HOPF BIFURCATIONS IN DYNAMICAL SYSTEMS VIA ALGEBRAIC TOPOLOGICAL METHOD

Authors

  • I. Jawarneh Department of Mathematics, Al-Hussein Bin Talal University, Ma'an 71111, Jordan Author
  • Z. Altawallbeh Department of Mathematics, Tafila Technical University, Tafila 66110, Jordan Author

DOI:

https://doi.org/10.57016/MV-rx451is8

Keywords:

Supercritical Hopf bifurcation, subcritical Hopf bifurcation, stable limit cycle, unstable limit cycle, homological Conley index, Morse sets

Subjects:

55-08, 37B30, 37G15, 37M20

Abstract

A nonlinear phenomenon in nature is often modeled by a system of differential equations with parameters. The bifurcation occurs when a parameter varies in such systems, causing a qualitative change in its solution. In this paper, we study one of the most exciting bifurcations, which is Hopf bifurcation. We use tools from algebraic topology to analyze and reveal supercritical and subcritical Hopf bifurcations.

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Published

2023-07-15

Issue

Vol. 75 No. 3 (2023): Vol. 75, Issue 3

Section

Articles

License

Copyright (c) 2023 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.