Design and analysis of discrete fractional-order chaotic map with offset-boosting behavior

Abstract

This paper presents a 3D discrete fractional-order chaotic map (DFOCM) with offset-boosting behavior based on the memristor. Different from the integer-order chaotic map, the offset-boosting behavior of the DFOCM with parameter offset is associated with the initial value, primarily due to the unique memory properties of fractional-order differences. In addition, rich dynamical properties of the DFOCM are examined using the 0-1 test, maximal Lyapunov exponent, phase diagram, and bifurcation diagram. Numerical simulations show that this DFOCM exhibits more complex dynamical behavior than its integer-order one. Meanwhile, the multistability and conditional symmetry of the DFOCM are studied. The unpredictability and high pseudo-randomness of the chaotic sequence produced by the DFOCM are confirmed by the SE complexity. Finally, the suggested DFOCM is implemented on the DSP hardware platform, demonstrating the physical feasibility of the numerical simulation.