X. Wang and M. Golubitsky
Singularity Theory of Strategy Functions under Dimorphism Equivalence
Journal of Mathematical Biology.
Submitted.
We apply adaptive dynamics theory and singularity theory to study
dimorphisms. Our approach is based on a new equivalence relation
called dimorphism equivalence. Dimorphism equivalence is the largest equivalence relation on strategy functions that preserves ESS singularities, CvSS singularities, and dimorphisms. Specifically, we classify singularties up to topological codimension two and compute their normal forms and universal unfoldings. These calculations lead to the classification of local mutual invasibility plots that can be seen generically in systems with two parameters.