The Stability of Entrainment Conditions for RLC Coupled Van Der Pol Oscillators Used As a Model for Intestinal Electrical Rhythms

Overview

Journal Bull Math Biol

Publisher Springer

Specialties Biology
Public Health

Date 1977 Jan 1

PMID 857985

Citations 9

Authors

D A Linkens

Affiliations

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Mode analysis of physiological oscillators intercoupled via pure time delays.

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References

Duthie H . Electrical activity of gastrointestinal smooth muscle. Gut. 1974; 15(8):669-81. PMC: 1413018. DOI: 10.1136/gut.15.8.669. View

Nelsen T, Becker J . Simulation of the electrical and mechanical gradient of the small intestine. Am J Physiol. 1968; 214(4):749-57. DOI: 10.1152/ajplegacy.1968.214.4.749. View

Sarna S, Daniel E, Kingma Y . Simulation of slow-wave electrical activity of small intestine. Am J Physiol. 1971; 221(1):166-75. DOI: 10.1152/ajplegacy.1971.221.1.166. View

Hermon-Taylor J, Code C . Localization of the duodenal pacemaker and its role in the organization of duodenal myoelectric activity. Gut. 1971; 12(1):40-7. PMC: 1411469. DOI: 10.1136/gut.12.1.40. View

DEWEY M, Barr L . A STUDY OF THE STRUCTURE AND DISTRIBUTION OF THE NEXUS. J Cell Biol. 1964; 23:553-85. PMC: 2106539. DOI: 10.1083/jcb.23.3.553. View

Linkens D . A mathematical model of the slow-wave electrical activity of the human small intestine. Med Biol Eng. 1974; 12(6):750-8. DOI: 10.1007/BF02477440. View

WANKLING W, Brown B, Collins C, Duthie H . Basal electrical activity in the anal canal in man. Gut. 1968; 9(4):457-60. PMC: 1552711. DOI: 10.1136/gut.9.4.457. View

Sarna S, Daniel E, Kingma Y . Simulation of the electric-control activity of the stomach by an array of relaxation oscillators. Am J Dig Dis. 1972; 17(4):299-310. DOI: 10.1007/BF02231729. View

Kwong N, Brown B, Whittaker G, Duthie H . Electrical activity of the gastric antrum in man. Br J Surg. 1970; 57(12):913-6. DOI: 10.1002/bjs.1800571211. View

10.

Moore J, Ramon F . On numerical integration of the Hodgkin and Huxley equations for a membrane action potential. J Theor Biol. 1974; 45(1):249-73. DOI: 10.1016/0022-5193(74)90054-x. View

11.

Sarna S, Daniel E, Kingma Y . Premature control potentials in the dog stomach and in the gastric computer model. Am J Physiol. 1972; 222(6):1518-23. DOI: 10.1152/ajplegacy.1972.222.6.1518. View

12.

Christensen J, Caprilli R, Lund G . Electric slow waves in circular muscle of cat colon. Am J Physiol. 1969; 217(3):771-6. DOI: 10.1152/ajplegacy.1969.217.3.771. View

13.

Waterfall W, Brown B, Duthie H, Whittaker G . The effects of humoral agents on the myoelectrical activity of the terminal ileum. Gut. 1972; 13(7):528-34. PMC: 1412272. DOI: 10.1136/gut.13.7.528. View

14.

Duthie H, Brown B, Kwong N, Whittaker G, Waterfall W . Electrical activity in the gastroduodenal area--slow waves in the proximal duodenum. A comparison of man and dog. Am J Dig Dis. 1972; 17(4):344-51. DOI: 10.1007/BF02231736. View

15.

Noble D . Applications of Hodgkin-Huxley equations to excitable tissues. Physiol Rev. 1966; 46(1):1-50. DOI: 10.1152/physrev.1966.46.1.1. View

16.

Fitzhugh R . Impulses and Physiological States in Theoretical Models of Nerve Membrane. Biophys J. 2009; 1(6):445-66. PMC: 1366333. DOI: 10.1016/s0006-3495(61)86902-6. View

17.

Taylor I, Duthie H, Smallwood R, Brown B, Linkens D . The effect of stimulation on the myoelectrical activity of the rectosigmoid in man. Gut. 1974; 15(8):599-607. PMC: 1413024. DOI: 10.1136/gut.15.8.599. View

18.

Christensen J, SCHEDL H, CLIFTON J . The small intestinal basic electrical rhythm (slow wave) frequency gradient in normal men and in patients with variety of diseases. Gastroenterology. 1966; 50(3):309-15. View