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Volumn 38, Issue 1, 1999, Pages 21-78

Glucose-induced period-doubling cascade in the electrical activity of pancreatic β-cells

Author keywords

Asymptotic expansion; Bursting spiking oscillations; Continuous spiking oscillations; Junction point; Junction fold point; Kneading sequence; Period doubling cascade; Poincar map; Slow manifold; Stable and unstable foliations; Turning point

Indexed keywords

CALCIUM; GLUCOSE; INSULIN;

EID: 0032603032     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002850050141     Document Type: Article
Times cited : (22)

References (26)
  • 2
    • 0000465402 scopus 로고
    • Singular perturbation of relaxed periodic orbits
    • Bonet, C., Singular perturbation of relaxed periodic orbits, J.D.E., 66(1987), pp. 301-339.
    • (1987) J.D.E. , vol.66 , pp. 301-339
    • Bonet, C.1
  • 3
    • 46549093797 scopus 로고
    • Chaos in a three-variable model of an excitable cell
    • Chay, T. R., Chaos in a three-variable model of an excitable cell, Phys. D. 16(1985), pp. 233-242.
    • (1985) Phys. D , vol.16 , pp. 233-242
    • Chay, T.R.1
  • 4
    • 0020957719 scopus 로고
    • Minimal model for membrane oscillations in the pancreatic β-cell
    • Chay, T. R. and Keizer, J., Minimal model for membrane oscillations in the pancreatic β-cell, J. Biophys., 42(1983), pp. 181-190.
    • (1983) J. Biophys. , vol.42 , pp. 181-190
    • Chay, T.R.1    Keizer, J.2
  • 5
    • 0022037388 scopus 로고
    • Bursting, beating, and chaos in an excitable membrane model
    • Chay, T. R. and J. Rinzel, Bursting, beating, and chaos in an excitable membrane model, J. Biophys., 47(1985), pp. 357-366.
    • (1985) J. Biophys. , vol.47 , pp. 357-366
    • Chay, T.R.1    Rinzel, J.2
  • 8
    • 0028308861 scopus 로고
    • A mathematical model that mimics the bursting oscillations in pancreatic β-cells
    • Deng, B., A mathematical model that mimics the bursting oscillations in pancreatic β-cells, Math. Biosciences 119(1993), pp. 241-250.
    • (1993) Math. Biosciences , vol.119 , pp. 241-250
    • Deng, B.1
  • 9
    • 21844517849 scopus 로고
    • Constructing homoclinic orbits and chaos
    • Deng, B., Constructing homoclinic orbits and chaos, Int. J. Bif. and Chaos, 4(1994), pp. 823-841.
    • (1994) Int. J. Bif. and Chaos , vol.4 , pp. 823-841
    • Deng, B.1
  • 10
    • 21844510580 scopus 로고
    • Constructing Lorenz type attractors through singular perturbations
    • Deng, B., Constructing Lorenz type attractors through singular perturbations, Int. J. Bif. and Chaos, 5(1995), pp. 1633-1642.
    • (1995) Int. J. Bif. and Chaos , vol.5 , pp. 1633-1642
    • Deng, B.1
  • 11
    • 0030093599 scopus 로고    scopus 로고
    • Spiral-plus-saddle attractors and elementary mechanisms for chaos generation
    • Deng, B., Spiral-plus-saddle attractors and elementary mechanisms for chaos generation, Int. J. Bif. and Chaos, 6(1996), pp. 513-527.
    • (1996) Int. J. Bif. and Chaos , vol.6 , pp. 513-527
    • Deng, B.1
  • 12
    • 0000553690 scopus 로고    scopus 로고
    • Folding at the genesis of chaos
    • ed. V. Lakshmikantham, Walter de Gruyter, Berlin/New York
    • Deng, B., Folding at the genesis of chaos, in Proceedings of the First World Congress of Nonlinear Analysts, ed. V. Lakshmikantham, Walter de Gruyter, pp. 3765-3777, Berlin/New York, 1996.
    • (1996) Proceedings of the First World Congress of Nonlinear Analysts , pp. 3765-3777
    • Deng, B.1
  • 13
    • 11844295560 scopus 로고
    • Geometric singular perturbation theory for ordinary differential equations
    • Fenichel, N., Geometric singular perturbation theory for ordinary differential equations, J.D.E., 73(1979), pp. 309-353.
    • (1979) J.D.E. , vol.73 , pp. 309-353
    • Fenichel, N.1
  • 14
    • 0038395012 scopus 로고
    • On bifurcations of maps of the interval
    • Guckenheimer, J., On bifurcations of maps of the interval, Invent. Math. 39(1977), pp. 165-178.
    • (1977) Invent. Math. , vol.39 , pp. 165-178
    • Guckenheimer, J.1
  • 15
    • 0023805174 scopus 로고
    • Electrical activity and insulin release in pancreatic β-cells
    • Keizer, J., Electrical activity and insulin release in pancreatic β-cells, Math. Biosc., 90(1988), pp. 127-138.
    • (1988) Math. Biosc. , vol.90 , pp. 127-138
    • Keizer, J.1
  • 16
    • 0024323358 scopus 로고
    • ATP-sensitive potassium channel and bursting in the pancreatic beta cell
    • Keizer, J. and Magnus, G., ATP-sensitive potassium channel and bursting in the pancreatic beta cell, J. Biophys., 56(1989), pp. 229-242.
    • (1989) J. Biophys. , vol.56 , pp. 229-242
    • Keizer, J.1    Magnus, G.2
  • 18
    • 0000117122 scopus 로고
    • Bursting oscillations in an excitable membrane model
    • eds., B.D. Sleeman and R.J. Jarvis, Springer, New York
    • Rinzel, J., Bursting oscillations in an excitable membrane model, in Ordinary and Partial Differential Equations, eds., B.D. Sleeman and R.J. Jarvis, pp. 304-316, Springer, New York, 1985.
    • (1985) Ordinary and Partial Differential Equations , pp. 304-316
    • Rinzel, J.1
  • 19
    • 24844441872 scopus 로고
    • Chaotic behavior in simple reaction systems
    • Rössler, O. E., Chaotic behavior in simple reaction systems, Z. Naturforsch., 31A(1976), pp. 259-264.
    • (1976) Z. Naturforsch. , vol.31 A , pp. 259-264
    • Rössler, O.E.1
  • 20
    • 84985456277 scopus 로고
    • Continuous chaos - Four prototype equations
    • Bifurcation Theory and Applications in Scientific Disciplines, ed. O. Gurel and O. E. Rössler
    • Rössler, O. E., Continuous chaos - four prototype equations, in Bifurcation Theory and Applications in Scientific Disciplines, ed. O. Gurel and O. E. Rössler, Annals of the New York Academy of Science # 316(1978), pp. 376-392.
    • (1978) Annals of the New York Academy of Science , vol.316 , pp. 376-392
    • Rössler, O.E.1
  • 21
    • 0009021792 scopus 로고
    • Glucose dose response of pancreatic β-cells: Experimental and theoretical results
    • eds., C. Hidalgo, J. Bacigalupo, E. Jaimovich, and J. Vergara, Plenum Publishing Co
    • Sherman, A., P., Carroll, R. M. Santos and I. Atwater, Glucose dose response of pancreatic β-cells: experimental and theoretical results, in Transduction in Biological Systems, eds., C. Hidalgo, J. Bacigalupo, E. Jaimovich, and J. Vergara, pp. 123-141, Plenum Publishing Co, 1990.
    • (1990) Transduction in Biological Systems , pp. 123-141
    • Sherman, A.1    Carroll, P.2    Santos, R.M.3    Atwater, I.4
  • 22
    • 0026587453 scopus 로고
    • 2+ currents and bursting mechanisms for the mouse pancreatic beta-cell
    • 2+ currents and bursting mechanisms for the mouse pancreatic beta-cell, J. Membrane Biol., 127(1992), pp. 9-19.
    • (1992) J. Membrane Biol. , vol.127 , pp. 9-19
    • Smolen, P.1    Keizer, J.2
  • 23
    • 0023791327 scopus 로고
    • Emergence of organized bursting in clusters of pancreatic β-cells by channel sharing
    • Sherman, A., Rinzel, J., and Keizer, J., Emergence of organized bursting in clusters of pancreatic β-cells by channel sharing, J. Biophys., 54(1988), pp. 411-425.
    • (1988) J. Biophys. , vol.54 , pp. 411-425
    • Sherman, A.1    Rinzel, J.2    Keizer, J.3
  • 24
    • 0026239399 scopus 로고
    • Chaotic spikes arising from a model of bursting in excitable membranes
    • Terman, D., Chaotic spikes arising from a model of bursting in excitable membranes, SIAM J. Appl. Math., 51(1991), pp. 1418-1450.
    • (1991) SIAM J. Appl. Math. , vol.51 , pp. 1418-1450
    • Terman, D.1
  • 25
    • 34249839599 scopus 로고
    • The transition from bursting to continuous spiking in excitable membrane models
    • Terman, D., The transition from bursting to continuous spiking in excitable membrane models, J. Nonlinear Science, 2(1992), pp. 135-182.
    • (1992) J. Nonlinear Science , vol.2 , pp. 135-182
    • Terman, D.1


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