A novel fractional memristor-based Grassi-Miller map: Hyperchaotic behavior and coexistence of attractors

Abstract

Referring to fractional memristor-based discrete systems, this paper contributes to the field by presenting a new fourth-dimensional (4D) hyperchaotic memristor-based fractional map. The conceived system, obtained by combining a non-integer order discrete memristor with the Grassi-Miller map, is characterized by some special features, which include the absence of equilibrium point and the coexistence of various chaotic and hypechaotic attractors. Numerical techniques including phase plots, Lyapunov exponents and bifurcation diagrams are used to highlight the complex dynamic behavior of the suggested 4D fractional memristor-based Grassi-Miller map.

Keywords

• Discrete fractional calculus
• Memristor
• Hidden dynamics
• Grassi-Miller map