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Mathematical Biosciences and Engineering

2006, Volume 3, Issue 1: 189-204. doi: 10.3934/mbe.2006.3.189
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A nonlinear L2-stability analysis for two-species population dynamics with dispersal

  • 1.
    University of Naples Federico II, Department of Mathematics and Applications ''R. Caccioppoli", Complesso Universitario Monte S. Angelo. Via Cinzia, 80126 Napoli
  • Received: 01 December 2004 Accepted: 29 June 2018 Published: 01 November 2005

  • MSC : 70K20, 76E30, 34D20, 37B25, 70K15, 93D30, 92A15,35K57.

  • The nonlinear L2-stability (instability) of the equilibrium states of two-species population dynamics with dispersal is studied. The obtained results are based on (i) the rigorous reduction of the L2-nonlinear stability to the stability of the zero solution of a linear binary system of ODEs and (ii) the introduction of a particular Liapunov functional V such that the sign of dVdt along the solutions is linked directly to the eigenvalues of the linear problem.

    Citation: Salvatore Rionero. A nonlinear L2-stability analysis for two-species population dynamics with dispersal[J]. Mathematical Biosciences and Engineering, 2006, 3(1): 189-204. doi: 10.3934/mbe.2006.3.189

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  • The nonlinear L2-stability (instability) of the equilibrium states of two-species population dynamics with dispersal is studied. The obtained results are based on (i) the rigorous reduction of the L2-nonlinear stability to the stability of the zero solution of a linear binary system of ODEs and (ii) the introduction of a particular Liapunov functional V such that the sign of dVdt along the solutions is linked directly to the eigenvalues of the linear problem.


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