@article {62552,
	title = {Hyperchaotic fractional Grassi\&ndash;Miller map and its hardware implementation},
	journal = {Integration},
	volume = {80},
	year = {2021},
	month = {2021},
	pages = {13-19},
	abstract = {
	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\&nbsp;mathematical modeling\&nbsp;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{\textendash}Letnikov difference operator, the paper introduces a new version of the fractional Grassi{\textendash}Miller map. The\&nbsp;system dynamics\&nbsp;are analyzed via\&nbsp;bifurcation diagrams\&nbsp;and\&nbsp;Lyapunov exponents, showing that the conceived map is hyperchaotic when the\&nbsp;fractional order\&nbsp;�\&nbsp;belongs to the interval\&nbsp;[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.

},
	isbn = {0167-9260},
	url = {https://www.sciencedirect.com/science/article/abs/pii/S0167926021000584},
	author = {Ouannas, Adel and KHENNAOUI, AMINA-AICHA and Oussaeif, Taki-Eddine and Pham, Viet-Thanh and Grassi, Giuseppe and Zohir Dibi}
}
