The DOI matches its Crossref record; 34 of the 34 references it cites were found in a registry or an index.
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
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Hodgkin, A. L., & Huxley, A. F. (1952) · The Journal of Physiology · doi:10.1113/jphysiol.1952.sp004764 · Cited by 23,191
Simple mathematical models with very complicated dynamics
May, R. M. (1976) · Nature · doi:10.1038/261459a0 · Cited by 7,001
The Geometry of Biological Time
Winfree, A. T. (1980) · doi:10.1007/978-3-662-22492-2 · Cited by 3,613
Li, T.-Y., & Yorke, J. A. (2004) · The Theory of Chaotic Attractors · doi:10.1007/978-0-387-21830-4_6 · Cited by 2,577
Li, T.-Y., & Yorke, J. A. (1975) · The American Mathematical Monthly · doi:10.1080/00029890.1975.11994008 · Cited by 1,588
Dynamics of Encoding in a Population of Neurons
Knight, B. W. (1972) · The Journal of General Physiology · doi:10.1085/jgp.59.6.734 · Cited by 709
Ordinary Differential Equations.
Brauer, F., Arnol'd, V. I., & Cook, R. (1993) · The American Mathematical Monthly · doi:10.2307/2324802 · Cited by 645
On finite limit sets for transformations on the unit interval
Metropolis, N., Stein, M. L., & Stein, P. R. (1973) · Journal of Combinatorial Theory, Series A · doi:10.1016/0097-3165(73)90033-2 · Cited by 602
Reconstruction of the electrical activity of cardiac Purkinje fibres.
McAllister, R. E., Noble, D., & Tsien, R. W. (1975) · The Journal of Physiology · doi:10.1113/jphysiol.1975.sp011080 · Cited by 557
Guevara, M. R., Glass, L., & Shrier, A. (1981) · Science · doi:10.1126/science.7313693 · Cited by 551
Self-citationBiological Oscillators: their Mathematical Analysis
(1973) · Elsevier eBooks · doi:10.1016/b978-0-12-547350-7.x5001-9 · Cited by 445
Physiology of Membrane Disorders
(1986) · Springer eBooks · doi:10.1007/978-1-4613-2097-5 · Cited by 351
ORDINARY DIFFERENTIAL EQUATIONS
Eastham, M. S. P. (1972) · Bulletin of the London Mathematical Society · doi:10.1112/blms/4.2.245a · Cited by 325
Pacemaker Neurons: Effects of Regularly Spaced Synaptic Input
Perkel, D. H., Schulman, J. H., Bullock, T. H., Moore, G. P., & Segundo, J. P. (1964) · Science · doi:10.1126/science.145.3627.61 · Cited by 302
Cartwright, M. L., & Littlewood, J. E. (1945) · Journal of the London Mathematical Society · doi:10.1112/jlms/s1-20.3.180 · Cited by 298
Integrate-and-Fire Models of Nerve Membrane Response to Oscillatory Input
Keener, J. P., Hoppensteadt, F. C., & Rinzel, J. (1981) · SIAM Journal on Applied Mathematics · doi:10.1137/0141042 · Cited by 291
Chaotic States of Anharmonic Systems in Periodic Fields
Huberman, B. A., & Crutchfield, J. P. (1979) · Physical Review Letters · doi:10.1103/physrevlett.43.1743 · Cited by 282
The simplest case of a strange attractor
Zaslavsky, G. M. (1978) · Physics Letters A · doi:10.1016/0375-9601(78)90195-0 · Cited by 280
A Second Order Differential Equation with Singular Solutions
Levinson, N. (1949) · The Annals of Mathematics · doi:10.2307/1969357 · Cited by 268
Clinical Disorders of the Heart Beat.
(1954) · Annals of Internal Medicine · doi:10.7326/0003-4819-41-3-653_2 · Cited by 260
A Second Order Differential Equation with Singular Solutions
Levinson, N. (1998) · Selected Papers of Norman Levinson Volume 1 · doi:10.1007/978-1-4612-5341-9_12 · Cited by 197
A biologic model of parasystole
Jalife, J., & Moe, G. K. (1979) · The American Journal of Cardiology · doi:10.1016/0002-9149(79)90076-6 · Cited by 161
Clinical Disorders of the Heart Beat.
(1972) · Annals of Internal Medicine · doi:10.7326/0003-4819-76-2-345_2 · Cited by 159
(2013) · Heart Disease · doi:10.5040/9798400662577.ch-006 · Cited by 152
Phase Control of Neural Pacemakers
Winfree, A. T. (1977) · Science · doi:10.1126/science.887919 · Cited by 119
Mesure de Lebesgue et Nombre de Rotation
Herman, M. R. (1977) · Lecture notes in mathematics · doi:10.1007/bfb0085359 · Cited by 113
Physiology of Membrane Disorders.
(1979) · Annals of Internal Medicine · doi:10.7326/0003-4819-91-2-338_2 · Cited by 100
Pinsker, H. M. (1977) · Journal of Neurophysiology · doi:10.1152/jn.1977.40.3.544 · Cited by 90
On visual detection of light sources
Ullman, S. (1976) · Biological Cybernetics · doi:10.1007/bf00344165 · Cited by 77
The response of excitable membrane models to a cyclic input
Holden, A. V. (1976) · Biological Cybernetics · doi:10.1007/bf00326666 · Cited by 67
The cardiac pacemaker: Effects of regularly spaced nervous input
Reid, J. V. O. (1969) · American Heart Journal · doi:10.1016/0002-8703(69)90259-2 · Cited by 60
Synaptic control of an endogenous pacemaker network.
Ayers, J. L., & Selverston, A. I. (1977) · PubMed · Cited by 56
Trajectory divergence for coupled relaxation oscillators: Measurements and models
Gollub, J. P., Romer, E. J., & Socolar, J. E. S. (1980) · Journal of Statistical Physics · doi:10.1007/bf01011372 · Cited by 39
Winfree, A. T. (1975) · Physics Today · doi:10.1063/1.3068875 · Cited by 32
Cited by
Cross-Frequency Phase–Phase Coupling between Theta and Gamma Oscillations in the Hippocampus
Belluscio, M. A., Mizuseki, K., Schmidt, R., Kempter, R., & Buzsáki, G. (2012) · The Journal of Neuroscience · doi:10.1523/jneurosci.4122-11.2012 · Cited by 784
Buzsáki, G., & Watson, B. O. (2012) · Dialogues in Clinical Neuroscience · doi:10.31887/dcns.2012.14.4/gbuzsaki · Cited by 579
Metadata
- Authors
- Guevara, M. R., & Glass, L.
- Venue
- Journal of Mathematical Biology
- Published
- 1982-03
- Volume
- 14
- Issue
- 1
- Pages
- 1-23
- ISSN
- 0303-6812 (ISSN-L)
- 1432-1416
- OpenAlex
- W1966877875
- Cited by
- 259
- References
- 34
- FWCI
- 19.74
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
