Buried Julia Components and Julia Sets

The aim of the present paper is to study the dynamics of a class of orbitally continuous non-linear mappings defined on the set of real numbers and to apply the results on dynamics of functions to obtain tests of divisibility. We show that this class of mappings contains chaotic mappings. We also draw Julia sets of certain iterations related to multiple lowering mappings and employ the variations in the complexity of Julia sets to illustrate the results on the quotient and remainder. The notion of orbital continuity was introduced by Lj. B. Ciric and is an important tool in establishing existence of fixed points.

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Locally connected models for Julia sets

Advances in Mathematics ◽

10.1016/j.aim.2010.08.011 ◽

2011 ◽

Vol 226 (2) ◽

pp. 1621-1661 ◽

Cited By ~ 8

Author(s):

Alexander M. Blokh ◽

Clinton P. Curry ◽

Lex G. Oversteegen

Keyword(s):

Julia Sets

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Graphics with Mathematica: fractals, Julia sets, patterns and natural forms, by Chonat Getz and Janet Helmstedt. Pp. 336. £103·50. 2004. ISBN 0 44451760 X(Elsevier).

The Mathematical Gazette ◽

10.1017/s0025557200180106 ◽

2006 ◽

Vol 90 (518) ◽

pp. 376-377

Author(s):

S. C. Coutinho

Keyword(s):

Julia Sets ◽

Natural Forms

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Fractal analysis and control of the competition model

International Journal of Biomathematics ◽

10.1142/s1793524516500455 ◽

2016 ◽

Vol 09 (03) ◽

pp. 1650045 ◽

Cited By ~ 6

Author(s):

Mianmian Zhang ◽

Yongping Zhang

Keyword(s):

Feedback Control ◽

Mathematical Models ◽

Fractal Analysis ◽

Fractal Geometry ◽

Julia Set ◽

Julia Sets ◽

Competition Model ◽

Simulation Results ◽

Population Competition ◽

And Control

Lotka–Volterra population competition model plays an important role in mathematical models. In this paper, Julia set of the competition model is introduced by use of the ideas and methods of Julia set in fractal geometry. Then feedback control is taken on the Julia set of the model. And synchronization of two different Julia sets of the model with different parameters is discussed, which makes one Julia set change to be another. The simulation results show the efficacy of these methods.

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