Theoretical Study of Algal Bloom Dynamics with Akinete Formation and Germination

The aim of this study is to investigate the population dynamics of harmful algal bloom by using the Joehnk’s model with some generalizations. The present mathematical model is a second-order nonlinear nonautonomous system based on delay differential equations. One variable is the biovolume of vegetative cells and the other one is the number of units of akinetes. The akinete is a thick-walled dormant cell derived from a vegetative cell and it is considered as a potential and significant factor triggering the algal bloom. The formation and germination of akinetes are modeled with time delays, and the coefficients in the model are described by piecewise continuous functions in time. The time delay related to the carrying capacity is considered in the form of the Hutchinson’s equation. The analysis is divided into two parts. In the first part, we investigate the local and global stability of an approximated autonomous system. In the second part, we discuss the numerical solutions of the original nonautonomous system for various simulation conditions.