Derivation of a Floquet formalism within a natural framework

Acta Biotheor. 2012 Sep;60(3):303-17. doi: 10.1007/s10441-012-9162-4. Epub 2012 Jun 29.

Abstract

Many biological systems experience a periodic environment. Floquet theory is a mathematical tool to deal with such time periodic systems. It is not often applied in biology, because linkage between the mathematics and the biology is not available. To create this linkage, we derive the Floquet theory for natural systems. We construct a framework, where the rotation of the Earth is causing the periodicity. Within this framework the angular momentum operator is introduced to describe the Earth's rotation. The Fourier operators and the Fourier states are defined to link the rotation to the biological system. Using these operators, the biological system can be transformed into a rotating frame in which the environment becomes static. In this rotating frame the Floquet solution can be derived. Two examples demonstrate how to apply this natural framework.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Animals
  • Circadian Rhythm
  • Communicable Diseases / epidemiology
  • Communicable Diseases / transmission
  • Disease Vectors
  • Fourier Analysis
  • Humans
  • Linear Models
  • Mathematical Concepts
  • Models, Biological*
  • Periodicity*
  • Population Dynamics
  • Seasons