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Volumn 4, Issue 3, 2005, Pages 588-606

Spiral waves in nonlocal equations

Author keywords

Bifurcation; Nonlocal; PDE; Spiral wave

Indexed keywords

BIFURCATION (MATHEMATICS); FEEDBACK; INTEGRODIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; WAVE EQUATIONS;

EID: 23944523647     PISSN: 15360040     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/040612890     Document Type: Article
Times cited : (64)

References (44)
  • 1
    • 6244299076 scopus 로고
    • Theory of interaction and bound states of spiral waves in oscillatory media
    • I. S. ARANSON, L. KRAMER, AND A. WEBER, Theory of interaction and bound states of spiral waves in oscillatory media, Phys. Rev. E, 47 (1993), pp. 3231-3241.
    • (1993) Phys. Rev. E , vol.47 , pp. 3231-3241
    • Aranson, I.S.1    Kramer, L.2    Weber, A.3
  • 2
    • 42749108525 scopus 로고    scopus 로고
    • Bifurcation and stability analysis of rotating chemical spirals in circular domains: Boundary-induced meandering and stabilization
    • M. BÄR, A. K. BANGIA, AND I. G. KEVREKIDIS, Bifurcation and stability analysis of rotating chemical spirals in circular domains: Boundary-induced meandering and stabilization, Phys. Rev. E (3), 67 (2003), 056126.
    • (2003) Phys. Rev. E (3) , vol.67 , pp. 056126
    • Bär, M.1    Bangia, A.K.2    Kevrekidis, I.G.3
  • 3
    • 7044228895 scopus 로고
    • Linear stability analysis of rotating spiral waves in excitable media
    • D. BARKLEY, Linear stability analysis of rotating spiral waves in excitable media, Phys. Rev. Lett., 68 (1992), pp. 2090-2093.
    • (1992) Phys. Rev. Lett. , vol.68 , pp. 2090-2093
    • Barkley, D.1
  • 4
    • 4243665470 scopus 로고
    • Euclidian symmetry and the dynamics of rotating spiral waves
    • D. BARKLEY, Euclidian symmetry and the dynamics of rotating spiral waves, Phys. Rev. Lett., 72 (1994), pp. 164-167.
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 164-167
    • Barkley, D.1
  • 6
    • 33644880119 scopus 로고    scopus 로고
    • Personal communication
    • S. COOMBES, Personal communication, 2004.
    • (2004)
    • Coombes, S.1
  • 7
    • 0037446036 scopus 로고    scopus 로고
    • Waves and bumps in neuronal networks with axo-dendritic synaptic interactions
    • S. COOMBES, G. J. LORD, AND M. R. OWEN, Waves and bumps in neuronal networks with axo-dendritic synaptic 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
  • 8
    • 0031011039 scopus 로고    scopus 로고
    • Self-induced splitting of spired-shaped spreading depression waves in chicken retina
    • M. A. DAHLEM AND S. C. MÜLLER, Self-induced splitting of spired-shaped spreading depression waves in chicken retina, Exp. Brain Res., 115 (1997), pp. 319-324.
    • (1997) Exp. Brain Res. , vol.115 , pp. 319-324
    • Dahlem, M.A.1    Müller, S.C.2
  • 9
    • 0001104658 scopus 로고    scopus 로고
    • Neural networks as spatio-temporal pattern-forming systems
    • 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, B.1
  • 10
    • 0029374551 scopus 로고
    • Spontaneous excitations in the visual cortex: Stripes, spirals, rings, and collective bursts
    • C. FOHLMEISTER, W. GERSTNEH, R. RITZ, AND J. L. VAN HEMMEN, Spontaneous excitations in the visual cortex: Stripes, spirals, rings, and collective bursts, Neural Comput., 7 (1995), pp. 905-914.
    • (1995) Neural Comput. , vol.7 , pp. 905-914
    • Fohlmeister, C.1    Gerstneh, W.2    Ritz, R.3    Van Hemmen, J.L.4
  • 11
    • 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. Dyn. Syst., 3 (2004), pp. 378-407.
    • (2004) SIAM J. Appl. Dyn. Syst. , vol.3 , pp. 378-407
    • Folias, S.E.1    Bressloff, P.C.2
  • 13
    • 4243706164 scopus 로고    scopus 로고
    • Theory of spiral wave dynamics in weakly excitable media: Asymptotic reduction to a kinematic model and applications
    • V. HAKIM AND A. KARMA, Theory of spiral wave dynamics in weakly excitable media: Asymptotic reduction to a kinematic model and applications, Phys. Rev. E (3), 60 (1999), pp. 5073-5105.
    • (1999) Phys. Rev. E (3) , vol.60 , pp. 5073-5105
    • Hakim, V.1    Karma, A.2
  • 16
    • 0034504068 scopus 로고    scopus 로고
    • Target waves in the complex Ginzburg-Landau equation
    • M. HENDREY, K. NAM, P. GUZDAR, AND E. OTT, Target waves in the complex Ginzburg-Landau equation, Phys. Rev. E (3), 62 (2000), pp. 7627-7631.
    • (2000) Phys. Rev. E (3) , vol.62 , pp. 7627-7631
    • Hendrey, M.1    Nam, K.2    Guzdar, P.3    Ott, E.4
  • 17
    • 0031573118 scopus 로고    scopus 로고
    • Solitary waves of integrate-and-fire neural models
    • D. HORN AND I. OPHER, Solitary waves of integrate-and-fire neural models, Neural Comput., 9 (1997), pp. 1677-1690.
    • (1997) Neural Comput. , vol.9 , pp. 1677-1690
    • Horn, D.1    Opher, I.2
  • 19
    • 0000392679 scopus 로고    scopus 로고
    • Modeling collective excitations in cortical tissue
    • W. M. KISTLER, R. SEITZ, AND J. L. VAN HEMMEN, Modeling collective excitations in cortical tissue, Phys. D, 114 (1998), pp. 273-295.
    • (1998) Phys. D , vol.114 , pp. 273-295
    • Kistler, W.M.1    Seitz, R.2    Van Hemmen, J.L.3
  • 21
  • 22
    • 0037446124 scopus 로고    scopus 로고
    • Two-bump solutions of Amari-type models of neuronal pattern formation
    • C. R. LAING AND W. C. TROY, Two-bump solutions of Amari-type models of neuronal pattern formation, Phys. D, 178 (2003), pp. 190-218.
    • (2003) Phys. D , vol.178 , pp. 190-218
    • Laing, C.R.1    Troy, W.C.2
  • 23
    • 0001248698 scopus 로고    scopus 로고
    • Transition from simple rotating chemical spirals to meandering and traveling spirals
    • G. LI, Q. OUYANG, V. PETROV, AND H. L. SWINNEY, Transition from simple rotating chemical spirals to meandering and traveling spirals, Phys. Rev. Lett., 77 (1996), pp. 2105-2108.
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 2105-2108
    • Li, G.1    Ouyang, Q.2    Petrov, V.3    Swinney, H.L.4
  • 24
    • 0000733852 scopus 로고    scopus 로고
    • Resonant phase patterns in a reaction-diffusion system
    • A. L. LIN, M. BERTRAM, K. MARTINEZ, AND H. L. SWINNEY, Resonant phase patterns in a reaction-diffusion system, Phys. Rev. Lett., 84 (2000), pp. 4240-4243.
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 4240-4243
    • Lin, A.L.1    Bertram, M.2    Martinez, K.3    Swinney, H.L.4
  • 25
    • 42749108438 scopus 로고    scopus 로고
    • Resonance tongues and patterns in periodically forced reaction-diffusion systems
    • A. L. LIN, A. HAGBERG, E. MERON, AND H. L. SWINNEY, Resonance tongues and patterns in periodically forced reaction-diffusion systems, Phys. Rev. E (3), 69 (2004), p. 066217.
    • (2004) Phys. Rev. E (3) , vol.69 , pp. 066217
    • Lin, A.L.1    Hagberg, A.2    Meron, E.3    Swinney, H.L.4
  • 26
    • 0035081994 scopus 로고    scopus 로고
    • Spike-frequency adaptation of a generalized leaky integrate-and-fire model neuron
    • Y. H. LIU AND X. J. WANG, Spike-frequency adaptation of a generalized leaky integrate-and-fire model neuron, J. Comput. Neurosci., 10 (2001), pp. 25-45.
    • (2001) J. Comput. Neurosci. , vol.10 , pp. 25-45
    • Liu, Y.H.1    Wang, X.J.2
  • 27
    • 33644932033 scopus 로고    scopus 로고
    • THE MATHWORKS, MATLAB, Natick, MA
    • THE MATHWORKS, MATLAB, Natick, MA.
  • 28
    • 0001108678 scopus 로고
    • Impact of global interaction on pattern formation on a disk
    • U. MIDDYA AND D. LUSS, Impact of global interaction on pattern formation on a disk, J. Chem. Phys., 102 (1995), pp. 5029-5036.
    • (1995) J. Chem. Phys. , vol.102 , pp. 5029-5036
    • Middya, U.1    Luss, D.2
  • 29
    • 0038772074 scopus 로고    scopus 로고
    • J. MILTON AND P. JUNG, EDS., Springer-Verlag, New York
    • J. MILTON AND P. JUNG, EDS., Epilepsy as a Dynamical Disease, Springer-Verlag, New York, 2003.
    • (2003) Epilepsy As A Dynamical Disease
  • 31
    • 0028516641 scopus 로고
    • The existence of spiral waves in an oscillatory reaction-diffusion system
    • J. PAULLET, B. ERMENTROUT, AND W. TROY, The existence of spiral waves in an oscillatory reaction-diffusion system, SIAM J. Appl. Math., 54 (1994), pp. 1386-1401.
    • (1994) SIAM J. Appl. Math. , vol.54 , pp. 1386-1401
    • Paullet, J.1    Ermentrout, B.2    Troy, W.3
  • 32
    • 0036226617 scopus 로고    scopus 로고
    • Spatially structured activity in synaptically coupled neuronal networks: 1. Traveling fronts and pulses
    • D. J. PINTO AND G. B. ERMENTROUT, Spatially structured activity in synaptically coupled neuronal networks: 1. 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
  • 33
    • 0036229681 scopus 로고    scopus 로고
    • Spatially structured activity in synaptically coupled neuronal networks: 11. Lateral inhibition and standing pulses
    • D. J. PINTO AND G. B. ERMENTROUT, Spatially structured activity in synaptically coupled neuronal networks: 11. 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
  • 35
    • 0040243453 scopus 로고    scopus 로고
    • Frequency locking of meandering spiral waves in cardiac tissue
    • B. J. ROTH, Frequency locking of meandering spiral waves in cardiac tissue, Phys. Rev. E (3), 57 (1998), pp. 3735-3738.
    • (1998) Phys. Rev. E (3) , vol.57 , pp. 3735-3738
    • Roth, B.J.1
  • 36
    • 0040332090 scopus 로고    scopus 로고
    • Meandering of spiral waves in anisotropic cardiac tissue
    • B. J. ROTH, Meandering of spiral waves in anisotropic cardiac tissue, Phys. D, 150 (2001), pp. 127-136.
    • (2001) Phys. D , vol.150 , pp. 127-136
    • Roth, B.J.1
  • 37
    • 0032361995 scopus 로고    scopus 로고
    • Bifurcation to spiral waves in reaction-diffusion systems
    • A. SCHEEL, Bifurcation to spiral waves in reaction-diffusion systems, SIAM J. Math. Anal., 29 (1998), pp. 1399-1418.
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 1399-1418
    • Scheel, A.1
  • 38
    • 0001091987 scopus 로고
    • Motions of spiral waves in oscillatory media and in the presence of obstacles
    • J. A. SEPULCHRE AND A. BABLOYANTZ, Motions of spiral waves in oscillatory media and in the presence of obstacles, Phys. Rev. E, 48 (1993), pp. 187-195.
    • (1993) Phys. Rev. E , vol.48 , pp. 187-195
    • Sepulchre, J.A.1    Babloyantz, A.2
  • 39
    • 0003027876 scopus 로고    scopus 로고
    • Oscillatory cortical activity during visual hallucinations
    • P. TASS, Oscillatory cortical activity during visual hallucinations, J. Biol. Phys., 23 (1997), pp. 21-66.
    • (1997) J. Biol. Phys. , vol.23 , pp. 21-66
    • Tass, P.1
  • 40
    • 0010423621 scopus 로고    scopus 로고
    • Multiarmed spirals in excitable media
    • B. VASIEV, F. SIEGERT, AND C. WEIJER, Multiarmed spirals in excitable media, Phys. Rev. Lett., 78 (1997), pp. 2489-2492.
    • (1997) Phys. Rev. Lett. , vol.78 , pp. 2489-2492
    • Vasiev, B.1    Siegert, F.2    Weijer, C.3
  • 41
    • 34548122257 scopus 로고    scopus 로고
    • Are cardiac waves relevant to epileptic wave propagation?
    • J. Milton and P. Jung, eds., Springer-Verlag, New York
    • A. WINFREE, Are cardiac waves relevant to epileptic wave propagation?, in Epilepsy as a Dynamical Disease, J. Milton and P. Jung, eds., Springer-Verlag, New York, 2003.
    • (2003) Epilepsy as a Dynamical Disease
    • Winfree, A.1
  • 42
    • 41349088575 scopus 로고    scopus 로고
    • Stable spiral structures and their interaction in two-dimensional excitable media
    • R. M. ZARITSKI AND A. M. PEHTSOV, Stable spiral structures and their interaction in two-dimensional excitable media, Phys. Rev. E (3), 66 (2002), 066120.
    • (2002) Phys. Rev. E (3) , vol.66 , pp. 066120
    • Zaritski, R.M.1    Pehtsov, A.M.2
  • 43
    • 37649030349 scopus 로고    scopus 로고
    • Dynamics of spiral waves under global feedback in excitable domains of different shapes
    • V. S. ZYKOV AND H. ENGEL, Dynamics of spiral waves under global feedback in excitable domains of different shapes, Phys. Rev. E (3), 70 (2004), 016201.
    • (2004) Phys. Rev. E (3) , vol.70 , pp. 016201
    • Zykov, V.S.1    Engel, H.2
  • 44
    • 4243094905 scopus 로고    scopus 로고
    • Controlling spiral waves in confined geometries by global feedback
    • V. S. ZYKOV, A. S. MIKHAILOV, AND S. C. MÜLLER, Controlling spiral waves in confined geometries by global feedback, Phys. Rev. Lett., 78 (1997), pp. 3398-3401.
    • (1997) Phys. Rev. Lett. , vol.78 , pp. 3398-3401
    • Zykov, V.S.1    Mikhailov, A.S.2    Müller, S.C.3


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