-
1
-
-
51249165655
-
Über die unvollständige störung der erregungsüberleitung zwischen Vorhof und Kammer des menschlichen Herzens
-
Mobitz, W., Über die unvollständige Störung der Erregungsüberleitung zwischen Vorhof und Kammer des menschlichen Herzens. Z. Gesamte Exp. Med, 1924, 41, 180-237.
-
(1924)
Z. Gesamte Exp. Med
, vol.41
, pp. 180-237
-
-
Mobitz, W.1
-
2
-
-
0000401026
-
The heartbeat considered as a relaxation oscillation and an electrical model of the heart
-
Van der Pol, B., van der Mark, J., The heartbeat considered as a relaxation oscillation and an electrical model of the heart. Phil. Mag. Suppl, 1928, 6, 763-775.
-
(1928)
Phil. Mag. Suppl
, vol.6
, pp. 763-775
-
-
Van Der Pol, B.1
Van Der Mark, J.2
-
3
-
-
84956515648
-
The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle
-
Wiener, N., Rosenblueth, A., The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle. Arch. Inst. Cardiol. Mex, 1946, 16, 205-265.
-
(1946)
Arch. Inst. Cardiol. Mex
, vol.16
, pp. 205-265
-
-
Wiener, N.1
Rosenblueth, A.2
-
4
-
-
35649001607
-
A quantitative description of membrane current and its application to conduction and excitation in nerve
-
Hodgkin, A. L., Huxley, A. F., A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol, 1952, 117, 500-544.
-
(1952)
J. Physiol
, vol.117
, pp. 500-544
-
-
Hodgkin, A.L.1
Huxley, A.F.2
-
5
-
-
0020471747
-
Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: A theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias
-
Guevara, M. R., Glass, L., Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: A theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias. J. Math. Biology, 1982, 14, 1-23.
-
(1982)
J. Math. Biology
, vol.14
, pp. 1-23
-
-
Guevara, M.R.1
Glass, L.2
-
6
-
-
0003102997
-
Periodic forcing of a limit-cycle oscillator: Fixed points, arnold tongues, and the global organization of bifurcations
-
Glass, L., Sun, J., Periodic forcing of a limit-cycle oscillator: Fixed points, Arnold tongues, and the global organization of bifurcations. Phys. Rev. E, 1994, 50, 5077-5084.
-
(1994)
Phys. Rev. E
, vol.50
, pp. 5077-5084
-
-
Glass, L.1
Sun, J.2
-
7
-
-
0023648366
-
Nonlinear dynamics, chaos and complex cardiac arrhythmias
-
Glass, L., Goldberger, A. L., Courtemanche, M., Shrier, A., Nonlinear dynamics, chaos and complex cardiac arrhythmias. Proc. R. Soc. Lond. A, 1987, 413, 9-26.
-
(1987)
Proc. R. Soc. Lond. A
, vol.413
, pp. 9-26
-
-
Glass, L.1
Goldberger, A.L.2
Courtemanche, M.3
Shrier, A.4
-
8
-
-
0021636588
-
Periodic and non-periodic responses of a periodically forced hodgkin-huxley oscillator
-
Aihara, K., Matsumoto, G., Ikegaya, Y., Periodic and non-periodic responses of a periodically forced Hodgkin-Huxley oscillator. J. Theor. Biol, 1984, 109, 249-269.
-
(1984)
J. Theor. Biol
, vol.109
, pp. 249-269
-
-
Aihara, K.1
Matsumoto, G.2
Ikegaya, Y.3
-
9
-
-
0001072892
-
An alternating periodic-chaotic sequence observed in neural oscillators
-
Aihara, K., Matsumoto, G., Ichikawa, M., An alternating periodic-chaotic sequence observed in neural oscillators. Phys. Lett, 1985, 111A, 251-255.
-
(1985)
Phys. Lett
, vol.111 A
, pp. 251-255
-
-
Aihara, K.1
Matsumoto, G.2
Ichikawa, M.3
-
10
-
-
0001030166
-
Structures of attractors in periodically forced neural oscillators
-
Aihara, K., Numajiri, T., Matsumoto, G., Kotani, M., Structures of attractors in periodically forced neural oscillators. Phys. Lett. A, 1986, 116, 313-317.
-
(1986)
Phys. Lett. A
, vol.116
, pp. 313-317
-
-
Aihara, K.1
Numajiri, T.2
Matsumoto, G.3
Kotani, M.4
-
11
-
-
21344483041
-
Bifurcation structure of the driven van der Pol oscillator
-
Mettin, R., Parlitz, U., Lauterborn, W., Bifurcation structure of the driven van der Pol oscillator. Int. J. Bifurcation and Chaos, 1993, 3, 1529-1555.
-
(1993)
Int. J. Bifurcation and Chaos
, vol.3
, pp. 1529-1555
-
-
Mettin, R.1
Parlitz, U.2
Lauterborn, W.3
-
12
-
-
46549091341
-
Nonlinear dynamics of the heartbeat
-
West, B. J., Goldberger, A. L., Rovner, G., Bhargava, V., Nonlinear dynamics of the heartbeat. Physica D, 1985, 17, 198-206.
-
(1985)
Physica D
, vol.17
, pp. 198-206
-
-
West, B.J.1
Goldberger, A.L.2
Rovner, G.3
Bhargava, V.4
-
13
-
-
0027749064
-
A bonhoeffer-van der Pol oscillator model of locked and non-locked behaviors of living pacemaker neurons
-
Nomura, T., Sato, S., Doi, S., Segundo, J. P., Stiber, M. D., A Bonhoeffer-van der Pol oscillator model of locked and non-locked behaviors of living pacemaker neurons. Biol. Cybern, 1993, 69, 429-437.
-
(1993)
Biol. Cybern
, vol.69
, pp. 429-437
-
-
Nomura, T.1
Sato, S.2
Doi, S.3
Segundo, J.P.4
Stiber, M.D.5
-
14
-
-
43949175578
-
Critical dynamics of the bonhoeffer-van der Pol equation and its chaotic response to periodic stimulation
-
Braaksma, B., Grasman, J., Critical dynamics of the Bonhoeffer-van der Pol equation and its chaotic response to periodic stimulation. Physica D, 1993, 68, 265-280.
-
(1993)
Physica D
, vol.68
, pp. 265-280
-
-
Braaksma, B.1
Grasman, J.2
-
15
-
-
0000328776
-
Dynamics underlying the patterning of cardiac dysrhythmias
-
Wang, H.-X., de Paola, R., Norwood, W. I., Dynamics underlying the patterning of cardiac dysrhythmias. Phys. Rev. Lett, 1993, 70, 3671-3674.
-
(1993)
Phys. Rev. Lett
, vol.70
, pp. 3671-3674
-
-
Wang, H.-X.1
De Paola, R.2
Norwood, W.I.3
-
16
-
-
0001823870
-
Cardiac arrhythmias and circle maps-A classical problem
-
Glass, L., Cardiac arrhythmias and circle maps-A classical problem. Chaos, 1991, 1, 13-19.
-
(1991)
Chaos
, vol.1
, pp. 13-19
-
-
Glass, L.1
-
17
-
-
0001690795
-
Chaos and phase locking in normal squid axons
-
Matsumoto, G., Aihara, K., Hanyu, Y., Takahashi, N., Yoshizawa, S., Nagumo, J., Chaos and phase locking in normal squid axons. Phys. Lett. A, 1987, 123, 162-166.
-
(1987)
Phys. Lett. A
, vol.123
, pp. 162-166
-
-
Matsumoto, G.1
Aihara, K.2
Hanyu, Y.3
Takahashi, N.4
Yoshizawa, S.5
Nagumo, J.6
-
18
-
-
0001343004
-
Global bifurcation structure in periodically stimulated giant axons of squid
-
Takahashi, N., Hanyu, Y., Musha, T., Kubo, R., Matsumoto, G., Global bifurcation structure in periodically stimulated giant axons of squid. Physica D, 1990, 43, 318-334.
-
(1990)
Physica D
, vol.43
, pp. 318-334
-
-
Takahashi, N.1
Hanyu, Y.2
Musha, T.3
Kubo, R.4
Matsumoto, G.5
-
19
-
-
0021642311
-
Electrical alternans and period doubling bifurcations
-
IEEE Computer Society, Silver Spring
-
Guevara, M. R., Ward, G., Shrier, A. and Glass, L., Electrical alternans and period doubling bifurcations. In Computers in Cardiology. IEEE Computer Society, Silver Spring, 1984, pp. 167-170.
-
(1984)
Computers in Cardiology
, pp. 167-170
-
-
Guevara, M.R.1
Ward, G.2
Shrier, A.3
Glass, L.4
-
20
-
-
0023546965
-
Non-linear dynamics of cardiac excitation and impulse propagation
-
Chialvo, D. R., Jalife, J., Non-linear dynamics of cardiac excitation and impulse propagation. Nature, 1987, 330, 749-752.
-
(1987)
Nature
, vol.330
, pp. 749-752
-
-
Chialvo, D.R.1
Jalife, J.2
-
21
-
-
0025178623
-
Low dimensional chaos in cardiac tissue
-
Chialvo, D. R., Gilmour, R. F. Jr., Jalife, J., Low dimensional chaos in cardiac tissue. Nature, 1990, 343, 653-657.
-
(1990)
Nature
, vol.343
, pp. 653-657
-
-
Chialvo, D.R.1
Gilmour R.F., Jr.2
Jalife, J.3
-
22
-
-
0027054459
-
Response characteristics of the BVP neuron model to periodic pulse inputs
-
Sato, S., Doi, S., Response characteristics of the BVP neuron model to periodic pulse inputs. Math. Biosci, 1992, 112, 243-259.
-
(1992)
Math. Biosci
, vol.112
, pp. 243-259
-
-
Sato, S.1
Doi, S.2
-
23
-
-
0028804589
-
The global bifurcation structure of the BVP neuronal model driven by periodic pulse trains
-
Doi, S., Sato, S., The global bifurcation structure of the BVP neuronal model driven by periodic pulse trains. Math. Biosci, 1995, 125, 229-250.
-
(1995)
Math. Biosci
, vol.125
, pp. 229-250
-
-
Doi, S.1
Sato, S.2
-
24
-
-
0002748706
-
Studies with artificial neurons, I: Properties and functions of an artificial neuron
-
Harmon, L. D., Studies with artificial neurons, I: Properties and functions of an artificial neuron. Kybernetik, 1961, 1, 89-101.
-
(1961)
Kybernetik
, vol.1
, pp. 89-101
-
-
Harmon, L.D.1
-
25
-
-
0015307115
-
On a response characteristic of a mathematical neuron model
-
Nagumo, J., Sato, S., On a response characteristic of a mathematical neuron model. Kybernetik, 1972, 10, 155-164.
-
(1972)
Kybernetik
, vol.10
, pp. 155-164
-
-
Nagumo, J.1
Sato, S.2
-
26
-
-
58149319863
-
Nonlinear phenomena in excitable physiological systems (special issue)
-
March/April
-
Holden, A. V. and El Naschie, M. S., (editors), Nonlinear phenomena in excitable physiological systems (special issue), Chaos, Solitons & Fractals, 5(3/4), March/April 1995.
-
(1995)
Chaos, Solitons & Fractals
, vol.5
, Issue.3-4
-
-
Holden, A.V.1
El Naschie, M.S.2
-
27
-
-
0017714604
-
Oscillation and chaos in physiological control systems
-
Mackey, M. C., Glass, L., Oscillation and chaos in physiological control systems. Science, 1977, 197, 287-289.
-
(1977)
Science
, vol.197
, pp. 287-289
-
-
Mackey, M.C.1
Glass, L.2
-
28
-
-
0022507709
-
The evolution of nonlinear waves in active media
-
Engelbrecht, J., The evolution of nonlinear waves in active media. Wave Motion, 1986, 8, 93-100.
-
(1986)
Wave Motion
, vol.8
, pp. 93-100
-
-
Engelbrecht, J.1
-
29
-
-
0011852207
-
On a model stationary nonlinear wave in an active medium
-
Engelbrecht, J., Tobias, T., On a model stationary nonlinear wave in an active medium. Proc. R. Soc. Lond, 1987, A411, 139-154.
-
(1987)
Proc. R. Soc. Lond
, vol.A411
, pp. 139-154
-
-
Engelbrecht, J.1
Tobias, T.2
-
30
-
-
53349102813
-
Impulses and physiological states in theoretical models of nerve membrane
-
FitzHugh, R., Impulses and physiological states in theoretical models of nerve membrane. Biophys. J, 1961, 1, 445-466.
-
(1961)
Biophys. J
, vol.1
, pp. 445-466
-
-
FitzHugh, R.1
-
31
-
-
6344238035
-
An active pulse transmission line simulating nerve axon
-
Nagumo, J., Arimoto, S., Yoshizawa, S., An active pulse transmission line simulating nerve axon. Proc. IRE, 1962, 50, 2061-2070.
-
(1962)
Proc. IRE
, vol.50
, pp. 2061-2070
-
-
Nagumo, J.1
Arimoto, S.2
Yoshizawa, S.3
-
32
-
-
0003123253
-
On the Hodgkin-Huxley partial differential equation
-
Lieberstein, H. M., On the Hodgkin-Huxley partial differential equation. Math. Biosci, 1967, 1, 45-69.
-
(1967)
Math. Biosci
, vol.1
, pp. 45-69
-
-
Lieberstein, H.M.1
-
33
-
-
0017620779
-
A mathematical model of automaticity in the sinus node and AV junction based on weakly coupled relaxation oscillators
-
Katholi, C. R., Urthaler, F., Macy, J. Jr., James, T. N., A mathematical model of automaticity in the sinus node and AV junction based on weakly coupled relaxation oscillators. Comp. Biomed. Res, 1977, 10, 529-543.
-
(1977)
Comp. Biomed. Res
, vol.10
, pp. 529-543
-
-
Katholi, C.R.1
Urthaler, F.2
Macy J., Jr.3
James, T.N.4
-
34
-
-
46549096085
-
Nonlinear dynamics of the heartbeat
-
Goldberger, A. L., Bhargava, V., West, B. J., Mandell, A. J., Nonlinear dynamics of the heartbeat. Physica D, 1985, 17, 207-214.
-
(1985)
Physica D
, vol.17
, pp. 207-214
-
-
Goldberger, A.L.1
Bhargava, V.2
West, B.J.3
Mandell, A.J.4
-
35
-
-
85033968659
-
Driven nonlinear oscillators for modeling cardiac phenomena
-
Cornell University, USA, to be published
-
Engelbrecht, J., von Hertzen, R. and Kongas, O., Driven nonlinear oscillators for modeling cardiac phenomena. Paper presented at Proc. IUTAM Symp. Chaos '97, Applications of Nonlinear and Chaotic Dynamics in Mechanics. Cornell University, USA, to be published.
-
Proc. IUTAM Symp. Chaos '97, Applications of Nonlinear and Chaotic Dynamics in Mechanics
-
-
Engelbrecht, J.1
Von Hertzen, R.2
Kongas, O.3
-
36
-
-
11744254346
-
Period-doubling cascades and devil's staircases of the driven van der Pol oscillator
-
Parlitz, U., Lauterborn, W., Period-doubling cascades and devil's staircases of the driven van der Pol oscillator. Phys. Rev. A, 1987, 36, 1428-1434.
-
(1987)
Phys. Rev. A
, vol.36
, pp. 1428-1434
-
-
Parlitz, U.1
Lauterborn, W.2
-
37
-
-
0001437760
-
Universal criterion for the breakup of invariant tori in dissipative systems
-
Ketoja, J. A., Universal criterion for the breakup of invariant tori in dissipative systems. Phys. Rev. Lett, 1992, 69, 2180-2183.
-
(1992)
Phys. Rev. Lett
, vol.69
, pp. 2180-2183
-
-
Ketoja, J.A.1
-
39
-
-
0001634226
-
Fine structure of phase locking
-
Glass, L., Perez, R., Fine structure of phase locking. Phys. Rev. Lett, 1982, 48, 1772-1775.
-
(1982)
Phys. Rev. Lett
, vol.48
, pp. 1772-1775
-
-
Glass, L.1
Perez, R.2
-
40
-
-
0003216805
-
Theory and applications of hopf bifurcation
-
Cambridge Univ. Press, Cambridge
-
Hassard, B. D., Kazarinoff, N. D. and Wan, Y.-H., Theory and Applications of Hopf Bifurcation. London Math. Soc. Lecture Note Series No. 41. Cambridge Univ. Press, Cambridge, 1981.
-
(1981)
London Math. Soc. Lecture Note Series No. 41
, vol.41
-
-
Hassard, B.D.1
Kazarinoff, N.D.2
Wan, Y.-H.3
-
41
-
-
0007668640
-
Universality of the topology of period doubling dynamical systems
-
Beiersdorfer, P., Universality of the topology of period doubling dynamical systems. Phys. Lett. A, 1984, 100, 379-382.
-
(1984)
Phys. Lett. A
, vol.100
, pp. 379-382
-
-
Beiersdorfer, P.1
-
42
-
-
0025151760
-
Chaotic dynamics in an ionic model of the propagated cardiac action potential
-
Lewis, T. J., Guevara, M. R., Chaotic dynamics in an ionic model of the propagated cardiac action potential. J. Theor. Biol, 1990, 146, 407-432.
-
(1990)
J. Theor. Biol
, vol.146
, pp. 407-432
-
-
Lewis, T.J.1
Guevara, M.R.2
-
43
-
-
0040107244
-
Dynamic equilibria and oscillations of a periodically stimulated excitable system
-
Brown, D., Foweraker, J. P. A., Marrs, R. W., Dynamic equilibria and oscillations of a periodically stimulated excitable system. Chaos, Solitons & Fractals, 1995, 5, 359-369.
-
(1995)
Chaos, Solitons & Fractals
, vol.5
, pp. 359-369
-
-
Brown, D.1
Foweraker, J.P.A.2
Marrs, R.W.3
-
44
-
-
0008410371
-
Periodic behaviour in automatic and non-automatic cardiac cells
-
Landau, M., Lorente, P., Periodic behaviour in automatic and non-automatic cardiac cells. Chaos, Solitons & Fractals, 1995, 5, 347-357.
-
(1995)
Chaos, Solitons & Fractals
, vol.5
, pp. 347-357
-
-
Landau, M.1
Lorente, P.2
-
45
-
-
0002505274
-
Chaotic and complex cardiac rhythms
-
ed. D. P. Zipes and J. Jalife. Saunders, Philadelphia
-
Guevara, M. R., Shrier, A. and Glass, L., Chaotic and complex cardiac rhythms. In Cardiac Electrophysiology: From Cell to Bedside, ed. D. P. Zipes and J. Jalife. Saunders, Philadelphia, 1990.
-
(1990)
Cardiac Electrophysiology: From Cell to Bedside
-
-
Guevara, M.R.1
Shrier, A.2
Glass, L.3
-
46
-
-
0002785574
-
Alternans in isolated ventricular myocytes
-
ed. A. Goldbeter. Academic Press, London
-
Guevara, M. R., Alonso, F., Jeandupeux, D. and van Ginneken, A. C. G., Alternans in isolated ventricular myocytes. In Cell to Cell Signalling: From Experiments to Theoretical Models, ed. A. Goldbeter. Academic Press, London, 1989, pp. 551-563.
-
(1989)
Cell to Cell Signalling: From Experiments to Theoretical Models
, pp. 551-563
-
-
Guevara, M.R.1
Alonso, F.2
Jeandupeux, D.3
Van Ginneken, A.C.G.4
-
47
-
-
0024787753
-
Regular and chaotic behaviour of cardiac cells stimulated at frequencies between 2 and 20 Hz
-
Hescheler, J., Speicher, R., Regular and chaotic behaviour of cardiac cells stimulated at frequencies between 2 and 20 Hz. Eur. Biophys. J, 1989, 17, 273-280.
-
(1989)
Eur. Biophys. J
, vol.17
, pp. 273-280
-
-
Hescheler, J.1
Speicher, R.2
-
48
-
-
0038923173
-
Chaos, phase locking and bifurcation in normal squid axons
-
ed. H. Degn, A. V. Holden and L. F. Olsen. Plenum, New York
-
Matsumoto, G., Takahashi, N. and Hanyu, Y., Chaos, phase locking and bifurcation in normal squid axons. In Chaos in Biological Systems, ed. H. Degn, A. V. Holden and L. F. Olsen. Plenum, New York, 1987, pp. 143-156.
-
(1987)
Chaos in Biological Systems
, pp. 143-156
-
-
Matsumoto, G.1
Takahashi, N.2
Hanyu, Y.3
-
49
-
-
0025224937
-
Irregular dynamics of excitation in biologic and mathematical models of cardiac cells
-
Vinet, A., Chialvo, D. R., Jalife, J., Irregular dynamics of excitation in biologic and mathematical models of cardiac cells. Ann. N.Y. Acad. Sci, 1990, 601, 281-298.
-
(1990)
Ann. N.Y. Acad. Sci
, vol.601
, pp. 281-298
-
-
Vinet, A.1
Chialvo, D.R.2
Jalife, J.3
-
50
-
-
0004069891
-
-
Springer-Verlag, New York
-
Glass, L., Hunter, P. J. and McCulloch, A., (editors), Theory of Heart: Biomechanics, Biophysics, and Nonlinear Dynamics of Cardiac Function. Springer-Verlag, New York, 1991.
-
(1991)
Theory of Heart: Biomechanics, Biophysics, and Nonlinear Dynamics of Cardiac Function
-
-
Glass, L.1
Hunter, P.J.2
McCulloch, A.3
-
51
-
-
0000272844
-
Transition to chaos by interaction of resonances in dissipative systems. I. Circle maps
-
Jensen, M. H., Bak, P., Bohr, T., Transition to chaos by interaction of resonances in dissipative systems. I. Circle maps. Phys. Rev. A, 1984, 30, 1960-1969.
-
(1984)
Phys. Rev. A
, vol.30
, pp. 1960-1969
-
-
Jensen, M.H.1
Bak, P.2
Bohr, T.3
|