Symbolic Methods for Analysing Bifurcations and Chaos of Two Five-Parameter Families of Planar Quadratic Maps

  • Sarbast H. Mikaeel Dept. of Mathematics, Faculty of Science, Soran University, Kurdistan Region, Iraq.
  • Bewar H. Othman Dept. of Mathematics, Faculty of Science, Soran University, Kurdistan Region, Iraq.
Keywords: Bifurcations, Chaos, Planar quadratic maps, Symbolic computation, Snapback repeller

Abstract

In this work, we analyze the dynamical behaviors of two five-parameter families of planar quadratic maps by utilizing strategies of symbolic computation. We are going to use computer algebra methods to clarify how to detect the stability of equilibrium points to analyze chaos and also the bifurcation of planar maps. Based on strategies for solving the systems in types of semi-algebraic and by utilizing an algorithmic approach, we obtain respectively for the two maps, sufficient conditions on the parameters to have a prescribed number of (stable) equilibrium points; necessary conditions on the parameters to undergo a certain type of bifurcation or to have chaotic behavior induced by snapback repeller.

Author Biographies

Sarbast H. Mikaeel, Dept. of Mathematics, Faculty of Science, Soran University, Kurdistan Region, Iraq.

Dept. of Mathematics, Faculty of Science, Soran University, Kurdistan Region, Iraq - (sarbast.mikael@soran.edu.iq).

Bewar H. Othman, Dept. of Mathematics, Faculty of Science, Soran University, Kurdistan Region, Iraq.

Dept. of Mathematics, Faculty of Science, Soran University, Kurdistan Region, Iraq (bewar.osman@soran.edu.iq).

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Published
2020-06-30
How to Cite
Mikaeel, S., & Othman, B. (2020). Symbolic Methods for Analysing Bifurcations and Chaos of Two Five-Parameter Families of Planar Quadratic Maps. Science Journal of University of Zakho, 8(2), 72-79. https://doi.org/10.25271/sjuoz.2020.8.2.723
Section
Science Journal of University of Zakho