This article investigates a non-equilibrium chaotic system in view of commensurate and incommensurate fractional orders and with only one signum function. By varying some values of the fractional-order derivative together with some parameter values of the proposed system, different dynamical behaviors of the system are explored and discussed via several numerical simulations. This system displays complex hidden dynamics such as inversion property, chaotic bursting oscillation, multistabilty, and coexisting attractors. Besides, by means of adapting certain controlled constants, it is shown that this system possesses a three-variable offset boosting system. In conformity with the performed simulations, it also turns out that the resultant hidden attractors can be distributively ordered in a grid of three dimensions, a lattice of two dimensions, a line of one dimension, and even arbitrariness in the phase space. Through considering the Caputo fractional-order operator in all performed simulations, phase portraits in two- and three-dimensional projections, Lyapunov exponents, and the bifurcation diagrams are numerically reported in this work as beneficial exit results.

In recent years, some efforts have been devoted to nonlinear dynamics of fractional discrete-time systems. A number of papers have so far discussed results related to the presence of chaos in fractional maps. However, less results have been published to date regarding the presence of hyperchaos in fractional discrete-time systems. This paper aims to bridge the gap by introducing a new three-dimensional fractional map that shows, for the first time, complex hyperchaotic behaviors. A detailed analysis of the map dynamics is conducted via computation of Lyapunov exponents, bifurcation diagrams, phase portraits, approximated entropy and Co complexity. Simulation results confirm the effectiveness of the approach illustrated herein.

Most of the papers published so far on fractional discrete systems are related to theoretical results on their chaotic behaviors or to applications based on the mathematical modeling of the chaotic phenomena. No paper has been published to date regarding the hardware implementation of hyperchaotic fractional maps. This manuscript makes a contribution to the topic by presenting the first example of hardware implementation of hyperchaotic fractional maps. In particular, by exploiting the Grunwald–Letnikov difference operator, the paper introduces a new version of the fractional Grassi–Miller map. The system dynamics are analyzed via bifurcation diagrams and Lyapunov exponents, showing that the conceived map is hyperchaotic when the fractional order � belongs to the interval [0.966,1]. Finally, a hardware implementation of the fractional map is illustrated, with the aim to concretely highlight the presence of hyperchaos in physical systems described by fractional difference equations. Arduino, an open-source platform, has been used to illustrate the simplicity as well as the feasibility of the implementation.

We propose a new approach for modeling a High Electron Mobility Transistor (HEMT) using that of Gaussian Process Regression one (GPR), to improve the current-voltage characteristics of HEMT transistor for using in electronic and biological domain or any other domain that needs it. The study and development of a new Atlas Silvaco device are taking into account the impact of several geometric and electric parameters; we focus on the electrical performances of the double gate field plate In0.2Ga0.8As/Al0.3Ga0.7As HEMT including double heterostructure; we compare the numerical simulation using 2D Atlas Silvaco simulator with the extracted experimental results. Then we validate our model by GPR approach. The GPR approach opens promising opportunities for devices modeling without knowing too much the device physics properties. The obtained results give better performances which lead to fabricate devices with better electrical properties for promoting further investigation.