The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: a mathematical model

DOI10.1007/BF00276069zbMath0476.92003OpenAlexW2021973929WikidataQ52730062 ScholiaQ52730062MaRDI QIDQ1160088

Avis H. Cohen, Philip J. Holmes, Richard H. Rand

Publication date: 1982

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00276069

zbMATH Keywords

limit cycle oscillator intersegmental coordination of neural networks pattern generator

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) General biology and biomathematics (92B05) Dynamical systems and ergodic theory (37-XX) Physiological, cellular and medical topics (92Cxx)

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Cites Work