Mathematical Biosciences and Engineering, 2006, 3(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

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

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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Keywords Liapunov direct method; nonlinear stability; reaction diffusion equations.; two-species population dynamics

Citation: Salvatore Rionero. A nonlinear $L^2$-stability analysis for two-species population dynamics with dispersal. Mathematical Biosciences and Engineering, 2006, 3(1): 189-204. doi: 10.3934/mbe.2006.3.189

 

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