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

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.

Keywords

• chaos theory
• logistic map
• bifurcation
• lyapunov exponent