Coupled Discrete Fractional-Order Logistic Maps

Abstract

This paper studies a system of coupled discrete fractional-order logistic maps, modeled by Caputo’s delta fractional difference, regarding its numerical integration and chaotic dynamics. Some interesting new dynamical properties and unusual phenomena from this coupled chaotic-map system are revealed. Moreover, the coexistence of attractors, a necessary ingredient of the existence of hidden attractors, is proved and analyzed.

Keywords

• discrete fractional-order system
• caputo delta fractional difference
• fractional-order difference equation
• stability
• hidden attractor