Hidden multistability of fractional discrete non-equilibrium point memristor based map
Mohd Taib Shatnawi, Abderrahmane Abbes, Adel Ouannas, Iqbal M. Batiha
Abstract
Abstract At present, the multistability analysis in discrete nonlinear fractional-order systems is a subject that is receiving a lot of attention. In this article, a new discrete non-equilibrium point memristor-based map with γ − th Caputo fractional difference is introduced. In addition, in the context of the commensurate and non-commensurate instances, the nonlinear dynamics of the suggested discrete fractional map, such as its multistability, hidden chaotic attractor, and hidden hyperchaotic attractor, are investigated through several numerical techniques, including Lyapunov exponents, phase attractors, bifurcation diagrams, and the 0 − 1 test. These dynamic behaviors suggest that the fractional discrete memristive map has a hidden multistability. Finally, to validate the presence of chaos, a complexity analysis is carried out using approximation entropy ( ApEn ) and the C 0 measure. The findings show that the model has a high degree of complexity, which is affected by the system parameters and the fractional values.