<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this article, a Modified Sprott <italic>C</italic> system is considered. The stability of equilibrium points and the occurrence of Hopf bifurcation in the system are investigated. It has been proved that the system displays a Hopf bifurcation at <italic>α</italic> = 0. Additionally, by applying normal form theory, the stability, direction and increase (or decrease) of the period of bifurcating periodic solutions of the system are illustrated. It has been shown that the solutions of bifurcating periodic solutions at the bifurcation value <italic>α</italic> = 0 are unstable. The type of Hopf bifurcation is subcritical and the periods of the bifurcating periodic solutions increase.</p>
</abstract>

In this article, a Modified Sprott C system is considered. The stability of equilibrium points and the occurrence of Hopf bifurcation in the system are investigated. It has been proved that the system displays a Hopf bifurcation at α = 0. Additionally, by applying normal form theory, the stability, direction and increase (or decrease) of the period of bifurcating periodic solutions of the system are illustrated. It has been shown that the solutions of bifurcating periodic solutions at the bifurcation value α = 0 are unstable. The type of Hopf bifurcation is subcritical and the periods of the bifurcating periodic solutions increase.

Stability and Hopf Bifurcation in a Modified Sprott <italic>C</italic> System

Department of Mathematics, College of Basic Education

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Stability and Hopf Bifurcation in a Modified Sprott  System

In this article, a Modified Sprott C system is considered. The stability of equilibrium points and the occurrence of Hopf bifurcation in the system are...

Stability and Hopf Bifurcation in a Modified Sprott C System

Online veröffentlicht: 19. Juli 2024

Seitenbereich: -

Eingereicht: 28. Dez. 2022

Akzeptiert: 13. Juni 2024

DOI: https://doi.org/10.2478/tmmp-2024-0012

Schlüsselwörter
Hopf Bifurcation, Normal Form Theory, Periodic Solutions

© 2024 Rizgar H. Salih et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Stability and Hopf Bifurcation in a Modified Sprott C System

Online veröffentlicht: 19. Juli 2024

Seitenbereich: -

Eingereicht: 28. Dez. 2022

Akzeptiert: 13. Juni 2024

DOI: https://doi.org/10.2478/tmmp-2024-0012

SchlüsselwörterHopf Bifurcation, Normal Form Theory, Periodic Solutions

© 2024 Rizgar H. Salih et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Schlüsselwörter
Hopf Bifurcation, Normal Form Theory, Periodic Solutions