Permanence and Stability of a Kill the Winner Model in Marine Ecology

Daniel A. Korytowski, Hal Smith

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We focus on the long-term dynamics of “killing the winner” Lotka–Volterra models of marine communities consisting of bacteria, virus, and zooplankton. Under suitable conditions, it is shown that there is a unique equilibrium with all populations present which is stable, the system is permanent, and the limiting behavior of its solutions is strongly constrained.

Original languageEnglish (US)
Pages (from-to)995-1004
Number of pages10
JournalBulletin of Mathematical Biology
Volume79
Issue number5
DOIs
StatePublished - May 1 2017

Fingerprint

Marine Biology
Zooplankton
Lotka-Volterra Model
marine science
Permanence
Limiting Behavior
Military Personnel
Ecology
Behavior of Solutions
Viruses
Bacteria
Virus
virus
zooplankton
viruses
bacterium
bacteria
Population
Model
Community

Keywords

  • Bacteria
  • Infection network
  • Kill the winner
  • Lotka–Volterra system
  • Parasite-mediated coexistence
  • Permanence
  • Virus
  • Zooplankton

ASJC Scopus subject areas

  • Neuroscience(all)
  • Immunology
  • Mathematics(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Pharmacology
  • Environmental Science(all)
  • Agricultural and Biological Sciences(all)
  • Computational Theory and Mathematics

Cite this

Permanence and Stability of a Kill the Winner Model in Marine Ecology. / Korytowski, Daniel A.; Smith, Hal.

In: Bulletin of Mathematical Biology, Vol. 79, No. 5, 01.05.2017, p. 995-1004.

Research output: Contribution to journalArticle

@article{611c797b571f4feca81996782d9cb778,
title = "Permanence and Stability of a Kill the Winner Model in Marine Ecology",
abstract = "We focus on the long-term dynamics of “killing the winner” Lotka–Volterra models of marine communities consisting of bacteria, virus, and zooplankton. Under suitable conditions, it is shown that there is a unique equilibrium with all populations present which is stable, the system is permanent, and the limiting behavior of its solutions is strongly constrained.",
keywords = "Bacteria, Infection network, Kill the winner, Lotka–Volterra system, Parasite-mediated coexistence, Permanence, Virus, Zooplankton",
author = "Korytowski, {Daniel A.} and Hal Smith",
year = "2017",
month = "5",
day = "1",
doi = "10.1007/s11538-017-0265-6",
language = "English (US)",
volume = "79",
pages = "995--1004",
journal = "Bulletin of Mathematical Biology",
issn = "0092-8240",
publisher = "Springer New York",
number = "5",

}

TY - JOUR

T1 - Permanence and Stability of a Kill the Winner Model in Marine Ecology

AU - Korytowski, Daniel A.

AU - Smith, Hal

PY - 2017/5/1

Y1 - 2017/5/1

N2 - We focus on the long-term dynamics of “killing the winner” Lotka–Volterra models of marine communities consisting of bacteria, virus, and zooplankton. Under suitable conditions, it is shown that there is a unique equilibrium with all populations present which is stable, the system is permanent, and the limiting behavior of its solutions is strongly constrained.

AB - We focus on the long-term dynamics of “killing the winner” Lotka–Volterra models of marine communities consisting of bacteria, virus, and zooplankton. Under suitable conditions, it is shown that there is a unique equilibrium with all populations present which is stable, the system is permanent, and the limiting behavior of its solutions is strongly constrained.

KW - Bacteria

KW - Infection network

KW - Kill the winner

KW - Lotka–Volterra system

KW - Parasite-mediated coexistence

KW - Permanence

KW - Virus

KW - Zooplankton

UR - http://www.scopus.com/inward/record.url?scp=85016115843&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85016115843&partnerID=8YFLogxK

U2 - 10.1007/s11538-017-0265-6

DO - 10.1007/s11538-017-0265-6

M3 - Article

C2 - 28349407

AN - SCOPUS:85016115843

VL - 79

SP - 995

EP - 1004

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

SN - 0092-8240

IS - 5

ER -