Bloom Formation and Turing Patterns in an Infochemical Mediated Multitrophic Plankton Model

A two-species predator–prey plankton model is studied, where the grazing pressure of microzooplankton on phytoplankton is controlled through external infochemical mediated predation. The system stability is analyzed in order to explain the conditions for phytoplankton bloom formation and to explore system bifurcations. The interplay between the level of infochemical-mediated external predation and the phytoplankton carrying capacity is considered over a range of parameter values and the resultant system dynamics is illustrated. The model is extended to include a spatial diffusion term leading to a reaction–diffusion system that is investigated by determining the Turing space of the model. Thereafter, the bifurcation analysis of specific time-independent patterns is explored. Through time integration, the system is also shown to exhibit the potential for temporally varying spatial patterns.

Dynamics in a Plankton Model with Toxic Substances and Phytoplankton Harvesting

In this paper, a phytoplankton–zooplankton model incorporating toxic substances and nonlinear phytoplankton harvesting is established. The existence and stability of the equilibrium of this model are first investigated. The occurrence of transcritical, saddle-node, Hopf and Bautin bifurcations at different equilibria is then verified. In addition, the properties of Hopf bifurcation and Bautin bifurcation are discussed by using normal form method. These results demonstrate that phytoplankton and zooplankton populations will oscillate periodically when the harvesting level is high. More interestingly, it is found that the oscillations are always unstable for small phytoplankton carrying capacity, while the dynamics have close relations with the initial population densities for a large environmental capacity. The existence of Bautin bifurcation theoretically indicates that toxic phytoplankton can cause extinction once there exist harmful algal blooms for some time. These results are numerically illustrated for the model with spatial diffusion, which shows that local phytoplankton blooms will lead to global populations extinction.