Dynamic behaviors of a non-autonomous allelopathic phytoplankton model with threshold inter-inhibition and feedback controls

This paper investigated a non-autonomous allelopathic phytoplankton model with threshold inhibition and feedback controls. We applied the comparison theorem of differential equations and constructed some suitable Lyapunov functions to obtain sufficient conditions for the permanence and global attractivity of the system. By constructing some suitable Lyapunov-type extinction functions, we further derived sufficient conditions for the extinction of one of the species. The analysis reveals that inter-specific inhibition and toxic substances critically influence the permanence, extinction, and global stability of the two-species system. Some known results are extended.