TY - JOUR
T1 - The effect of maps permutation on the global attractor of a periodic Beverton–Holt model
AU - Al-Ghassani, Asma S.
AU - AlSharawi, Ziyad
N1 - Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2020/4/1
Y1 - 2020/4/1
N2 - Consider a p-periodic difference equation xn+1=fn(xn) with a global attractor. How does a permutation [fσ(p−1),…,fσ(1),fσ(0)] of the maps affect the global attractor? In this paper, we limit this general question to the Beverton–Holt model with p-periodic harvesting. We fix a set of harvesting quotas and give ourselves the liberty to permute them. The total harvesting yield is unchanged by the permutation, but the population geometric-mean may fluctuate. We investigate this notion and characterize the cases in which a permutation of the harvesting quotas has no effect or tangible effect on the population geometric-mean. In particular, as long as persistence is assured, all permutations within the dihedral group give same population geometric-mean. Other permutations may change the population geometric-mean. A characterization theorem has been obtained based on block reflections in the harvesting quotas. Finally, we associate directed graphs to the various permutations, then give the complete characterization when the periodicity of the system is four or five.
AB - Consider a p-periodic difference equation xn+1=fn(xn) with a global attractor. How does a permutation [fσ(p−1),…,fσ(1),fσ(0)] of the maps affect the global attractor? In this paper, we limit this general question to the Beverton–Holt model with p-periodic harvesting. We fix a set of harvesting quotas and give ourselves the liberty to permute them. The total harvesting yield is unchanged by the permutation, but the population geometric-mean may fluctuate. We investigate this notion and characterize the cases in which a permutation of the harvesting quotas has no effect or tangible effect on the population geometric-mean. In particular, as long as persistence is assured, all permutations within the dihedral group give same population geometric-mean. Other permutations may change the population geometric-mean. A characterization theorem has been obtained based on block reflections in the harvesting quotas. Finally, we associate directed graphs to the various permutations, then give the complete characterization when the periodicity of the system is four or five.
KW - Beverton–Holt
KW - Combinatorial dynamics
KW - Cycles
KW - Periodic harvesting
KW - Permutations
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U2 - 10.1016/j.amc.2019.124905
DO - 10.1016/j.amc.2019.124905
M3 - Article
AN - SCOPUS:85075978263
SN - 0096-3003
VL - 370
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
M1 - 124905
ER -