Development and Evaluation of an Innovative Three-Dimensional Hyperchaotic map

Walaa Hadi Abdulnabi; Sadiq A. Mehdi; Sawsen Abdulhadi Mahmood

doi:10.47831/mjpas.v3i2.223

Authors

Walaa Hadi Abdulnabi Department of Computer Science, Collage of Education, Mustansiriyah University
Sadiq A. Mehdi Department of Computer Science, Collage of Education, Mustansiriyah University
Sawsen Abdulhadi Mahmood Department of Computer Science, Collage of Education, Mustansiriyah University

DOI:

https://doi.org/10.47831/mjpas.v3i2.223

Keywords:

chaotic, Lyapunov exponents, hyper, three-dimensional, unstable, Kaplan-York dimension, sensitivity for initial conditions.

Abstract

we are designing the new system which is 3D hyper-chaotic and subsequently examined the most critical characteristics of this proposed system with a dynamic behavior by using Mathematica software that performs numerical simulations of these dynamic behaviors. The findings indicated that the suggested system has three-dimensional with generates hyper-chaotic attractors, as it has two positive exponents of Lyapunov in (LE1= 1.14247, LE2= 0.01498), which makes it hyper-chaotic, and that it is unstable and possesses the butterfly effect, as its wave form is non-periodic and therefore has non-periodic properties and is dissipative. It has a Kaplan-York dimension as (2.07643). Also the new system is sensitive to any, even very slight, change in initial conditions, is unpredictable, and is complex, and thus possesses the basic dynamical properties of chaotic systems.