On The Bifurcation Diagrams of Fractional Logistic Map


Güzel N. , Yavcın F.

International Conference on Mathematical Advances and Applications, İstanbul, Türkiye, 11 - 13 Mayıs 2018, cilt.1, ss.60

  • Cilt numarası: 1
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.60

Özet

In this study new chaotic maps are generated from logistic map and behaviour of these chaotic maps is investigated. Dependence of the control parameter is presented with bifurcation diagrams. Dynamics of the fractional logistic map for the various degree of fractional integral is investigated. Then we demonstrate that fractional logistic map has similar bifurcation diagram and when degree of integral increases, value of bifurcation points increases.

Keywords: Bifurcation Diagram, Fractional Order Logistic Equation, Chaos

References

1. Das, S., Gupta, P.K. and Vishal, K. Approximate Approach to the Das Model of Fractional Logistic Population Growth. Appl. Math. Vol. 05, Issue 2 (2010), pp. 605 611.

2. Martelli, M. Introduction to Discrete Dynamical Systems and Chaos. John Willey and Sons, Inc. New York, Chichester, Weinheim, Brisbane, Singapore, Toronto, 1999.

3. Miller, K. and Ross, B. An introduction to fractional calculus and fractional differential equations, Wiley, New York, 1993.

4. Munkhammar, J.D. Numerical Chaos in Fractional Order Logistic Equation. arXiv:1011.2389v1 [math.GM], 2010.

5. Munkhammar, J.D. Chaos in a Fractional Order Logistic Map. Fract. Calc. Appl. Anal. Vol. 16, Issue 3 (2013), pp. 411-519.