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

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

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