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Computation 2018, 6(4), 59; https://doi.org/10.3390/computation6040059

Pattern Formation in a Model Oxygen-Plankton System

1
Department of Mathematics, Arts and Science Faculty, Amasya University, Amasya 05189, Turkey
2
Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, UK
*
Author to whom correspondence should be addressed.
Received: 22 August 2018 / Revised: 4 November 2018 / Accepted: 5 November 2018 / Published: 14 November 2018
(This article belongs to the Special Issue Pattern Formation in Population Dynamics)
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Abstract

Decreasing level of dissolved oxygen has recently been reported as a growing ecological problem in seas and oceans around the world. Concentration of oxygen is an important indicator of the marine ecosystem’s health as lack of oxygen (anoxia) can lead to mass mortality of marine fauna. The oxygen decrease is thought to be a result of global warming as warmer water can contain less oxygen. Actual reasons for the observed oxygen decay remain controversial though. Recently, it has been shown that it may as well result from a disruption of phytoplankton photosynthesis. In this paper, we further explore this idea by considering the model of coupled plankton-oxygen dynamics in two spatial dimensions. By means of extensive numerical simulations performed for different initial conditions and in a broad range of parameter values, we show that the system’s dynamics normally lead to the formation of a rich variety of patterns. We reveal how these patterns evolve when the system approaches the tipping point, i.e., the boundary of the safe parameter range beyond which the depletion of oxygen is the only possibility. In particular, we show that close to the tipping point the spatial distribution of the dissolved oxygen tends to become more regular; arguably, this can be considered as an early warning of the approaching catastrophe. View Full-Text
Keywords: oxygen; phytoplankton; predator-prey; pattern formation oxygen; phytoplankton; predator-prey; pattern formation
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Sekerci, Y.; Petrovskii, S. Pattern Formation in a Model Oxygen-Plankton System. Computation 2018, 6, 59.

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