Research paperControl effect of periodic variation on the growth of harmful algal bloom causative species

•There has been few agreed explanation unanimously about the effect of the periodic environmental factor on the causative species theoretically.•Based on the theoretical and real empirical results of the causative species, a nonlinear controlled system is obtained.•Three theorems about the effect of the periodic environmental factor on the cell density and the growth rate of the causative species are presented.•According to the main control results, simulations and experimental data are used to assess the effectiveness of the controlled results.

Blue-green algae and Dinoflagellate etc. are common types of phytoplankton as causative species which cause the harmful algal blooms (HABs). The growth process of causative species is complex according to the variation of the environmental disturbance such as the periodic factor in reality and recent studies have not revealed the secret of the growth complexity yet. Based on the empirical and theoretical results of the growth of causative species, a nonlinear controlled system with periodic factor was obtained and the different effects of the periodic factor on the control of the cell density and the growth rate of causative species were studied by three theorems using the norm theory and finite difference method. Simulations and experimental data were also used to assess the effectiveness of the controlled results.