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Oscillators for Modeling Biomass Growth Adaptation to Circadian Rhythms

Two types of oscillators suitable for modeling the growth rate adaptation of biomass production process to circadian influences are presented and compared. These oscillators are forced by cyclic inputs representing basically the diurnal cycles corresponding to the periodical changes of light and dark phases and adapt their own natural circadian rhythm to them. This adaptation is referred to as entrainment and the oscillators considered for this circadian rhythm entrainment are based on Van der Pol and Lorenz type models. The Van der Pol type oscillator is proposed in a matrix form and subsequently compared with a generalized Lorenz model. The proposed oscillators are linked to a delayed Volterra model and the generic structure is applied to the case of cyanobacteria population growth. Using data recently obtained from the measurements on a laboratory-scale photobioreactor the parameters of oscillators are tuned to fit measured excited growth responses of cyanobacteria concentration.