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Mathematical Biosciences and Engineering

2016, Volume 13, Issue 1: 101-118. doi: 10.3934/mbe.2016.13.101
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The global stability of coexisting equilibria for three models of mutualism

  • 1.
    Department of Mathematics, Technical University of Iaşi, Bd. Copou 11, 700506 Iaşi
  • 2.
    Department of Financial Mathematics, Jiangsu University, ZhenJiang, Jiangsu, 212013
  • Received: 01 January 2015 Accepted: 29 June 2018 Published: 01 October 2015

  • MSC : Primary: 92D25, 92D40; Secondary: 34D20, 34D23, 93D30.

  • We analyze the dynamics of three models of mutualism, establishing the global stability of coexisting equilibria by means of Lyapunov's second method. This further establishes the usefulness of certain Lyapunov functionals of an abstract nature introduced in an earlier paper. As a consequence, it is seen that the use of higher order self-limiting terms cures the shortcomings of Lotka-Volterra mutualisms, preventing unbounded growth and promoting global stability.

    Citation: Paul Georgescu, Hong Zhang, Daniel Maxin. The global stability of coexisting equilibria for three models of mutualism[J]. Mathematical Biosciences and Engineering, 2016, 13(1): 101-118. doi: 10.3934/mbe.2016.13.101

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  • We analyze the dynamics of three models of mutualism, establishing the global stability of coexisting equilibria by means of Lyapunov's second method. This further establishes the usefulness of certain Lyapunov functionals of an abstract nature introduced in an earlier paper. As a consequence, it is seen that the use of higher order self-limiting terms cures the shortcomings of Lotka-Volterra mutualisms, preventing unbounded growth and promoting global stability.


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