Modeling and analysis of a marine plankton system with nutrient recycling and diffusion

Abstract

This article describes a nutrient‐phytoplankton‐zooplankton system with nutrient recycling in the presence of toxicity. We have studied the dynamical behavior of the system with delayed nutrient recycling in the first part of the article. Uniform persistent of the system is examined. In the second part of the article, we have incorporated diffusion of the plankton population to the system and dynamical behavior of the system is analyzed with instantaneous nutrient recycling. The condition of the diffusion driven instability is obtained. The conditions for the occurrence of Hopf and Turing bifurcation critical line in a spatial domain are derived. Variation of the system with small periodicity of diffusive coefficient has been studied. Stability condition of the plankton system subject to the periodic diffusion coefficient of the zooplankton is derived. It is observed that nutrient‐phytoplankton‐zooplankton interactions are very complex and situation specific. Moreover, we have obtained different exciting results, ranging from stable situation to cyclic oscillatory behavior may occur under different favorable conditions, which may give some insights for predictive management. © 2014 Wiley Periodicals, Inc. Complexity 21: 229–241, 2015

Stability and Hopf Bifurcation in a Three-Component Planktonic Model with Spatial Diffusion and Time Delay

“…In view of the ocean current and monsoon, the plankton can freely drift and this spatial dispersal is subject to Fickian diffusion. So the effect of spatial diffusion has been investigated by many authors [12][13][14][15][16][17]. The results indicate that spatial diffusion has a vital role in the spatiotemporal dynamics of the planktonic model and spatial pattern may occur.…”

Evolution and Differentiation of High-Quality Development of Marine Economy: A Case Study from China

“…Given the concept of sustainability and the development of marine economy, examining how to shift the marine economy away from an extensive type has become a topic of research among scholars and governments. e common objective now for coastal countries is to achieve sustainable growth of the marine economy by solving historical environmental issues such as "inadaptability" and "incompatibility" [6][7][8].…”

“…e negative effects of the external environment, such as shrinking demand and diminishing demographic dividend, have forced the development of the marine economy, under the constraint of a structural slowdown crisis, to shift to the long-term perspective in terms of speed, structure, and power changes in time and space, so as to achieve sustainable growth and improve human welfare [24]. It aims to optimize the structure of marine industries, promote marine social welfare, and enhance the marine ecological environment based on the improvement of the comprehensive strength of the marine economy [8,22,25]. In particular, the human-ocean system and its subsystems are the main areas where high-quality development can improve the marine economy, while carriers that support the development of the marine economy are areas that can improve marine economic activity at all levels.…”

Dynamics Induced by Delay in a Nutrient-Phytoplankton Model with Multiple Delays

“…Hence, the delay may indeed exist in the phytoplankton growth, which means that it is necessary to consider delay in nutrient-phytoplankton models. An approach that has been attempted by researchers to model the dynamics of phytoplankton is the role of delay since delay appears as an important component in biosystems and ecosystems [25][26][27][28][29][30].…”