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Volumn 202, Issue 3-4, 2005, Pages 177-199

Inhomogeneity-induced bifurcation of stationary and oscillatory pulses

Author keywords

Hopf bifurcation; Inhomogeneous excitable media; Integro differential equations; Oscillatory pulses; Reaction diffusion equations; Stationary pulses

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; INTEGRODIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; OSCILLATORS (ELECTRONIC); PULSATILE FLOW; TURING MACHINES;

EID: 16344386615     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2005.02.005     Document Type: Article
Times cited : (23)

References (32)
  • 1
    • 0030573542 scopus 로고    scopus 로고
    • Modeling of heart excitation patterns caused by a local inhomogeneity
    • R. Aliev, and A. Panfilov Modeling of heart excitation patterns caused by a local inhomogeneity J. Theoret. Biol. 181 1996 33 40
    • (1996) J. Theoret. Biol. , vol.181 , pp. 33-40
    • Aliev, R.1    Panfilov, A.2
  • 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 Biol. Cybernet. 27 1977 77 87
    • (1977) Biol. Cybernet. , vol.27 , pp. 77-87
    • Amari, S.1
  • 3
    • 0031207518 scopus 로고    scopus 로고
    • Front-bifurcations in reaction-diffusion systems with inhomogeneous parameter distributions
    • M. Bode Front-bifurcations in reaction-diffusion systems with inhomogeneous parameter distributions Physica D 106 1997 270 286
    • (1997) Physica D , vol.106 , pp. 270-286
    • Bode, M.1
  • 5
    • 0030216813 scopus 로고    scopus 로고
    • Reflected waves in an inhomogeneous excitable medium
    • G.B. Ermentrout, and J. Rinzel Reflected waves in an inhomogeneous excitable medium SIAM J. Appl. Math. 56 1996 1107 1128
    • (1996) SIAM J. Appl. Math. , vol.56 , pp. 1107-1128
    • Ermentrout, G.B.1    Rinzel, J.2
  • 6
    • 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 378 407
    • (2004) SIAM J. Appl. Dyn. Syst. , vol.3 , pp. 378-407
    • Folias, S.E.1    Bressloff, P.C.2
  • 8
    • 0016289012 scopus 로고
    • Changes of action potential shape and velocity for changing core conductor geometry
    • S.S. Goldstein, and W. Rall Changes of action potential shape and velocity for changing core conductor geometry Biophys. J. 14 1974 731 757
    • (1974) Biophys. J. , vol.14 , pp. 731-757
    • Goldstein, S.S.1    Rall, W.2
  • 10
    • 35649001607 scopus 로고
    • A quantitative description of membrane current and its application to conduction and excitation in nerve
    • A.L. Hodgkin, and A.F. Huxley A quantitative description of membrane current and its application to conduction and excitation in nerve J. Physiol. 117 1952 500 544
    • (1952) J. Physiol. , vol.117 , pp. 500-544
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 11
    • 0034456182 scopus 로고    scopus 로고
    • Propagation of waves in an excitable medium with discrete release sites
    • J.P. Keener Propagation of waves in an excitable medium with discrete release sites SIAM J. Appl. Math. 61 1 2000 317 334
    • (2000) SIAM J. Appl. Math. , vol.61 , Issue.1 , pp. 317-334
    • Keener, J.P.1
  • 12
    • 0344010964 scopus 로고    scopus 로고
    • Model for the onset of fibrillation following coronary artery occlusion
    • J.P. Keener Model for the onset of fibrillation following coronary artery occlusion J. Cardiovasc. Electrophysiol. 14 2003 1225 1232
    • (2003) J. Cardiovasc. Electrophysiol. , vol.14 , pp. 1225-1232
    • Keener, J.P.1
  • 16
    • 0034456883 scopus 로고    scopus 로고
    • Wave-block in excitable media due to regions of depressed excitability
    • T.J. Lewis, and J.P. Keener Wave-block in excitable media due to regions of depressed excitability SIAM J. Appl. Math. 61 1 2000 293 316
    • (2000) SIAM J. Appl. Math. , vol.61 , Issue.1 , pp. 293-316
    • Lewis, T.J.1    Keener, J.P.2
  • 17
    • 0242544110 scopus 로고    scopus 로고
    • Tango waves in a bidomain model of fertilization calcium waves
    • Y.-X. Li Tango waves in a bidomain model of fertilization calcium waves Physica D 186 2003 27 49
    • (2003) Physica D , vol.186 , pp. 27-49
    • Li, Y.-X.1
  • 18
    • 0028178965 scopus 로고
    • i oscillations derived from a detailed kinetic model: A Hodgkin-Huxley like formalism
    • i oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism J. Theoret. Biol. 166 1994 461 473
    • (1994) J. Theoret. Biol. , vol.166 , pp. 461-473
    • Li, Y.-X.1    Rinzel, J.2
  • 21
    • 0000130504 scopus 로고
    • Layer oscillations in reaction-diffusion systems
    • Y. Nishiura, and M. Mimura Layer oscillations in reaction-diffusion systems SIAM J. Appl. Math. 49 1989 481 514
    • (1989) SIAM J. Appl. Math. , vol.49 , pp. 481-514
    • Nishiura, Y.1    Mimura, M.2
  • 22
    • 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 206 225; 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 226 243
    • (2001) SIAM J. Appl. Math. , vol.62 , pp. 206-225
    • Pinto, D.J.1    Ermentrout, G.B.2
  • 23
    • 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. I. Traveling fronts and pulses SIAM J. Appl. Math. 62 2001 206 225; 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 226 243
    • (2001) SIAM J. Appl. Math. , vol.62 , pp. 226-243
    • Pinto, D.J.1    Ermentrout, G.B.2
  • 24
    • 0242544111 scopus 로고    scopus 로고
    • Stability of front solutions in inhomogeneous media
    • A. Prat, and Y.-X. Li Stability of front solutions in inhomogeneous media Physica D 186 2003 50 68
    • (2003) Physica D , vol.186 , pp. 50-68
    • Prat, A.1    Li, Y.-X.2
  • 25
    • 0033590472 scopus 로고    scopus 로고
    • A model for the propagation of action potentials in non-uniformly excitable media
    • A. Rabinovitch, I. Aviram, N. Gulko, and E. Ovsyshcher A model for the propagation of action potentials in non-uniformly excitable media J. Theoret. Biol. 196 1999 141 154
    • (1999) J. Theoret. Biol. , vol.196 , pp. 141-154
    • Rabinovitch, A.1    Aviram, I.2    Gulko, N.3    Ovsyshcher, E.4
  • 26
    • 0020191444 scopus 로고
    • Propagation phenomenon in a bistable reaction-diffusion system
    • J. Rinzel, and D. Terman Propagation phenomenon in a bistable reaction-diffusion system SIAM J. Appl. Math. 42 5 1982 1111 1137
    • (1982) SIAM J. Appl. Math. , vol.42 , Issue.5 , pp. 1111-1137
    • Rinzel, J.1    Terman, D.2
  • 27
    • 12244273201 scopus 로고    scopus 로고
    • Stability, bifurcations, and edge oscillations for standing pulse solutions to an inhomogeneous reaction-diffusion system
    • J. Rubin Stability, bifurcations, and edge oscillations for standing pulse solutions to an inhomogeneous reaction-diffusion system Proc. R. Soc. Edinburgh, Ser. A 129 1999 1033 1079
    • (1999) Proc. R. Soc. Edinburgh, Ser. A , vol.129 , pp. 1033-1079
    • Rubin, J.1
  • 30
    • 45449123944 scopus 로고
    • Singular perturbation theory of traveling waves in excitable media
    • J.J. Tyson, and J.P. Keener Singular perturbation theory of traveling waves in excitable media Physica D 32 1988 327 361
    • (1988) Physica D , vol.32 , pp. 327-361
    • Tyson, J.J.1    Keener, J.P.2
  • 31
    • 0041511859 scopus 로고    scopus 로고
    • Analytic solutions for monotonic and oscillating fronts in a reaction-diffusion system under external fields
    • E.P. Zemskov, V.S. Zykov, K. Kassner, and S.C. Muller Analytic solutions for monotonic and oscillating fronts in a reaction-diffusion system under external fields Physica D 183 2003 117 132
    • (2003) Physica D , vol.183 , pp. 117-132
    • Zemskov, E.P.1    Zykov, V.S.2    Kassner, K.3    Muller, S.C.4
  • 32
    • 0028362541 scopus 로고
    • Study of propagation along nonuniform excitable fibers
    • Y. Zhou, and J. Bell Study of propagation along nonuniform excitable fibers Math. Biosci. 119 1994 169 203
    • (1994) Math. Biosci. , vol.119 , pp. 169-203
    • Zhou, Y.1    Bell, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.