A qualitative mathematical model of the ontogeny of a circadian rhythm in crayfish

Based on experimental work on the ontogeny of the electroretinogram circadian rhythm in crayfish, we present a mathematical model simulating changes in both frequency and amplitude of the electroretinogram oscillation during several developmental stages until shortly before the adult age. Simultaneously, we propose a hypothetical oscillation in the hormonal release whose frequency is imposed on the electroretinogram oscillation. The model consists of two coupled nonlinear oscillators in which a dynamical response is obtained mainly through an Andronov-Hopf bifurcation. Through the construction of the model, a biological hypothesis about the essential elements underlying the ERG circadian rhythm and their interrelations is formulated and discussed.