A mathematical model has been examined that attempts to mimic the effects of changes in environmental conditions on circadian rhythms. The basis of the model claims that for a given set of environmental conditions (e.g., light, temperature and chemical concentrations) there exists a limit cycle that has a given position. When an environmental treatment is applied that is different from the control conditions, the position of the new limit cycle changes and the oscillating parameters of the circadian system are now attracted toward this newly positioned limit cycle. If conditions are subsequently returned back to control levels, the control limit cycle again takes effect and the displaced parameters are attracted back to the postion of control limit cycle. The model provides a description of what happens as a result of a pulse of new environmental conditions as well as what happens while the new conditions are in effect. Actual results involving entrainment, phase-release, and pulse experiments are compared to modeled results and a positive correlation is seen. Equations in closed form have been developed from the model that describe release-assay curves and phase response curves (including the transition between type 1 and type 0 behavior). Presumably a change in environmental conditions changes several aspects of a circadian rhythm limit cycle, but this work suggests that most of the features of a circadian rhythm experiment can be qualitatively mimicked by simply shifting the position of the limit cycle relative to new environmental conditions.
Gooch, Van D., "Limit Cycle Displacement Model of Circadian Rhythms" (2007). Faculty Working Papers. 11.