메뉴 건너뛰기




Volumn 3, Issue 4, 2004, Pages 574-600

Evans functions for integral neural field equations with heaviside firing rate function

Author keywords

Evans functions; Integral equations; Neural networks; Traveling waves

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTATIONAL METHODS; COMPUTER SIMULATION; INTEGRAL EQUATIONS; MICROSTRUCTURE; NEURAL NETWORKS; STABILITY;

EID: 17744400704     PISSN: 15360040     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/040605953     Document Type: Article
Times cited : (115)

References (41)
  • 1
    • 0005235678 scopus 로고
    • A topological invariant arising in the stability analysis of travelling waves
    • J. ALEXANDER, R. GARDNER, AND C. JONES, A topological invariant arising in the stability analysis of travelling waves, J. Reine Angew. Math., 410 (1990), pp. 167-212.
    • (1990) J. Reine Angew. Math. , vol.410 , pp. 167-212
    • Alexander, J.1    Gardner, R.2    Jones, C.3
  • 2
    • 0017713690 scopus 로고
    • Dynamics of pattern formation in lateral-inhibition type neural fields
    • S. AMARI, Dynamics of pattern formation in lateral-inhibition type neural fields, Bio. Cybernet., 27 (1977), pp. 77-87.
    • (1977) Bio. Cybernet. , vol.27 , pp. 77-87
    • Amari, S.1
  • 5
    • 0035400302 scopus 로고    scopus 로고
    • 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
  • 6
    • 16244415210 scopus 로고    scopus 로고
    • Front bifurcations in an excitatory neural network
    • P. C. BRESSLOFF AND S. E. FOLIAS, Front bifurcations in an excitatory neural network, SIAM J. Appl. Math., 65 (2004), pp. 131-151.
    • (2004) SIAM J. Appl. Math. , vol.65 , pp. 131-151
    • Bressloff, P.C.1    Folias, S.E.2
  • 7
    • 0348220911 scopus 로고    scopus 로고
    • Oscillatory waves in inhomogeneous neural media
    • P. C. BRESSLOFF, S. E. FOLIAS, A. PRAT, AND Y. X. Li, Oscillatory waves in inhomogeneous neural media, Phys. Rev. Lett., 91 (2003), pp. 178101-1-178101-4.
    • (2003) Phys. Rev. Lett. , vol.91 , pp. 1781011-1781014
    • Bressloff, P.C.1    Folias, S.E.2    Prat, A.3    Li, Y.X.4
  • 8
    • 0037112236 scopus 로고    scopus 로고
    • Stability and instability of solitary waves of the fifth-order KdV equation: A numerical framework
    • T. J. BRIDGES, G. DERKS, AND G. GOTTWALD, Stability and instability of solitary waves of the fifth-order KdV equation: A numerical framework, Phys. D, 172 (2002), pp. 190-216.
    • (2002) Phys. D , vol.172 , pp. 190-216
    • Bridges, T.J.1    Derks, G.2    Gottwald, G.3
  • 9
    • 3042626066 scopus 로고    scopus 로고
    • Travelling waves for a neural network
    • F. CHEN, Travelling waves for a neural network, Electron. J. Differential Equations, 2003 (2003), pp. 1-4.
    • (2003) Electron. J. Differential Equations , vol.2003 , pp. 1-4
    • Chen, F.1
  • 10
    • 0001203924 scopus 로고    scopus 로고
    • Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations
    • X. CHEN, Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations, Adv. Differential Equations, 2 (1997), pp. 125-160.
    • (1997) Adv. Differential Equations , vol.2 , pp. 125-160
    • Chen, X.1
  • 11
    • 85064295896 scopus 로고    scopus 로고
    • Traveling fronts for a class of nonlocal convolution differential equation
    • Z. CHEN, G. B. ERMENTROUT, AND J. B. McLEOD, Traveling fronts for a class of nonlocal convolution differential equation, Appl. Anal., 64 (1997), pp. 235-253.
    • (1997) Appl. Anal. , vol.64 , pp. 235-253
    • Chen, Z.1    Ermentrout, G.B.2    McLeod, J.B.3
  • 12
    • 0023734648 scopus 로고
    • Propagation of excitation in neural network models
    • R. D. CHERVIN, P. A. PIERCE, AND B. W. CONNORS, Propagation of excitation in neural network models, J. Neurophysiology, 60 (1988), pp. 1695-1713.
    • (1988) J. Neurophysiology , vol.60 , pp. 1695-1713
    • Chervin, R.D.1    Pierce, P.A.2    Connors, B.W.3
  • 13
    • 0037446036 scopus 로고    scopus 로고
    • Waves and bumps in neuronal networks with axo-dendritic synoptic interactions
    • S. COOMBES, G. J. LORD, AND M. R. OWEN, Waves and bumps in neuronal networks with axo-dendritic synoptic interactions, Phys. D, 178 (2003), pp. 219-241.
    • (2003) Phys. D , vol.178 , pp. 219-241
    • Coombes, S.1    Lord, G.J.2    Owen, M.R.3
  • 14
    • 0036635729 scopus 로고    scopus 로고
    • Traveling waves of excitation in neural field models: Equivalence of rate descriptions and integrate-and-fire dynamics
    • D. CREMERS AND A. V. M. HERZ, Traveling waves of excitation in neural field models: Equivalence of rate descriptions and integrate-and-fire dynamics, Neural Computation, 14 (2002), pp. 1651-1667.
    • (2002) Neural Computation , vol.14 , pp. 1651-1667
    • Cremers, D.1    Herz, A.V.M.2
  • 15
    • 0001104658 scopus 로고    scopus 로고
    • Neural nets as spatio-temporal pattern forming systems
    • G. B. ERMENTROUT, Neural nets 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
  • 16
    • 84971116294 scopus 로고
    • 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
  • 17
    • 0016578299 scopus 로고
    • Nerve axon equations IV: The stable and unstable impulse
    • J. EVANS, Nerve axon equations IV: The stable and unstable impulse, Indiana Univ. Math. J., 24 (1975), pp. 1169-1190.
    • (1975) Indiana Univ. Math. J. , vol.24 , pp. 1169-1190
    • Evans, J.1
  • 18
    • 16344393249 scopus 로고    scopus 로고
    • Breathing pulses in an excitatory neural network
    • S. E. FOLIAS AND P. C. BRESSLOFF, Breathing pulses in an excitatory neural network, SIAM J. Appl. Dynam. Sys., 3 (2004), pp. 378-407.
    • (2004) SIAM J. Appl. Dynam. Sys. , vol.3 , pp. 378-407
    • Folias, S.E.1    Bressloff, P.C.2
  • 19
    • 0030874847 scopus 로고    scopus 로고
    • Propagating neuronal discharges in neocortical slices: Computational and experimental study
    • D. GOLOMB AND Y. AMITAI, Propagating neuronal discharges in neocortical slices: Computational and experimental study, J. Neurophysiology, 78 (1997), pp. 1199-1211.
    • (1997) J. Neurophysiology , vol.78 , pp. 1199-1211
    • Golomb, D.1    Amitai, Y.2
  • 20
    • 0000085224 scopus 로고
    • Pattern formation in non-gradient reaction-diffusion systems: The effects affront bifurcations
    • A. HAGBERG AND E. MERON, Pattern formation in non-gradient reaction-diffusion systems: The effects affront bifurcations, Nonlinearity, 7 (1994), pp. 805-835.
    • (1994) Nonlinearity , vol.7 , pp. 805-835
    • Hagberg, A.1    Meron, E.2
  • 21
    • 2942662407 scopus 로고    scopus 로고
    • The Evans function and stability criteria for degenerate viscous shock waves
    • P. HOWARD AND K. ZUMBRUN, The Evans function and stability criteria for degenerate viscous shock waves, Discrete Contin. Dyn. Syst. Ser. A, 4 (2004), pp. 837-855.
    • (2004) Discrete Contin. Dyn. Syst. Ser. A , vol.4 , pp. 837-855
    • Howard, P.1    Zumbrun, K.2
  • 22
    • 0346847617 scopus 로고    scopus 로고
    • Pattern formation in intracortical neuronal fields
    • A. HUTT, M. BESTEHORN, AND T. WENNEKERS, Pattern formation in intracortical neuronal fields, Network, 14 (2003), pp. 351-368.
    • (2003) Network , vol.14 , pp. 351-368
    • Hutt, A.1    Bestehorn, M.2    Wennekers, T.3
  • 23
    • 0000420960 scopus 로고
    • Propagation of excitation in neural network models
    • M. A. P. IDIART AND L. F. ABBOTT, Propagation of excitation in neural network models, Network, 4 (1993), pp. 285-294.
    • (1993) Network , vol.4 , pp. 285-294
    • Idiart, M.A.P.1    Abbott, L.F.2
  • 24
    • 84967743294 scopus 로고
    • Stability of the traveling wave solutions of the FitzHugh-Nagumo system
    • C. K. R. T. JONES, Stability of the traveling wave solutions of the FitzHugh-Nagumo system, Trans. Amer. Math. Soc., 286 (1984), pp. 431-469.
    • (1984) Trans. Amer. Math. Soc. , vol.286 , pp. 431-469
    • Jones, C.K.R.T.1
  • 26
    • 0036373932 scopus 로고    scopus 로고
    • Edge bifurcations for near integrable systems via Evans function techniques
    • T. KAPITULA AND B. SANDSTEDE, Edge bifurcations for near integrable systems via Evans function techniques, SIAM J. Math. Anal., 33 (2002), pp. 1117-1143.
    • (2002) SIAM J. Math. Anal. , vol.33 , pp. 1117-1143
    • Kapitula, T.1    Sandstede, B.2
  • 27
    • 2942679820 scopus 로고    scopus 로고
    • Eigenvalues and resonances using the Evans function
    • T. KAPITULA AND B. SANDSTEDE, Eigenvalues and resonances using the Evans function, Discrete Contin. Dynam. Systems, 10 (2004), pp. 857-869.
    • (2004) Discrete Contin. Dynam. Systems , vol.10 , pp. 857-869
    • Kapitula, T.1    Sandstede, B.2
  • 28
    • 0029076314 scopus 로고
    • Spindle waves are propagating synchronized oscillations in the ferret LGNd in vitro
    • U. KIM, T. BAL, AND D. A. McCORMICK, Spindle waves are propagating synchronized oscillations in the ferret LGNd in vitro, J. Neurophysiology, 74 (1995), pp. 1301-1323.
    • (1995) J. Neurophysiology , vol.74 , pp. 1301-1323
    • Kim, U.1    Bal, T.2    McCormick, D.A.3
  • 30
    • 0034347554 scopus 로고    scopus 로고
    • The mechanism of the polarization mode instability in birefringent fiber optics
    • Y. A. LI AND K. PROMISLOW, The mechanism of the polarization mode instability in birefringent fiber optics, SIAM J. Math. Anal., 31 (2000), pp. 1351-1373.
    • (2000) SIAM J. Math. Anal. , vol.31 , pp. 1351-1373
    • Li, Y.A.1    Promislow, K.2
  • 31
    • 0023757093 scopus 로고
    • Spread of synchronous firing in longitudinal slices from the CA3 region of the hippocampus
    • R. MILES, R. D. TRAUB, AND R. K. S. WONG, Spread of synchronous firing in longitudinal slices from the CA3 region of the hippocampus, J. Neurophysiology, 60 (1988), pp. 1481-1496.
    • (1988) J. Neurophysiology , vol.60 , pp. 1481-1496
    • Miles, R.1    Traub, R.D.2    Wong, R.K.S.3
  • 33
    • 21844510556 scopus 로고
    • Asymptotic stability of solitary waves
    • R. L. PEGO AND M. I. WEINSTEIN, Asymptotic stability of solitary waves, Comm. Math. Phys., 164 (1994), pp. 305-349.
    • (1994) Comm. Math. Phys. , vol.164 , pp. 305-349
    • Pego, R.L.1    Weinstein, M.I.2
  • 34
    • 0036226617 scopus 로고    scopus 로고
    • 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
  • 35
    • 0036229681 scopus 로고    scopus 로고
    • Spatially structured activity in synaptically coupled neuronal networks: II. Lateral inhibition and standing pulses
    • D. J. PINTO AND G. B. ERMENTROUT, Spatially structured activity in synaptically coupled neuronal networks: II. Lateral inhibition and standing pulses, SIAM J. Appl. Math., 62 (2001), pp. 226-243.
    • (2001) SIAM J. Appl. Math. , vol.62 , pp. 226-243
    • Pinto, D.J.1    Ermentrout, G.B.2
  • 36
    • 67649363651 scopus 로고    scopus 로고
    • Stability of travelling waves
    • North-Holland, Amsterdam
    • B. SANDSTEDE, Stability of travelling waves, in Handbook of Dynamical Systems, Vol. 2, North-Holland, Amsterdam, 2002, pp. 983-1055.
    • (2002) Handbook of Dynamical Systems , vol.2 , pp. 983-1055
    • Sandstede, B.1
  • 37
    • 0000649277 scopus 로고    scopus 로고
    • Neural 'bubble' dynamics in two dimensions: Foundations
    • J. G. TAYLOR, Neural 'bubble' dynamics in two dimensions: Foundations, Biol. Cybernet., 80 (1999), pp. 393-409.
    • (1999) Biol. Cybernet. , vol.80 , pp. 393-409
    • Taylor, J.G.1
  • 38
    • 0035458994 scopus 로고    scopus 로고
    • Circular stationary solutions in two-dimensional neural fields
    • H. WERNER AND T. RICHTER, Circular stationary solutions in two-dimensional neural fields, Biol. Cybernet., 85 (2001), pp. 211-217.
    • (2001) Biol. Cybernet. , vol.85 , pp. 211-217
    • Werner, H.1    Richter, T.2
  • 39
    • 0015868589 scopus 로고
    • A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue
    • H. R. WILSON AND J. D. COWAN, A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue, Kybernetik, 13 (1973), pp. 55-80.
    • (1973) Kybernetik , vol.13 , pp. 55-80
    • Wilson, H.R.1    Cowan, J.D.2
  • 40
    • 0033564772 scopus 로고    scopus 로고
    • Propagating activation during oscillations and evoked responses in neocortical slices
    • J.-Y. Wu, L. GUAN, AND Y. TSAU, Propagating activation during oscillations and evoked responses in neocortical slices, J. Neuroscience, 19 (1999), pp. 5005-5015.
    • (1999) J. Neuroscience , vol.19 , pp. 5005-5015
    • Wu, J.-Y.1    Guan, L.2    Tsau, Y.3
  • 41
    • 1042287949 scopus 로고    scopus 로고
    • 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.