Prediction of limit cycles in mathematical models of biological oscillations |
| |
Authors: | Leon Glass Joel S Pasternack |
| |
Institution: | (1) Department of Physiology, McGill University, Montreal, Quebec, Canada;(2) Department of Mathematics, University of Rochester, Rochester, New York, USA |
| |
Abstract: | Three conjectures are given which predict the existence of unique stable limit cycle oscillations in a class of piecewise
linear (PL) differential equations. The equations are appropriate to model biological or other complex systems in which there
are switchlike interactions between the elements of the network. Methods are presented which can be used to develop mathematical
models which are conjectured to display stable limit cycle oscillations, from qualitative experimental information about relative
phases of activity in the dynamical systems. Several illustrative numerical examples are given, and one experimental example
from neurobiology is discussed.
Presented at the Society for Mathematical Biology Meeting, University of Pennsylvania, Philadelphia, August 19–21, 1976. |
| |
Keywords: | |
本文献已被 ScienceDirect SpringerLink 等数据库收录! |
|