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Some combinatorial aspects of discrete non-linear population dynamics

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  • Grosjean, Nicolas
  • Huillet, Thierry

Abstract

Motivated by issues arising in population dynamics, we consider the problem of iterating a given analytic function a number of times. We use the celebrated technique known as Carleman linearization that turns (for a certain class of functions) this problem into simply taking the power of a real number. We expand this method, showing in particular that it can be used for population models with immigration, and we also apply it to the famous logistic map. We also are able to give a number of results for the invariant density of this map, some being related to the Carleman linearization.

Suggested Citation

  • Grosjean, Nicolas & Huillet, Thierry, 2016. "Some combinatorial aspects of discrete non-linear population dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 71-79.
    • Handle: RePEc:eee:chsofr:v:93:y:2016:i:c:p:71-79
    DOI: 10.1016/j.chaos.2016.10.004
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    Cited by:

    1. Brechtl, Jamieson & Xie, Xie & Liaw, Peter K. & Zinkle, Steven J., 2018. "Complexity modeling and analysis of chaos and other fluctuating phenomena," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 166-175.

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