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Volumn 9, Issue , 2007, Pages

Bumps and rings in a two-dimensional neural field: Splitting and rotational instabilities

Author keywords

[No Author keywords available]

Indexed keywords

ANGULAR VELOCITY; COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; FUNCTION EVALUATION; ROTATION; SYSTEM STABILITY;

EID: 35748962631     PISSN: 13672630     EISSN: None     Source Type: Journal    
DOI: 10.1088/1367-2630/9/10/378     Document Type: Article
Times cited : (78)

References (36)
  • 1
    • 0015260274 scopus 로고
    • Excitatory and inhibitory interactions in localized populations of model neurons
    • Wilson H R and Cowan J D 1972 Excitatory and inhibitory interactions in localized populations of model neurons Biophys. J. 12 1-24
    • (1972) Biophys. J , vol.12 , pp. 1-24
    • Wilson, H.R.1    Cowan, J.D.2
  • 2
    • 0015868589 scopus 로고
    • A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue
    • Wilson H R and Cowan J D 1973 A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue Kybernetik 13 55-80
    • (1973) Kybernetik , vol.13 , pp. 55-80
    • Wilson, H.R.1    Cowan, J.D.2
  • 3
    • 0016640311 scopus 로고
    • Homogeneous nets of neuron-like elements
    • Amari S 1975 Homogeneous nets of neuron-like elements Biol. Cybern. 17 211-20
    • (1975) Biol. Cybern , vol.17 , pp. 211-220
    • Amari, S.1
  • 4
    • 0017713690 scopus 로고
    • Dynamics of pattern formation in lateral-inhibition type neural fields
    • Amari S 1977 Dynamics of pattern formation in lateral-inhibition type neural fields Biol. Cybern. 27 77-87
    • (1977) Biol. Cybern , vol.27 , pp. 77-87
    • Amari, S.1
  • 5
    • 23944441267 scopus 로고    scopus 로고
    • Waves, bumps and patterns in neural field theories
    • Coombes S 2005 Waves, bumps and patterns in neural field theories Biol. Cybern. 93 91-108
    • (2005) Biol. Cybern , vol.93 , pp. 91-108
    • Coombes, S.1
  • 6
    • 0018700147 scopus 로고
    • A mathematical theory of visual hallucination patterns
    • Ermentrout G B and Cowan J D 1979 A mathematical theory of visual hallucination patterns Biol. Cybern. 34 137-50
    • (1979) Biol. Cybern , vol.34 , pp. 137-150
    • Ermentrout, G.B.1    Cowan, J.D.2
  • 7
    • 0005562472 scopus 로고
    • Cortical pattern formation during visual hallucinations
    • Tass P 1995 Cortical pattern formation during visual hallucinations J. Biol. Phys. 21 177-210
    • (1995) J. Biol. Phys , vol.21 , pp. 177-210
    • Tass, P.1
  • 8
    • 0035967087 scopus 로고    scopus 로고
    • Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex
    • Bressloff P C, Cowan J D, Golubitsky M, Thomas P J and Wiener M 2001 Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex Phil. Trans. R. Soc. B 40 299-330
    • (2001) Phil. Trans. R. Soc. B , vol.40 , pp. 299-330
    • Bressloff, P.C.1    Cowan, J.D.2    Golubitsky, M.3    Thomas, P.J.4    Wiener, M.5
  • 9
    • 0018649243 scopus 로고
    • Existence and stability of local excitations in homogeneous neural fields
    • Kishimoto K and Amari S 1979 Existence and stability of local excitations in homogeneous neural fields J. Math. Biol. 7 303-18
    • (1979) J. Math. Biol , vol.7 , pp. 303-318
    • Kishimoto, K.1    Amari, S.2
  • 11
    • 0028971729 scopus 로고
    • Oculocentric spatial representation in parietal cortex
    • Colby C L, Duhamel J R and Goldberg M E 1995 Oculocentric spatial representation in parietal cortex Cerebral Cortex 5 470-81
    • (1995) Cerebral Cortex , vol.5 , pp. 470-481
    • Colby, C.L.1    Duhamel, J.R.2    Goldberg, M.E.3
  • 12
    • 0028938076 scopus 로고
    • Cellular basis of working memory
    • Goldman-Rakic P S 1995 Cellular basis of working memory Neuron 14 477-85
    • (1995) Neuron , vol.14 , pp. 477-485
    • Goldman-Rakic, P.S.1
  • 13
    • 0037757598 scopus 로고    scopus 로고
    • The dynamical stability of reverberatory neural circuits
    • Tegner J, Compte A and Wang X-J 2002 The dynamical stability of reverberatory neural circuits Biol. Cybern. 87 471-81
    • (2002) Biol. Cybern , vol.87 , pp. 471-481
    • Tegner, J.1    Compte, A.2    Wang, X.-J.3
  • 15
    • 0000649277 scopus 로고    scopus 로고
    • Neural 'bubble' dynamics in two dimensions: Foundations
    • Taylor J G 1999 Neural 'bubble' dynamics in two dimensions: foundations Biol. Cybern. 80 393-409
    • (1999) Biol. Cybern , vol.80 , pp. 393-409
    • Taylor, J.G.1
  • 16
    • 0035458994 scopus 로고    scopus 로고
    • Circular stationary solutions in two-dimensional neural fields
    • Werner H and Richter T 2001 Circular stationary solutions in two-dimensional neural fields Biol. Cybern. 85 211-7
    • (2001) Biol. Cybern , vol.85 , pp. 211-217
    • Werner, H.1    Richter, T.2
  • 17
    • 17744400704 scopus 로고    scopus 로고
    • Evans functions for integral neural field equations with Heaviside firing rate function
    • Coombes S and Owen M R 2004 Evans functions for integral neural field equations with Heaviside firing rate function SIAM J. Appl. Dyn. Syst. 34 574-600
    • (2004) SIAM J. Appl. Dyn. Syst , vol.34 , pp. 574-600
    • Coombes, S.1    Owen, M.R.2
  • 18
    • 18144391211 scopus 로고    scopus 로고
    • Localized activations in a simple neural field model
    • Herrmann J M, Schrobsdorff H and Geisel T 2005 Localized activations in a simple neural field model Neurocomputing 65 679-84
    • (2005) Neurocomputing , vol.65 , pp. 679-684
    • Herrmann, J.M.1    Schrobsdorff, H.2    Geisel, T.3
  • 19
    • 0016578299 scopus 로고
    • Nerve axon equations: IV The stable and unstable impulse
    • Evans J 1975 Nerve axon equations: IV The stable and unstable impulse Indian Univ. Math. J. 24 1169-90
    • (1975) Indian Univ. Math. J , vol.24 , pp. 1169-1190
    • Evans, J.1
  • 20
    • 23944491928 scopus 로고    scopus 로고
    • Existence and stability of traveling pulses in a continuous neuronal network
    • Pinto D J, Jackson R K and Wayne C E 2005 Existence and stability of traveling pulses in a continuous neuronal network SIAM J. Appl. Dyn. Syst. 4 954-84
    • (2005) SIAM J. Appl. Dyn. Syst , vol.4 , pp. 954-984
    • Pinto, D.J.1    Jackson, R.K.2    Wayne, C.E.3
  • 21
    • 34748836908 scopus 로고    scopus 로고
    • Evans functions and nonlinear stability of travelling waves in neuronal network models
    • Sandstede B 2007 Evans functions and nonlinear stability of travelling waves in neuronal network models Int. J. Bifurcat. Chaos 17 2693-704
    • (2007) Int. J. Bifurcat. Chaos , vol.17 , pp. 2693-2704
    • Sandstede, B.1
  • 22
    • 27144516292 scopus 로고    scopus 로고
    • Spontaneous symmetry breaking in self-organizing neural fields
    • Bressloff P C 2005 Spontaneous symmetry breaking in self-organizing neural fields Biol. Cybern. 93 256-74
    • (2005) Biol. Cybern , vol.93 , pp. 256-274
    • Bressloff, P.C.1
  • 23
    • 16344393249 scopus 로고    scopus 로고
    • Breathing pulses in an excitatory neural network
    • Folias S E and Bressloff P C 2004 Breathing pulses in an excitatory neural network SIAM J. Appl. Dyn. Syst. 3 378-407
    • (2004) SIAM J. Appl. Dyn. Syst , vol.3 , pp. 378-407
    • Folias, S.E.1    Bressloff, P.C.2
  • 25
    • 1842831268 scopus 로고    scopus 로고
    • Axisymmetric ring solutions of the 2D Gray-Scott model and their destabilization into spots
    • Morgan D S and Kaper T J 2004 Axisymmetric ring solutions of the 2D Gray-Scott model and their destabilization into spots Physica D 192 33-62
    • (2004) Physica D , vol.192 , pp. 33-62
    • Morgan, D.S.1    Kaper, T.J.2
  • 26
    • 0004469897 scopus 로고    scopus 로고
    • Hopfield J J 1984 Neurons with graded response have collective computational properties like those of two-state neurons Proc. Nat Acad. Sci. 81 3088-92
    • Hopfield J J 1984 Neurons with graded response have collective computational properties like those of two-state neurons Proc. Nat Acad. Sci. 81 3088-92
  • 27
    • 10644281036 scopus 로고    scopus 로고
    • Identification of a free energy functional in an integro-differential equation model for neuronal network activity
    • French D A 2004 Identification of a free energy functional in an integro-differential equation model for neuronal network activity Appl. Math. Lett. 17 1047-51
    • (2004) Appl. Math. Lett , vol.17 , pp. 1047-1051
    • French, D.A.1
  • 28
    • 0035081994 scopus 로고    scopus 로고
    • Spike-frequency adaptation of a generalized leaky integrate-and-fire model neuron
    • Liu Y H and Wang X J 2001 Spike-frequency adaptation of a generalized leaky integrate-and-fire model neuron J. Comput. Neurosci. 25-45
    • (2001) J. Comput. Neurosci , pp. 25-45
    • Liu, Y.H.1    Wang, X.J.2
  • 29
    • 0037446036 scopus 로고    scopus 로고
    • Waves and bumps in neuronal networks with axo-dendritic synaptic interactions
    • Coombes S, Lord G J and Owen M R 2003 Waves and bumps in neuronal networks with axo-dendritic synaptic interactions Physica D 178 219-41
    • (2003) Physica D , vol.178 , pp. 219-241
    • Coombes, S.1    Lord, G.J.2    Owen, M.R.3
  • 30
    • 0036226617 scopus 로고    scopus 로고
    • Spatially structured activity in synaptically coupled neuronal networks: I. Travelling fronts and pulses
    • Pinto D J and Ermentrout G B 2001 Spatially structured activity in synaptically coupled neuronal networks: I. Travelling fronts and pulses SIAM J. Appl. Math. 62 206-25
    • (2001) SIAM J. Appl. Math , vol.62 , pp. 206-225
    • Pinto, D.J.1    Ermentrout, G.B.2
  • 31
    • 23944523647 scopus 로고    scopus 로고
    • Spiral waves in nonlocal equations
    • Laing C R 2004 Spiral waves in nonlocal equations SIAM J. Appl. Dyn. Syst. 4 588-606
    • (2004) SIAM J. Appl. Dyn. Syst , vol.4 , pp. 588-606
    • Laing, C.R.1
  • 32
    • 0041361957 scopus 로고    scopus 로고
    • Rotational bifurcation of localized dissipative structures
    • Moskalenko A S, Liehr A W and Purwins H G 2003 Rotational bifurcation of localized dissipative structures Europhys. Lett. 63 361-7
    • (2003) Europhys. Lett , vol.63 , pp. 361-367
    • Moskalenko, A.S.1    Liehr, A.W.2    Purwins, H.G.3
  • 33
    • 0001102631 scopus 로고
    • Complex patterns in a simple system
    • Pearson J E 1993 Complex patterns in a simple system Science 261 189-92
    • (1993) Science , vol.261 , pp. 189-192
    • Pearson, J.E.1
  • 34
    • 0000518461 scopus 로고    scopus 로고
    • Interface proliferation and the growth of labyrinths in a reaction-diffusion system
    • Goldstein R E, Muraki D J and Petrich D M 1996 Interface proliferation and the growth of labyrinths in a reaction-diffusion system Phys. Rev. E 53 3933
    • (1996) Phys. Rev. E , vol.53 , pp. 3933
    • Goldstein, R.E.1    Muraki, D.J.2    Petrich, D.M.3
  • 35
    • 18144426424 scopus 로고    scopus 로고
    • Bumps, breathers, and waves in a neural network with spike frequency adaptation
    • Coombes S and Owen M R 2005 Bumps, breathers, and waves in a neural network with spike frequency adaptation Phys. Rev. Lett. 94 148102
    • (2005) Phys. Rev. Lett , vol.94 , pp. 148102
    • Coombes, S.1    Owen, M.R.2
  • 36
    • 14644413458 scopus 로고    scopus 로고
    • Conditions of activity bubble uniqueness in dynamic neural fields
    • Mikhailova I and Goerick C 2005 Conditions of activity bubble uniqueness in dynamic neural fields Biol. Cybern. 92 82-91
    • (2005) Biol. Cybern , vol.92 , pp. 82-91
    • Mikhailova, I.1    Goerick, C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.