The circadian activity in crayfish has been extensively studied, in particular
in reference to the organization of oscillators underlying the circadian systems
(Fuentes-Pardo et al., 1995; Lara-Aparicio et al., 1993). In this point, it is important
to emphasize some theoretical studies about the mathematical modeling of the main
elements involved in the ontogeny of both electrical response to light (electroretinogram,
ERG) of retinular cells and motor circadian rhythms (Fuentes-Pardo et al., 2001
and Lara-Aparicio et al., 1993).
When the ERG circadian rhythm of an adult, male crayfish is recorded, and in
the bath is put either a female crayfish or a solution of a hormone, the ecdysterone
(which has been proposed as a pheromone or sexual hormone), the ERG rhythm shows
a disturbance in amplitude, excitation level and noise level which is highly increased.
The analysis of the time series before and after the disturbance shows qualitative
and quantitative differences between them. The spectral density suggests that the time
series are not stationary series. In this analysis is present too a noise level notoriously
higher after the disturbance, particularly over some finite frequency ranges. Lastly, it
is also detected that the changes induced by the disturbance are irreversible during all
the time of the experiment (about 20 days).
On the basis of both experimental results and frequency analysis of the ERG circadian
rhythm in the crayfish, before and after the presence of the sexual hormone,
we have incorporated some modifications in the original mathematical model about
the ERG circadian rhythm which, in essence, consists of two coupled oscillators (Lara-
Aparicio et al., 1993). The present mathematical model has three main oscillators.
From these, two of them are coupled for describing the generation of the ERG circadian
rhythm (Fuentes-Pardo et al., 2001 and Lara-Aparicio et al., 1993) , and the third
one has also a circadian frequency but with a period slightly larger than those of the
first oscillator. A noisy component has been also incorporated in this model.