an:05580406
Zbl 1165.37311
Alsharawi, Ziyad
Periodic orbits in periodic discrete dynamics
EN
Comput. Math. Appl. 56, No. 8, 1966-1974 (2008).
00232516
2008
j
37C25 39A11 39B12 26A18
periodic difference equations; periodic orbits; combinatorial dynamics; population models
Summary: We study the combinatorial structure of periodic orbits of nonautonomous difference equations \(x_{n+1}=f_n(x_n)\) in a periodically fluctuating environment. We define the \(\Gamma \)-set to be the set of minimal periods that are not multiples of the phase period. We show that when the functions \(f_n\) are rational functions, the \(\Gamma \)-set is a finite set. In particular, we investigate several mathematical models of single-species without age structure, and find that periodic oscillations are influenced by periodic environments to the extent that almost all periods are divisors or multiples of the phase period.