Stability and dynamic transition of a toxin-producing phytoplankton-zooplankton model with additional food

The article aims to investigate the dynamic transitions of a toxin-producing phytoplankton zooplankton model with additional food in 2D-rectangular domain. The investigation is based on transition theory for dissipative dynamical systems. Firstly, we verify principle exchange stability by analysing corresponding linear eigenvalue problem. Secondly, using technique center manifold reduction, determine types transitions. Our results imply that may bifurcate two new steady state solutions, which are either attractors or saddle points. In addition, also periodic solution as control parameter passes critical value. Finally, some numerical given illustrate our conclusions.