Summary
In Fisher's model for the migration of advantageous genes, in epidemic models and in the theory of combustion similar existence problems for travelling fronts and waves occur. For a general two-dimensional system of ordinary differential equations depending on a parameter the existence of trajectories connecting stationary points is established. For systems derived from diffusion problems these trajectories describe the shape of a travelling front, the corresponding value of the parameter is the propagation speed. The method allows to determine the exact value of the minimal speed in Fisher's model for all interesting choices of selection parameters, i.e. for intermediate heterozygotes and for inferior heterozygotes.
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Hadeler, K.P., Rothe, F. Travelling fronts in nonlinear diffusion equations. J. Math. Biology 2, 251–263 (1975). https://doi.org/10.1007/BF00277154
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DOI: https://doi.org/10.1007/BF00277154