A MATHEMATICAL MODEL FOR THE BIOLOGICAL CLOCK OF PASSER DOMESTICUS.
Abstract
The work presented in this report is a novel application of modeling and nonlinear differential equation theory to the life sciences. The field of circadian rhythms is briefly discussed along with the use and need for a mathematical model of biological clocks. The general properties of oscillators are discussed, and the qualitative agreement between nonlinear oscillators and circadian rhythm data is demonstrated. The case of two coupled weakly nonlinear oscillators is treated in detail with particular emphasis on coupled Rayleigh oscillators. A method for obtaining approximations for the multifrequency solutions of two unforced weakly coupled weakly nonlinear oscillators is presented. An illustrative example of coupled Rayleigh oscillators is included. The method for obtaining experimental data of activity rhythms of the house sparrow Passer domesticus is given. The specific mathematical model of a forced pair of coupled Rayleigh oscillators is then postulated. The comparisons between the model and the data are (1) the model forcing function is analogous to the light cycle to which the organisms are subjected and (2) the zero crossings of the model solution with positive slope are analogous to the onsets of the activity rhythm.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 12, 1966
- Accession Number
- AD0807995
Entities
People
- Baxter F. Womack
- Charles G. Richie
Organizations
- University of Texas at Austin