A Reliable Numerical Algorithm for Stabilizing of the 2-Dimensional Logistic Hyperchaotic Trajectory

Authors

  • Shaymaa H. Salih Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, IRAQ.
  • Nadia Al-Saidi Department of Applied Sciences, University of Technology, Baghdad, IRAQ
  • Radhi A. Zboon Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, IRAQ.

DOI:

https://doi.org/10.23851/mjs.v33i1.1048

Keywords:

Chaos theory, Logistic map, Bifurcation, Lyapunov exponent

Abstract

The dynamical system is the concept used to describe the behavior of several phenomena in our daily life. It comes in two types; linear and nonlinear. Two essential properties characterize the latter, stability and chaos, which in turn are classified into two categories, continuous and discrete, for the models that exhibiting chaotic behavior, which sometimes needs to be stabilized and synchronized. There are various approaches for such a purpose. In this work, the chaotic behavior of the 2D-logistic map is stabilized without adding any control parameters. This approach is considered efficient for models whose analytic solutions are challenging to find. Moreover, the modulus for the Jacobian matrix eigenvalues is greater than unity. Finally, the feasibility and effectiveness of this stabilizing method are demonstrated through some Numerical analysis.

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Published

2022-03-10

How to Cite

[1]
S. H. Salih, N. Al-Saidi, and R. A. Zboon, “A Reliable Numerical Algorithm for Stabilizing of the 2-Dimensional Logistic Hyperchaotic Trajectory”, MJS, vol. 33, no. 1, pp. 51–56, Mar. 2022.

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Section

Mathematics