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
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.
References