Chaotic behavior and controlling chaos in a fast-slow plankton-fish model

The interaction of different time scales in predator-prey models has become a common research topic. In the present article, we concentrated on the dynamics of interactions at two time scales in a plankton-fish system. To investigate the effects of the two time scales on plankton-fish dynamics, we constructed a new parameter with a corrected type that differs from the traditional slow parameter. In addition, zooplankton's refuge from the predator and phytoplankton mortality due to competition are incorporated into the model. Positivity and boundedness of solutions were proved. We then discussed feasibility and stability conditions of the equilibrium. We used a variety of means to support the existence of chaos in the system. Hopf bifurcation conditions were also obtained. Chaos control in the plankton-fish model is one of the main motivations for this study. In the slow-variable parameter case, we explored the control mechanism of gestation delay on chaotic systems, which are calmed by different periodic solutions. Moreover, under seasonal mechanisms, external driving forces can stabilize the system from chaos to periodic oscillations. Meanwhile, the sliding mode control (SMC) approach quickly calms chaotic oscillations and stabilizes it to an internal equilibrium state. The necessary numerical simulation experiments support the theoretical results.