DOI: 10.1126/science.267326. Oscillation and Chaos in Physiological Control Systems

Oscillation and Chaos in Physiological Control Systems

10.1126/science.267326

Crossref journal-article

American Association for the Advancement of Science (AAAS)

Science (221)

Abstract

First-order nonlinear differential-delay equations describing physiological control systems are studied. The equations display a broad diversity of dynamical behavior including limit cycle oscillations, with a variety of wave forms, and apparently aperiodic or "chaotic" solutions. These results are discussed in relation to dynamical respiratory and hematopoietic diseases.

Bibliography

Mackey, M. C., & Glass, L. (1977). Oscillation and Chaos in Physiological Control Systems. Science, 197(4300), 287â289.

Authors 2

Michael C. Mackey (first)
Leon Glass (additional)

References 45 Referenced 3,274

BARCROFT, J, JOURNAL OF PHYSIOLOGY-LONDON 72: 175 (1931). (10.1113/jphysiol.1931.sp002769) / JOURNAL OF PHYSIOLOGY-LONDON (1931)
BROWN, H.W., NEUROLOGIC BASIS OF CHEYNE-STOKES RESPIRATION, AMERICAN JOURNAL OF MEDICINE 30: 849 (1961). (10.1016/0002-9343(61)90173-5) / AMERICAN JOURNAL OF MEDICINE (1961)
CHERNIACK, N.S., CHEYNE-STOKES BREATHING - INSTABILITY IN PHYSIOLOGIC CONTROL, NEW ENGLAND JOURNAL OF MEDICINE 288: 952 (1973). (10.1056/NEJM197305032881810) / NEW ENGLAND JOURNAL OF MEDICINE (1973)
CHIKKAPPA, G, PERIODIC OSCILLATION OF BLOOD LEUKOCYTES, PLATELETS, AND RETICULOCYTES IN A PATIENT WITH CHRONIC MYELOCYTIC-LEUKEMIA, BLOOD 47: 1023 (1976). (10.1182/blood.V47.6.1023.1023) / BLOOD (1976)
CRONINSCANLON, J, MATHEMATICAL-MODEL FOR CATATONIC SCHIZOPHRENIA, ANNALS OF THE NEW YORK ACADEMY OF SCIENCES 231: 112 (1974). (10.1111/j.1749-6632.1974.tb20561.x) / ANNALS OF THE NEW YORK ACADEMY OF SCIENCES (1974)
DALE, D.C., APPLICATION OF TIME SERIES ANALYSIS TO SERIAL BLOOD NEUTROPHIL COUNTS IN NORMAL INDIVIDUALS AND PATIENTS RECEIVING CYCLOPHOSPHAMIDE, BRITISH JOURNAL OF HAEMATOLOGY 24: 57 (1973). (10.1111/j.1365-2141.1973.tb05727.x) / BRITISH JOURNAL OF HAEMATOLOGY (1973)
GATTI, R.A., CYCLIC LEUKOCYTOSIS IN CHRONIC MYELOGENOUS LEUKEMIA - NEW PERSPECTIVES ON PATHOGENESIS AND THERAPY, BLOOD 41: 771 (1973). (10.1182/blood.V41.6.771.771) / BLOOD (1973)
GUERRY, D, HUMAN CYCLIC NEUTROPENIA - URINARY COLONY-STIMULATING FACTOR AND ERYTHROPOIETIN LEVELS, BLOOD 44: 257 (1974). (10.1182/blood.V44.2.257.257) / BLOOD (1974)
GUERRY, D, PERIODIC HEMATOPOIESIS IN HUMAN CYCLIC NEUTROPENIA, JOURNAL OF CLINICAL INVESTIGATION 52: 3220 (1973). (10.1172/JCI107522) / JOURNAL OF CLINICAL INVESTIGATION (1973)
GUYTON, A.C., BASIC OSCILLATING MECHANISM OF CHEYNE-STOKES BREATHING, AMERICAN JOURNAL OF PHYSIOLOGY 187: 395 (1956). (10.1152/ajplegacy.1956.187.2.395) / AMERICAN JOURNAL OF PHYSIOLOGY (1956)
HAYES, N.D., J LOND MATH SOC 25: 226 (1950). / J LOND MATH SOC (1950)
Kellog, R. H., Handbook of Physiology 1: 507 (1964). / Handbook of Physiology (1964)
KINGSMITH, E.A., BLOOD-THE JOURNAL OF HEMATOLOGY 36: 254 (1970). / BLOOD-THE JOURNAL OF HEMATOLOGY (1970)
KIRK, J, A MATHEMATICAL ANALYSIS OF RED BLOOD CELL AND BONE MARROW STEM CELL CONTROL MECHANISMS, BRITISH JOURNAL OF HAEMATOLOGY 15: 35 (1968). (10.1111/j.1365-2141.1968.tb01510.x) / BRITISH JOURNAL OF HAEMATOLOGY (1968)
KOLATA, G.B., CASCADING BIFURCATIONS - MATHEMATICS OF CHAOS, SCIENCE 189: 984 (1975). (10.1126/science.189.4207.984) / SCIENCE (1975)
Lambertsen, C. J., Handbook of Medical Physiology: 1522 (1974). / Handbook of Medical Physiology (1974)
LANGE, R.L., MECHANISM OF CHEYNE-STOKES RESPIRATION, JOURNAL OF CLINICAL INVESTIGATION 41: 42 (1962). (10.1172/JCI104465) / JOURNAL OF CLINICAL INVESTIGATION (1962)
LI, T.Y., PERIOD 3 IMPLIES CHAOS, AMERICAN MATHEMATICAL MONTHLY 82: 985 (1975). (10.1080/00029890.1975.11994008) / AMERICAN MATHEMATICAL MONTHLY (1975)
LONGOBARDO, G.S., CHEYNE-STOKES BREATHING PRODUCED BY A MODEL OF HUMAN RESPIRATORY SYSTEM, JOURNAL OF APPLIED PHYSIOLOGY 21: 1839 (1966). (10.1152/jappl.1966.21.6.1839) / JOURNAL OF APPLIED PHYSIOLOGY (1966)
Mackey M. C. in preparation.
MAY, R.M., BIFURCATIONS AND DYNAMIC COMPLEXITY IN SIMPLE ECOLOGICAL MODELS, AMERICAN NATURALIST 110: 573 (1976). (10.1086/283092) / AMERICAN NATURALIST (1976)
MAY, R.M., SIMPLE MATHEMATICAL-MODELS WITH VERY COMPLICATED DYNAMICS, NATURE 261: 459 (1976). (10.1038/261459a0) / NATURE (1976)
10.1126/science.186.4164.645
Metcalf, D., Haemopoietic Cells: 362 (1971). / Haemopoietic Cells (1971)
MILHORN, H.T., A MATHEMATICAL MODEL OF HUMAN RESPIRATORY CONTROL SYSTEM, BIOPHYSICAL JOURNAL 5: 27 (1965). (10.1016/S0006-3495(65)86701-7) / BIOPHYSICAL JOURNAL (1965)
MILHORN, H.T., AN ANALOG COMPUTER ANALYSIS OF CHEYNE-STOKES BREATHING, JOURNAL OF APPLIED PHYSICS 20: 328 (1965). / JOURNAL OF APPLIED PHYSICS (1965)
MORLEY, A, AUSTRALASIAN ANNALS OF MEDICINE 19: 244 (1970). (10.1111/imj.1970.19.3.244) / AUSTRALASIAN ANNALS OF MEDICINE (1970)
MORLEY, A.A., CYCLIC LEUCOCYTOSIS AS EVIDENCE FOR RETENTION OF NORMAL HOMOEOSTATIC CONTROL IN CHRONIC GRANULOCYTIC LEUKAEMIA, LANCET 2: 1320 (1967). / LANCET (1967)
PAGE, A.R., STUDIES ON CYCLIC NEUTROPENIA - A CLINICAL AND EXPERIMENTAL INVESTIGATION, AMA JOURNAL OF DISEASES OF CHILDREN 94: 623 (1957). (10.1001/archpedi.1957.04030070035006) / AMA JOURNAL OF DISEASES OF CHILDREN (1957)
READ, DJC, BLOOD-BRAIN TISSUE PCO2 RELATIONSHIPS AND VENTILATION DURING REBREATHING, JOURNAL OF APPLIED PHYSIOLOGY 23: 53 (1967). (10.1152/jappl.1967.23.1.53) / JOURNAL OF APPLIED PHYSIOLOGY (1967)
REEVE, J, ANALOG MODEL OF GRANULOPOIESIS FOR ANALYSIS OF ISOTOPIC AND OTHER DATA OBTAINED IN NON-STEADY STATE, BRITISH JOURNAL OF HAEMATOLOGY 25: 15 (1973). (10.1111/j.1365-2141.1973.tb01712.x) / BRITISH JOURNAL OF HAEMATOLOGY (1973)
ROBINSON, W.A., KINETICS AND REGULATION OF GRANULOPOIESIS, SEMINARS IN HEMATOLOGY 12: 7 (1975). / SEMINARS IN HEMATOLOGY (1975)
RODRIGUEZ, A.R., MARKED CYCLIC LEUKOCYTOSIS LEUKOPENIA IN CHRONIC MYELOGENOUS LEUKEMIA, AMERICAN JOURNAL OF MEDICINE 60: 1041 (1976). (10.1016/0002-9343(76)90578-7) / AMERICAN JOURNAL OF MEDICINE (1976)
RUBINOW, S.I., MATHEMATICAL-MODEL OF NEUTROPHIL PRODUCTION AND CONTROL IN NORMAL MAN, JOURNAL OF MATHEMATICAL BIOLOGY 1: 187 (1975). (10.1007/BF01273744) / JOURNAL OF MATHEMATICAL BIOLOGY (1975)
SHADDUCK, R.K., CYCLIC LEUKEMIC CELL PRODUCTION IN CML, CANCER 29: 399 (1972). (10.1002/1097-0142(197202)29:2<399::AID-CNCR2820290221>3.0.CO;2-N) / CANCER (1972)
SPECT, H, INCIDENCE OF PERIODIC BREATHING IN 2000 SUBJECTS WITHOUT PULMONARY OR NEUROLOGICAL DISEASE, BULLETIN DE PHYSIO-PATHOLOGIE RESPIRATOIRE 8: 1075 (1972). / BULLETIN DE PHYSIO-PATHOLOGIE RESPIRATOIRE (1972)
Steinschneider, A., SIDS: 1974 Proceedings of the Francis E. Camps International Symposium on Sudden and Unexpected Deaths in Infancy: 177 (1974). / SIDS: 1974 Proceedings of the Francis E. Camps International Symposium on Sudden and Unexpected Deaths in Infancy (1974)
Stohlman, F., Platelets: Production, Function, Transfusion and Storage: 1 (1973). / Platelets: Production, Function, Transfusion and Storage (1973)
Vincent, P. C., Leukemia: 189 (1974). / Leukemia (1974)
VODOPICK, H, SPONTANEOUS CYCLIC LEUKOCYTOSIS AND THROMBOCYTOSIS IN CHRONIC GRANULOCYTIC LEUKEMIA, NEW ENGLAND JOURNAL OF MEDICINE 286: 284 (1972). (10.1056/NEJM197202102860603) / NEW ENGLAND JOURNAL OF MEDICINE (1972)
West, J. B., Respiratory Physiology: The EssentialS: 120 (1974). / Respiratory Physiology: The EssentialS (1974)
WEWERKA, J.R., COLONY-STIMULATING FACTOR IN PATIENTS WITH CHRONIC NEUTROPENIA, BLOOD 47: 861 (1976). (10.1182/blood.V47.5.861.861) / BLOOD (1976)
WHELDON, T.E., CYCLICAL GRANULOPOIESIS IN CHRONIC GRANULOCYTIC LEUKEMIA - SIMULATION STUDY, BLOOD 43: 379 (1974). (10.1182/blood.V43.3.379.379) / BLOOD (1974)
Wintrobe M. M. Clinical Hematology (1976).
WYMAN, J, ALLOSTERIC EFFECTS IN HEMOGLOBIN, COLD SPRING HARBOR SYMPOSIA ON QUANTITATIVE BIOLOGY 28: 483 (1963). (10.1101/SQB.1963.028.01.064) / COLD SPRING HARBOR SYMPOSIA ON QUANTITATIVE BIOLOGY (1963)

Dates

Type	When
Created	18 years, 10 months ago (Oct. 5, 2006, 12:03 p.m.)
Deposited	1 year, 7 months ago (Jan. 12, 2024, 5:10 p.m.)
Indexed	18 minutes ago (Aug. 25, 2025, 11:26 p.m.)
Issued	48 years, 1 month ago (July 15, 1977)
Published	48 years, 1 month ago (July 15, 1977)
Published Print	48 years, 1 month ago (July 15, 1977)

Funders 0

None

BibTeX

@article{Mackey_1977, title={Oscillation and Chaos in Physiological Control Systems}, volume={197}, ISSN={1095-9203}, url={http://dx.doi.org/10.1126/science.267326}, DOI={10.1126/science.267326}, number={4300}, journal={Science}, publisher={American Association for the Advancement of Science (AAAS)}, author={Mackey, Michael C. and Glass, Leon}, year={1977}, month=jul, pages={287–289} }

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