A nonlinear $L^2$-stability analysis for two-species population dynamics with dispersal

  • Received: 01 December 2004 Accepted: 29 June 2018 Published: 01 November 2005
  • MSC : 70K20, 76E30, 34D20, 37B25, 70K15, 93D30, 92A15,35K57.

  • The nonlinear $L^2$-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 $L^2$-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 $\frac{dV}{dt}$ along the solutions is linked directly to the eigenvalues of the linear problem.

    Citation: Salvatore Rionero. A nonlinear $L^2$-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 $L^2$-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 $L^2$-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 $\frac{dV}{dt}$ along the solutions is linked directly to the eigenvalues of the linear problem.
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    © 2006 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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