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