# Dynamics of S-unimodal maps used in population modeling. - Open Research Data - MOST Wiedzy

## Dynamics of S-unimodal maps used in population modeling.

### Opis

S-unimodal maps are maps of the interval with negative Schwarzian derivative and having only one turning point (such that the map is increasing to the left of the turning point and decreasing to the right of it). Theory of S-unimodal maps is now a well-developed branch of discrete dynamical systems, including famous Singer theorem which implies existence of at most one attracting periodic orbit, necessarily attracting the turning point. Despite these special properties, S-unimodal maps have various applications. Simultaneously strong tools from dynamical system theory allow to describe effectively their dynamics.

The dataset is concerned with Hassel and Ricker maps that appear as models of population dynamics. These maps in particular were studied in the paper Periodicity versus chaos in one-dimensional dynamics (SIAM Rev. 43, no. 1, 3–30, 2001) by H. Thunberg (see also references therein). For the formulas and further properties of these functions we refer to this paper or to the master thesis “S-unimodal interval maps: theory and applications to population dynamics” of Zuzanna Kontna (Gdansk University of Technology, 2020).

The folder includes txt-file codes.txt which contains R-program codes for creating:
• graphs of Hassel and Ricker maps with arbitrary parameters,
• bifurcation diagrams of Ricker and Hassel maps,
• bifurcation diagram of logistic mapping,
• histograms of points of the orbit of Ricker map.

The programs were created for the purpose of the above mentioned master thesis. We also include the following graphical files obtained using this program:
• Ricker_lambda1_6beta_0_7.jpg showing a graph of the Ricker mapping with parameters λ = 1, 6 and β = 0, 7.
• Hassel_lambda4beta2.jpg showing a graph of the Hassell mapping for parameters λ = 4 and β = 2.
• BifurcationRicker_beta2.jpeg presenting bifurcation diagram for Ricker map with β = 2 and λ as a bifurcation parameter.
• BifurcationHassel_beta20.jpeg presenting bifurcation diagram for Hassel map with β = 20 and λ as a bifurcation parameter.
• BifurcationLogistic.jpeg presenting bifurcation diagram for the logistic map
• HistogramRicker1.jpeg showing orbit distribution for the Ricker map with parameters λ = 16,999 and β = 2 and the starting point x0 = 0,3.
• HistogramRicker2.jpeg showing orbit distribution for the Ricker map with parameters λ = 16,999 and β = 2 and the starting point x0 = 2.

s-unimodal (2).zip
681.1 kB, S3 ETag da2b186ef95fb86dc743da9806e0d48a-1, pobrań: 16

### Informacje szczegółowe o pliku

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### Informacje szczegółowe

Rok publikacji:
2020
Data zatwierdzenia:
2020-12-17