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Numerical investigation of the bifurcation diagram and invariant domains of logistic mapping in the complex plane

TitleNumerical investigation of the bifurcation diagram and invariant domains of logistic mapping in the complex plane
AuthorsY. N. Deryugin1, E. Y. Kireicheva1, T. F. Mamedova2, A. V. Pukhkoy2
1Russian Federal Nuclear Center All-Russioan Research Institute of Experimental Physics
2Ogarev Mordovia State University
AnnotationThe aim of the paper is to investigate the logistic mapping of a complex plane. Such a model can be used to study the innovative development of logistics centers (distribution centers), depending on the control parameter. Since logistic centers are based on a certain distance around megacities and large cities, then considering the logistic mapping in the set of complex numbers, it is possible to take into account the spatial distribution of logistic centers. The starting point in this study is the logistic mapping in the real domain. Therefore, the paper gives general properties of discrete mappings and a numerical investigation of the logistic map on the real axis.
KeywordsLogistic mapping, bifurcation, limit mapping function, complex plane
CitationDeryugin Y. N., Kireicheva E. Y., Mamedova T. F., Pukhkoy A. V. ''Numerical investigation of the bifurcation diagram and invariant domains of logistic mapping in the complex plane'' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 267-272. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper37.pdf. - Date of access: 15.10.2019.