A new mathematical model for the glycolysis phenomenon involving Caputo fractional derivative: Well posedness, stability and bifurcation. (January 2021)

• Record Type: Journal Article
• Authors: Belmahi, Naziha; Shawagfeh, Nabil
• Is Part Of: Chaos, solitons and fractals. Volume 142(2021)
• Publication Date: 2021-01
• Subjects: Fractional derivative -- Selkov model -- Reaction diffusion system -- Global existence -- Spatially homogeneous -- Hopf bifurcation; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.110520
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: In this work, we propose a new model for the glycolysis phenomenon involving Caputo derivative. We establish rigourously the existence and uniqueness of a positive solution to this system, then we discuss the stability and the Hopf bifurcation. The dynamics exhibited by the fractional system showed that the new model represents the glycolysis phenomenon more accurately than the corresponding classical first order system. Differences are illustrated by performing some numerical simulations, in which our main findings are confirmed.