Circadian rhythms are approximately 24-hour internally controlled biological changes that occur in the absence of environmental cues- although they can be altered by the environment. The first example that might pop in your mind when you hear circadian rhythms is the sleep-wake cycle. Other examples include daily fluctuations in fluctuations in body temperature, hormones, behavior, and heart rate. Individual neurons in the suprachiasmatic nucleus, a cluster of cells in the region of the brain called the hypothalamus, generates this "biological clock" in mammals. But you don't need to have a brain to have a biological clock. Circadian rhythms are found in a wide variety of organisms- from single-celled yeast to plants.

Photo Credit: Julie Donoghue

Mathematically, circadian rhythms can be modeled using trigonometric functions. There is not a general equation that encompasses all circadian rhythms. Instead, biologists and mathematicians must use empirical data to determine best model. For this module, we will consider a hypothetical example. Suppose a particular species exhibits daily regular fluctuations in body temperature that can be approximated by the equation,

where T represents temperature in°C, t represents time (in hours), and t = 0 corresponds to 12 o'clock midnight (i.e. 12:00 AM).