Vol. 9 No. 2 (2025): Vol 9, Iss 2, Year 2025
Articles

A Study of Hopf and Pitchfork Bifurcations in Planar Dynamical Systems

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  • Geethalakshmi S,
  • Kalaiyarasi S,
  • Saraswathi D,
  • Vignesh K
Geethalakshmi S
Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur, Tamil Nadu, South India
Kalaiyarasi S
Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur, Tamil Nadu, South India.
Saraswathi D
Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur, Tamil Nadu, South India.
Vignesh K
Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur, Tamil Nadu, South India
DOI: https://doi.org/10.26524/cm217
Published December 20, 2025
Keywords
  • Bifurcation , Hopf bifurcation, Non-autonomous , Supercritical, planar system.
How to Cite
Geethalakshmi S, Kalaiyarasi S, Saraswathi D, & Vignesh K. (2025). A Study of Hopf and Pitchfork Bifurcations in Planar Dynamical Systems. Journal of Computational Mathematica, 9(2), 39-50. https://doi.org/10.26524/cm217

Abstract

Hopf bifurcation in continuous and discrete planar systems is analyzed in this study along with the prerequisites for periodic solution emergence. It investigates the stability of both supercritical and subcritical conditions. Using examples and normal form analysis, the connection between Hopf and pitchfork bifurcations is also demonstrated.

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