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Discrete Dynamics in Nature and Society
Volume 2 (1998), Issue 4, Pages 215-242

How and why do neurons generate complex rhythms with various frequencies?

1Department of Biological Sciences, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
2Department of Biochemistry, Hanyang University, Kyung-Gi-Do, Ansan, Korea

Received 20 May 1998

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Some neurons generate endogenous rhythms with a period of a few hundred milliseconds,while others generate rhythms with a period of a few tens of seconds. Sometimes rhythms appear chaotic. Explaining how these neurons can generate various modes of oscillation with a widely ranging frequency is a challenge. In the first part of this review, we illustrate that such rhythms can be generated from simple yet elegant mathematical models. Chaos embedded in rhythmic activity has interesting characteristics that are not seen in other physical systems. Understanding of how these neurons utilizes endogenous rhythms to communicate with each other is important in elucidating where the brain gets various rhythms and why it can pervert into abnormal rhythms under diseased conditions. Using the islet of Langerhans in pancreas as an example, in the second part of this review, we illustrate how insulin secreting β-cells communicate with glucagon secreting α-cells to achieve an optimal insulin release.