Stability Switches and Hopf Bifurcation Induced by Nutrient Recycling Delay in a Reaction-Diffusion Nutrient-Phytoplankton Model. (20th October 2021)

• Record Type: Journal Article
• Authors: Zhuang, Kejun; Li, Ying; Gong, Bin
• Other Names: Jiang Zhichao Academic Editor.
• Is Part Of: Complexity. Volume 2021(2021)
• Publication Date: 2021-10-20
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2021/7943788
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : In this paper, we study a reaction-diffusion nutrient-phytoplankton model with nutrient recycling delay and toxin-producing phytoplankton. For the delay-free case, we prove that the release rate of toxic chemicals by the toxin-producing phytoplankton can destabilize the system and cause periodic oscillation. For the time-delayed case, we observe that nutrient recycling delay may bring about stability switches and Hopf bifurcation. Moreover, we derive the formula for determining the direction and stability of the bifurcating periodic solutions. Finally, we give some numerical simulations to support the theoretical analyses.