A NEW FRACTIONAL ORDER 6D CHAOTIC MODEL: STUDY OF MODEL DYNAMICS, SYSTEM STRUCTURE GRAPH, ELECTRONIC CIRCUIT REALIZATION AND FRACTIONAL CONTROL

Abstract

A new fractional 6D chaotic model is constructed in this paper. The new fractional 6D chaotic model has six positive parameters plus the fractional order with eight nonlinear terms. The complicated chaotic dynamics of the new fractional 6D model is presented and analyzed. The basic properties of this model are studied and its chaotic attractors, dissipative feature, symmetry, equilibrium points, Lyapunov Exponents are investigated. The new dynamics of the 6D fractional model is numerically simulated using Matlab software. In addition, utilizing the graph theory tools certain structural characteristics are calculated. An electrical circuit is built to implement the new 5.4 fractional order 6D model. Finally, an active fractional order controller is proposed to control the new model at different fractional orders. The chaos of the new model is very useful and can be used to produce random keys for data encryption.