Existence of positive solutions of a genotype selection model. (Chinese. English summary) Zbl 1150.39315
Summary: By using Mawhin’s coincidence degree theory, we study the existence of a positive periodic solution to the following genotype selection model
\[
x_{n+1}=\frac {x_n \exp[\beta_n (1-\alpha x_{n-k})]}{1-x_n+x_n\exp[\beta_n (1-\alpha x_{n-k})]} , \, n=0, 1, 2, \cdots
\]
and obtain a new sufficient condition for the existence of positive periodic solution of the difference model.
MSC:
39A11 | Stability of difference equations (MSC2000) |
39A12 | Discrete version of topics in analysis |
39A20 | Multiplicative and other generalized difference equations |
92D10 | Genetics and epigenetics |