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This paper investigates Turing instability and Hopf bifurcation for a diffusive plankton system with time delay and cell size. To determine the effects of diffusion and cell size on the dynamics of the system, we first study the system without time delay, where the conditions of stability of coexisting equilibrium and Turing instability are obtained through Routh-Hurwitz criterion. Then we give the existence of Hopf bifurcation using time delay as bifurcation parameter by analyzing the distribution of eigenvalues, and derive the property of Hopf bifurcation by applying the centre manifold theory. Finally, numerical simulation shows that different cell size increases the variety of dynamics for diffusive plankton system. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effect of water temperature on phytoplankton–zooplankton dynamics with Holling type III functional response. Remarkably, growth rate, capture rate, handling time, death rate and Holling parameter are considered to be temperature dependent, which makes the model different from those in the existing related literatures. First, the relationships between model parameters and water temperature are presented. Then we give the positivity and boundedness of the solutions. And parameters dependent equilibrium analysis and stability analysis are obtained, respectively. It shows that when the water temperature is lower or higher than the optimal temperature, the equilibrium density of phytoplankton increases with decreasing capture rate and increasing handling time. Meanwhile, we show that the decrease of capture rate and increase of handing time cause the density of zooplankton also increases without the optimal temperature, while the population of zooplankton tends to decrease with decrease of growth rate. In addition, sensitivity of coexisting equilibrium to the parameters of the phytoplankton–zooplankton model is analyzed. Finally, one parameter bifurcation analysis is done. [ABSTRACT FROM AUTHOR]