HX-TYPE CHAOTIC (HYPERCHAOTIC) SYSTEM BASED ON FUZZY INFERENCE MODELING

Abstract

In this paper, we investigate HX equations of autonomous system.  The right-hand side of n-dimensional HX equations theoretically consists of 2ⁿ terms.  HX equations seems to be more complicated than the original system.  For autonomous chaotic (hyperchaotic) system with polynomial right-hand side, we obtain its HX equations by termwise modeling.  We find not all coefficients are variable in HX equations.  Even some HX equations are equal to the original chaotic (hyperchaotic) systems.  Under some fuzzy partition, HX-type chaotic (hyperchaotic) system is defined if some of its coefficients is exactly variable.  By adjusting fuzzy partition, a family of chaotic (hyperchaotic) systems can be defined.  They are different but qualitatively similar.  Numerical simulations are provided to verify the existence of HX-type chaotic (hyperchaotic) system.