Dynamics Complexity Induced by Salinity in a Stochastic Phytoplankton–Zooplankton Model Under Acid–Base Changes

ABSTRACT In this paper, on the basis of the theories and methods of ecology, a deterministic phytoplankton–zooplankton (PZ) model as well as its stochastic differential equation version, which takes into account the synergistic effect of salinity and pH, is established. A key advantage of considering salinity and pH effects is that it can make the dynamic behaviors of the PZ models more realistic, which is fundamentally different from current related researches. The main purpose of this paper is to explore how the synergistic effects of salinity and pH affect the growth dynamics of phytoplankton in deterministic and stochastic disturbance environments. For the deterministic PZ model, we explore the existence of possible equilibrium points, local and global stability, as well as the existence of Hopf bifurcation. For the stochastic PZ model, we study the properties of persistence in the mean, stochastic extinction, and the existence of a unique ergodic stationary distribution. In addition, we explore the dynamics of critical point extinction, which is often overlooked in most current PZ model studies. Ecologically, via numerical simulations, we find that salinity and pH have a great influence on the dynamics of phytoplankton growth in the deterministic and stochastic environments. It is worth emphasizing that the increase of downstream salinity can destabilize the phytoplankton–zooplankton dynamics, while the decrease of downstream salinity is able to stabilize the phytoplankton–zooplankton dynamics. Additionally, it is revealed that an increase in downstream salinity or a decrease in upstream salinity is not conducive to the growth of zooplankton, but it can trigger the occurrence of phytoplankton blooms when the pH value is in the middle range. These results provide new insights into understanding the complexity of phytoplankton–zooplankton models.