The effect of maps permutation on the global attractor of a periodic Beverton–Holt model
| Autor: | Ziyad AlSharawi, Asma Al-Ghassani |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Beverton–Holt model
0209 industrial biotechnology education.field_of_study Applied Mathematics Population Block (permutation group theory) 020206 networking & telecommunications 02 engineering and technology Characterization (mathematics) Dihedral group Combinatorics Computational Mathematics Permutation 020901 industrial engineering & automation Attractor 0202 electrical engineering electronic engineering information engineering Limit (mathematics) education Mathematics |
| Zdroj: | Applied Mathematics and Computation. 370:124905 |
| ISSN: | 0096-3003 |
| Popis: | Consider a p-periodic difference equation x n + 1 = f n ( x n ) with a global attractor. How does a permutation [ f σ ( p − 1 ) , … , f σ ( 1 ) , f σ ( 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. |
| Databáze: | OpenAIRE |
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