Chemotaxis Effect on Algae by Inorganic Polymer Flocculants: Backward Bifurcations and Traveling Wave Solutions

Abstract

In recent years, inorganic polymer flocculants have been developed into a new type of water treatment reagents, which are more efficient than traditional inorganic flocculants and much cheaper than organic polymer flocculants. Based on the mechanism of inorganic polymer flocculants, a diffusive model is proposed to study the chemotaxis effect on algae. The chemotaxis flux of algae depends on not only its own density, but also the density of flocculants and the density gradient of flocculants. For the spatially heterogeneous model in the absence of chemotaxis, threshold dynamics can be expressed by the basic reproduction number [Formula: see text] which describes the average number of new population generated by initial fertile algae individuals. Further, the phenomenon of backward and forward bifurcations, local asymptotic stability properties and the existence of traveling wave solutions are studied for the spatially homogeneous model in the presence of chemotaxis. Our results suggest that reducing [Formula: see text] to be smaller than one may not be sufficient to eradicate the algae. Numerical analysis reveals that the minimal wave speed may be linearly deterministic in the absence of chemotaxis, while it is not linearly deterministic in the presence of chemotaxis.