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Zbl 1176.92039
Hatvani, L.; Toókos, F.; Tusnády, G.
A mutation-selection-recombination model in population genetics. (English)
[J] Dyn. Syst. Appl. 18, No. 2, 335-361 (2009). ISSN 1056-2176

Summary: We construct a new continuous time selection-mutation-recombination model for population dynamics, which describes the development of the distribution of the different gametes in the population. We show that cyclic mutation rates can result in stable and unstable limit cycles due to Hopf bifurcations. In addition, we give a qualitative characterization of the whole dynamics in the simplex, which is the phase space of the system. If only selection acts, then Fisher's Fundamental Law is valid: the mean fitness is a Lyapunov function and every orbit converges to some rest point.

MSC 2000:: *92D15 Problems related to evolution
92D10 Genetics
37G15 Bifurcations of limit cycles and periodic orbits
92D25 Population dynamics
37N25 Dynamical systems in biology

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