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

Salvatore Rionero

doi:10.3934/mbe.2006.3.189

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2006, Volume 3, Issue 1: 189-204. Doi: 10.3934/mbe.2006.3.189

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

Salvatore Rionero^1,

1.
University of Naples Federico II, Department of Mathematics and Applications ''R. Caccioppoli", Complesso Universitario Monte S. Angelo. Via Cinzia, 80126 Napoli

Received: November 30, 2004

Revised: March 31, 2005

Published: October 2005

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Abstract

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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Mathematics Subject Classification: 70K20, 76E30, 34D20, 37B25, 70K15, 93D30, 92A15,35K57.

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

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