Fractal characteristics of Heterocapsa Circularisquama and Prorocentrum Dentatum cells growth

Abstract

This paper investigates behaviors that a set of initial cell densities of Heterocapsa Circularisquama (HC) and Prorocentrum Dentatum (PD) and a set of environmental factors disturbing the growth of HC and PD cells formed in their growth process, which are actually fractal phenomena. First, the calculation of the fractal dimension of the set of initial cell densities of HC and PD is given in the paper. Second, by controlling the set of initial cell density, HC and PD cells grow according to a given growth target. The approximate or same behaviors of two different sets of initial cell densities of HC and PD are realized by introducing the coupling terms. Finally, the set of environmental factors disturbing the growth of HC and PD cells is constructed by introducing real parameters. Then the result that makes HC and PD cells growing according to a given growth target is reached by a proper mathematical transform to the real parameters. The approximate or same behaviors of the set of environmental factors disturbing the growth of HC and PD cells are realized by introducing the coupling terms.