-882
-
-
Sagues, F.1
Sancho, J.M.2
Garcia-Ojalvo, J.3
-
55
-
-
84981886894
-
Effects of fluctuations on plane front propagation in bistable nonequilibrium systems
-
L. Schimansky-Geier, A. S. Mikhailov, and W. Ebeling, Effects of fluctuations on plane front propagation in bistable nonequilibrium systems, Ann. Phys., 40 (1983), pp. 277-286.
-
(1983)
Ann. Phys.
, vol.40
, pp. 277-286
-
-
Schimansky-Geier, L.1
Mikhailov, A.S.2
Ebeling, W.3
-
56
-
-
0142119503
-
Front propagation into unstable states
-
W. van Saarloos, Front propagation into unstable states, Phys. Rep., 386 (2003), pp. 29-222.
-
(2003)
Phys. Rep.
, vol.386
, pp. 29-222
-
-
Van Saarloos, W.1
-
58
-
-
0035974894
-
Dynamics of traveling waves in visual perception
-
H. R. Wilson, R. Blake, and S. H. Lee, Dynamics of traveling waves in visual perception, Nature, 412 (2001), pp. 907-910.
-
(2001)
Nature
, vol.412
, pp. 907-910
-
-
Wilson, H.R.1
Blake, R.2
Lee, S.H.3
-
59
-
-
1042287949
-
On stability of traveling wave solutions in synaptically coupled neuronal networks
-
L. Zhang, On stability of traveling wave solutions in synaptically coupled neuronal networks, Differential Integral Equations, 16 (2003), pp. 513-536.
-
(2003)
Differential Integral Equations
, vol.16
, pp. 513-536
-
-
Zhang, L.1
|