Stability and Hopf bifurcation analysis of a delayed phytoplankton-zooplankton model with Allee effect and linear harvesting.

In this article, a delayed phytoplankton-zooplankton system with Allee effect and linear harvesting is proposed, where phytoplankton species protects themselves from zooplankton by producing toxin and taking shelter. First, the existence and stability of the possible equilibria of system are explored. Next, the existence of Hopf bifurcation is investigated when the system has no time delay. What's more, the stability of limit cycle is demonstrated by calculating the first Lyapunov number. Then, the condition that Hopf bifurcation occurs is obtained by taking the time delay describing the maturation period of zooplankton species as a bifurcation parameter. Furthermore, based on the normal form theory and the central manifold theorem, we derive the direction of Hopf bifurcation and the stability of bifurcating periodic solutions. In addition, by regarding the harvesting effort as control variable and employing the Pontryagin's Maximum Principle, the optimal harvesting strategy of the system is obtained. Finally, in order to verify the validity of the theoretical results, some numerical simulations are carried out.

Wastewater treatment high rate algal ponds for biofuel production.

While research and development of algal biofuels are currently receiving much interest and funding, they are still not commercially viable at today's fossil fuel prices. However, a niche opportunity may exist where algae are grown as a by-product of high rate algal ponds (HRAPs) operated for wastewater treatment. In addition to significantly better economics, algal biofuel production from wastewater treatment HRAPs has a much smaller environmental footprint compared to commercial algal production HRAPs which consume freshwater and fertilisers. In this paper the critical parameters that limit algal cultivation, production and harvest are reviewed and practical options that may enhance the net harvestable algal production from wastewater treatment HRAPs including CO(2) addition, species control, control of grazers and parasites and bioflocculation are discussed.