To ultimately address this serious issue, this book begins with the nonlinear dynamic characteristics of marine plankton, focusing on the dynamic behavior of both two-dimensional and spatiotemporal patterns. As a critical foundation of marine ecosystems, the frequent outbreaks of marine phytoplankton and the toxicity of planktonic animals pose significant threats to marine ecological security and human health. One of the primary reasons we currently struggle to effectively manage the safety issues surrounding marine plankton is the extremely complex nature of their growth environment, which exhibits intricate dynamic and nonlinear characteristics. By constructing reaction-diffusion models and fractional diffusion systems of the planktonic ecosystem, the book characterizes the various factors in different environments and studies the nonlinear behavior of marine organisms. Employing linear stability theory, multi-scale analysis, comparison principle, analytical techniques, and the construction of Lyapunov functions, the book delves into the following topic: the stability of the plankton ecosystem, Hopf bifurcation, Turing bifurcation and other local bifurcations, spatial self-organization behavior of marine plankton, the formation of spatiotemporal patterns, and the persistence and extinction properties and characteristics. Marine ecology and the marine environment are currently hot research topics internationally, with the behavior of marine organisms being a core area of this research. The goal of exploring these issues is to scientifically understand the features of marine organisms, control their behavior, manage ocean pollution effectively, contribute to human development, and support social advancement. Additionally, the authors aime to make academic contributions and provide guidance to graduate students and researchers dedicated to this field.