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Chaos and bifurcations in a discretized fractional model of quasi-periodic plasma perturbations

  • Ahmed Ezzat Matouk ORCID logo EMAIL logo

Abstract

The nonlinear dynamics of a discretized form of quasi-periodic plasma perturbations model (Q-PPP) with nonlocal fractional differential operator possessing singular kernel are investigated. For example, the conditions for the stability and occurrence of Neimark–Sacker (NS) and flip bifurcations in the proposed discretized equations are provided. Moreover, analysis of nonlinearities such as the existence of chaos in this map is proved numerically via bifurcation diagrams, Lyapunov exponents and analytically via Marotto’s Theorem. Also, some simulation results are utilized to confirm the theoretical results and to show that the obtained map exhibits double routes to chaos: one is via flip bifurcation and the other is via NS bifurcation. Furthermore, more complex dynamical phenomena such as existence of closed invariant curves, homoclinic orbits, homoclinic connections, period 3 and period 4 attractors are shown. This kind of research is useful for physicists who work with tokamak models.


Corresponding author: Ahmed Ezzat Matouk, Department of Mathematics, College of Science, Majmaah University, Al-Zulfi, Al-Majmaah 11952, Saudi Arabia; and College of Engineering, Majmaah University, Al-Majmaah 11952, Saudi Arabia, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2020-05-06
Revised: 2021-02-10
Accepted: 2021-02-16
Published Online: 2021-05-13
Published in Print: 2022-12-16

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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