Stability analysis of the phytoplankton vertical steady states in a laboratory test tube

✍ Scribed by Edoardo Beretta; Antonio Fasano; Yuzo Hosono; V. B. Kolmanovskii

• Publisher: John Wiley and Sons
• Year: 1994
• Tongue: English
• Weight: 843 KB
• Volume: 17
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1670170705

✦ Synopsis

Abstract

The positive vertical equilibrium profiles of a phytoplankton population growing in a vertical test tube under controlled experimental conditions (temperature, salinity, light intensity at the top surface) for nutrients are discussed with reference to their stability properties for arbitrary positive initial values of the biomass concentration along the tube. Two different approaches are followed. First a stability result is established in the Sobolev norm H^2^ by estimating the norms of the perturbations recursively in successive subintervals of suitably small amplitude. The second approach provides stability in the sense of the uniform convergence as a corollary of a stability theorem for a rather general class of integro‐differential equations.