Special Issue "Pattern Formation in Population Dynamics"

A special issue of Computation (ISSN 2079-3197). This special issue belongs to the section "Computational Biology".

Deadline for manuscript submissions: closed (15 July 2018).

Special Issue Editors

Dr. Vitaly Volpert
E-Mail Website
Guest Editor
Directeur de recherche au CNRS, Institut Camille Jordan, University Lyon 1, 69622 Villeurbanne, France
Interests: mathematical modeling in biology; multi-scale models; hybrid models; partial differential equations; mathematical modelling; population dynamics; biomedical modelling
Special Issues and Collections in MDPI journals
Prof. Dr. Malay Banerjee
E-Mail Website
Guest Editor
Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur-208016, India
Interests: mathematical ecology and eco-epidemiology; nonlinear dynamics; stochastic modelling in population dynamics; spatio-temporal pattern formation
Dr. Moitri Sen
E-Mail Website
Guest Editor
Department of Mathematics, National Institute of Technology Patna, Patna 800005, India
Interests: nonlinear dynamics; pattern formation; population dynamics

Special Issue Information

Dear Colleagues,

Spatio-temporal pattern formation resulting from the heterogeneous distribution of interacting populations are capable of producing a wide variety of patterns. The heterogeneous distributions themselves can be classified as stationary patterns, oscillatory patterns, spatio-temporal chaotic patterns, and so on. Nonlinear parabolic partial differential equations (for single or multi-species interaction with one or higher dimensional space) are the basic modelling approach to study the pattern formation for single or multi-species population growth. Several mathematical aspects are involved in the investigation of spatio-temporal pattern formation, namely: existence of travelling and periodic travelling waves, Turing instability, Turing–Hopf bifurcation, invasion, wave of invasion, wave of chaos, etc. Existence of various types of spatial patterns can describe the size and nature of population patches, changes of habitats, movement of the individuals or groups of individuals from one location to another, invasion of new species and so on. These are examples from an expanding list of interpretations of the spatial patterns.

Recently, researchers have become interested in studying various types of stationary and non-stationary patterns produced by the models with cross-diffusion terms, nonlocal interaction terms, and advection terms, along with various types of boundary conditions. The basic mechanisms behind the generation of various patterns and their bifurcations are still an active area of research.

The aim of this special issue is to present state-of-the-art research work in the area of spatial pattern formation by interacting populations, to enhance the understanding of the basic mechanisms responsible for various types of pattern formation and their ecological interpretations. Authors are invited to submit their original and review papers devoted to patterns and waves in the context of ecology and cell population dynamics.

Prof. Dr. Vitaly Volpert
Dr. Malay Banerjee
Dr. Moitri Sen
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Computation is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


  • spatial pattern
  • travelling wave
  • Turing instability
  • Turing–Hopf bifurcation
  • invasion
  • spatio-temporal chaos

Published Papers (1 paper)

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Pattern Formation in a Model Oxygen-Plankton System
Computation 2018, 6(4), 59; https://doi.org/10.3390/computation6040059 - 14 Nov 2018
Cited by 5 | Viewed by 1747
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Pattern Formation in Population Dynamics)
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