On Class of Fractional-Order Chaotic or Hyperchaotic Systems in the Context of the Caputo Fractional-Order Derivative
In this paper, we consider a class of fractional-order systems described by the Caputo derivative. &e behaviors of the
dynamics of this particular class of fractional-order systems will be proposed and experienced by a numerical scheme to
obtain the phase portraits. Before that, we will provide the conditions under which the considered fractional-order system’s
solution exists and is unique. &e fractional-order impact will be analyzed, and the advantages of the fractional-order
derivatives in modeling chaotic systems will be discussed. How the parameters of the model influence the considered
fractional-order system will be studied using the Lyapunov exponents. &e topological changes of the systems and the
detection of the chaotic and hyperchaotic behaviors at the assumed initial conditions and the considered fractional-order
systems will also be investigated using the Lyapunov exponents. &e investigations related to the Lyapunov exponents in the
context of the fractional-order derivative will be the main novelty of this paper. &e stability analysis of the model’s
equilibrium points has been focused in terms of the Matignon criterion.
Auteur(s) : Ndolane Sene and Ameth Ndiaye
Pages : 15
Année de publication : 2020
Revue : Journal of Mathematics
N° de volume : 2020
Type : Article
Statut Editorial : Internationale
Mise en ligne par : NDIAYE Ameth