Dynamical behavior of the Family of cubic functions

Main Article Content

Mizal H. Alobaidi
Murtada M. Alkazraji

Abstract

May R.M. gave the example of the family of cubic maps of the interval . Rogers T. D. extends the analysis of May beyond that region . “


In this paper we are trying to introduce comprehensive study of the cubic family which defined in the form:


The fixed points of the family are determined and described according to the values of the parameter  . Dynamical and chaotic behaviours of the family  discussed according to different definitions of chaos and via conjugacy .

Article Details

How to Cite
Mizal H. Alobaidi, & Murtada M. Alkazraji. (2019). Dynamical behavior of the Family of cubic functions. Tikrit Journal of Pure Science, 24(3), 125–127. https://doi.org/10.25130/tjps.v24i3.380
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References

[1] Alligood, K. T., Sauer T.D. and Yourke J.A.

(1996). Chaos: An introduction to dynamical systems.

New York :Springer-Verlage.

[2] Devany, R.L. (1989). An introduction to chaotic

dynamical systems, 2nd ed., United Kingdom:

Addison-Welly.

[3] Elayadi, S. (2000). Discrete chaos.: Chapman and

hall.

[4] Goodson, G.R. (2017). Chaotic dynamics

Fractals, Tilling’s and Substitutions. UK: Cambridge

University Press.

[5] Gulick, D. (1992). Encounters with chaos. USA :

McGraw – Hill.

[6] Kulkarni, P.R. and Borkar, V.C. (2014).

Topological conjugacy and the Chaotic Nature of the

Family of Mappings

2 ( ) c f x  x  x  c. International

Journal of Scientific and Innovative Mathematical

Research (IJSIMR) .Volume 2, Issue 11 :868-875.

[7] Layek, G.C.(2015). An introduction to dynamical

systems and chaos . India: springer.

[8] May, R.M. (1974). Biological populations with

nonoverlapping generations: Stable points, a stable

cycles and chaos. Science 86: 645-647.

[9] Rogers, T.D. and Whitley, D.C. (1983). Chaos in

the cubic mapping. Mathematical modelling , vol. 4 ,

pp. 9-25.

[10] Thakar, R.S. and Bhat, P.J.(2011). Entering into

Chaos for a cubic function 3x  x . Mathematics

Today, Vol.27 : pp. 42-46.