| Abstract: |
| This talk is concerned with the asymptotic behavior of coexistence steady-states
of the Lotka-Volterra competition model as a cross-diffusion coefficient tends to infinity.
In a typical asymptotic behavior, almost all steady-states can be
characterized by either of two limiting systems (Lou-Ni 1999).
One of two limiting systems (the 1st limiting system)
has been extensively studied by Lou, Ni, and Yotsutani.
This talk introduces the global bifurcation structure of
the other limiting system (the 2nd limiting system).
A combination of researches for the 1st and 2nd limiting systems implies that a saddle-node bifurcation curve appears when the cross-diffusion coefficient is sufficiently large,
and moreover, the upper branch can be approximated by the set of solutions of the first limiting system,
while the lower branch can be characterized by those of the second limiting system. |
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