A discrete fractional-order prion model motivated by Parkinson's disease
type: Item
instance of: scholarly article
title: A discrete fractional-order prion model motivated by Parkinson's disease
zbMATH Open document ID: 1459.92040
DOI: 10.1155/2020/4308589
author: M. F. Elettreby
author: E. Ahmed
author: Ali S. Al-Qahtani
published in: Mathematical Problems in Engineering
publication date: 2020-10-12T00:00:00Z
review text: Summary: A prion differential equation model motivated by Parkinson's disease (PD) is studied. A fractional-order form of this model is proposed. After that, we discretized fractional-order Parkinson's disease model. A sufficient condition for the existence and the uniqueness of a solution to the system is obtained. The stability of the fixed points of the system is achieved by using the Jury test. The impacts of varying the parameters of the system are examined. Under certain conditions, the system undergoes some kinds of bifurcations. We observe that the model loses its stability through double-period bifurcation to chaotic behavior as the growth rate increases. Also, the system stabilizes by increasing the memory parameter, and the contact rate between the two types of prions increases. The system shows rich dynamical behavior for a wide range of the values of the parameters.
Mathematics Subject Classification ID: 92C50
Mathematics Subject Classification ID: 34A08
zbMATH DE Number: 7259604
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/4308589
OpenAlex ID: W3049106832
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description: scientific article; zbMATH DE number 7259604