Startseite A modified simple chaotic hyperjerk circuit: coexisting bubbles of bifurcation and mixed-mode bursting oscillations
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A modified simple chaotic hyperjerk circuit: coexisting bubbles of bifurcation and mixed-mode bursting oscillations

  • Gervais Dolvis Leutcho ORCID logo EMAIL logo , Jacques Kengne , Alexis Ngoumkam Negou , Theophile Fonzin Fozin , Viet-Thanh Pham und Sajad Jafari
Veröffentlicht/Copyright: 23. Juni 2020
Zeitschrift für Naturforschung A
Aus der Zeitschrift Zeitschrift für Naturforschung A Band 75 Heft 7

Abstract

A relatively simple chaotic hyperjerk circuit, which is the modified chaotic hyperjerk system [Dalkiran and Sprott, IJBC 2016] is proposed and investigated in this paper. Only one semiconductor diode modelled the nonlinear function capable of rich and complex dynamical behaviours of the system. We investigate a new kind of behaviours name “bubbles of bifurcation’’ (referred as BsB hereafter) observed here for the first time in the hyperjerk system. An interesting phenomenon of mixed-mode bursting oscillations (MMBOs) is also investigated. The complex dynamics of the novel oscillator (such as MMBOs, BsB, offset boosting and multistability) with respect to its parameters and initial conditions are uncovered using bifurcation diagrams, Lyapunov exponents (LE) and phase portraits. As another interesting property of this circuit, some parameter regions are determined for the existence of coexisting BsB and the coexistence of asymmetric mixed-mode bursting oscillations. Let us emphasized that the complex phenomena observed in this work is very rare in the literature and henceforth merit dissemination. Finally, a physical circuit is constructed to demonstrate some experimental observation of MMBOs.

Keywords: bubbles of bifurcation (BsB); hyperjerk circuit; mixed-mode bursting oscillation (MMBOs); multistability
Corresponding author: Gervais Dolvis Leutcho, Research Unit of Laboratory of Condensed Matter, Electronics and Signal Processing (UR-MACETS) Department of Physics, Faculty of Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon; Research Unit of Laboratory of Automation and Applied Computer (LAIA), Electrical Engineering Department of IUT-FV, University of Dschang, P.O. Box 134, Bandjoun, Cameroon, E-mail:

Funding source: Agence Universitaire de la Francophonie

Award Identifier / Grant number: AUF/EI/DF/2019

Funding source: Romania government

Acknowledgments

Gervais Dolvis Leutcho acknowledges AUF (Agence Universitaire de la Francophonie) through the Doctoral Fellowship Program « Eugen Ionescu» (AUF/EI/DF/2019) for the financial support. He is indebted to Prof. Dr. Ing. M. Borda and Prof. Dr. Ing. R. Terebes (TUCN) for the hospitality under « Eugen Ionescu » Fellowship as well as all the valuable discussions and reading of this paper. He would like to thank the Romania government for its financial support.

  1. Research funding: The research was funded by the Agence Universitaire de la Francophonie and Romania government.

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

  3. Employment or leadership: None declared.

  4. Honorarium: None declared.

  5. Conflict of interest statement: The authors declare no conflict of interest.

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Received: 2020-01-21
Accepted: 2020-05-03
Published Online: 2020-06-23
Published in Print: 2020-07-28

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. General
  3. Remote magnetically controlled drug release from electrospun composite nanofibers: design of a smart platform for therapy of psoriasis
  4. Dynamical Systems & Nonlinear Phenomena
  5. A modified simple chaotic hyperjerk circuit: coexisting bubbles of bifurcation and mixed-mode bursting oscillations
  6. Dynamics of a discrete-time system with Z-type control
  7. Dynamic response of axially loaded end-bearing rectangular closed diaphragm walls
  8. Hydrodynamics
  9. Admissibility conditions for Riemann data in shallow water theory
  10. Numerical study on the rotating electro-osmotic flow of third grade fluid with slip boundary condition
  11. Solid State Physics & Materials Science
  12. Ultrasonic study of Si-oil based magneto-rheological fluid
  13. Electromagnetic propagation characteristics of one-dimensional photonic crystals with metal layers in quasi-parity-time (PT)-symmetric system
  14. Thermodynamics & Statistical Physics
  15. Combined influence of axial electron temperature and exponential plasma density ramp on the self-focusing of a chirped laser in plasma
https://doi.org/10.1515/zna-2020-0022
Schlagwörter für diesen Artikel
bubbles of bifurcation (BsB); hyperjerk circuit; mixed-mode bursting oscillation (MMBOs); multistability

Artikel in diesem Heft

  1. Frontmatter
  2. General
  3. Remote magnetically controlled drug release from electrospun composite nanofibers: design of a smart platform for therapy of psoriasis
  4. Dynamical Systems & Nonlinear Phenomena
  5. A modified simple chaotic hyperjerk circuit: coexisting bubbles of bifurcation and mixed-mode bursting oscillations
  6. Dynamics of a discrete-time system with Z-type control
  7. Dynamic response of axially loaded end-bearing rectangular closed diaphragm walls
  8. Hydrodynamics
  9. Admissibility conditions for Riemann data in shallow water theory
  10. Numerical study on the rotating electro-osmotic flow of third grade fluid with slip boundary condition
  11. Solid State Physics & Materials Science
  12. Ultrasonic study of Si-oil based magneto-rheological fluid
  13. Electromagnetic propagation characteristics of one-dimensional photonic crystals with metal layers in quasi-parity-time (PT)-symmetric system
  14. Thermodynamics & Statistical Physics
  15. Combined influence of axial electron temperature and exponential plasma density ramp on the self-focusing of a chirped laser in plasma
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