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.