### Journals Information

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Universal Journal of Computational Mathematics Vol. 7(1), pp. 14 - 20 DOI: 10.13189/ujcmj.2019.070103 Reprint (PDF) (498Kb) **

## Mathematical Modeling of the Flight of the Starlings. A Particular Case of an Attractor Repeller Pairs

**Araceli Giménez Lorente ^{*}**

Higher Education School of Art and Design 1, Plaça de Fadrell, 1, 12002 Castelló de la Plana, Spain

**ABSTRACT**

It presents a mathematical modeling of a biological system, this is a particular case of two fractal sets, an attractor repeller pair, according to the definition given by the Morse-Smalle theory; these are complementary fractal sets, since the complementary of the fractal repeller set is the attractor set, as we can see in the demonstration. The existence of this model in Nature is found in the flight of starlings. This dynamic system works like a beat of a heart, where the movement of the systole is equivalent to the contraction (attractor set) of the flight trajectory of birds and the diastole movement to its expansion (repeller set).The modeling is presented with differential equations written in Matlab code, and several images of the fractal sets associated with the flight pattern of the starlings are generated, so that we can see this model more clearly. We will begin with a definition and its subsequent mathematical demonstration to study this complex system of complementary fractals.

**KEYWORDS**

Mathematical Modeling, Biological System, Fractal Sets, Attractor-Repeller Pair, the Flight of Starlings, Matlab Code

**Cite this paper**

Araceli Giménez Lorente . "Mathematical Modeling of the Flight of the Starlings. A Particular Case of an Attractor Repeller Pairs." Universal Journal of Computational Mathematics 7.1 (2019) 14 - 20. doi: 10.13189/ujcmj.2019.070103.