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On the Double-Zero Bifurcation of Jerk Systems

Author

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  • Cristian Lăzureanu

    (Department of Mathematics, Politehnica University Timişoara, P-ta Victoriei 2, 300006 Timişoara, Romania
    Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara, Parvan Blv. 4, 300223 Timişoara, Romania)

Abstract

In this paper, we construct approximate normal forms of the double-zero bifurcation for a two-parameter jerk system exhibiting a non-degenerate fold bifurcation. More precisely, using smooth invertible variable transformations and smooth invertible parameter changes, we obtain normal forms that are also jerk systems. In addition, we discuss some of their parametric portraits.

Suggested Citation

  • Cristian Lăzureanu, 2023. "On the Double-Zero Bifurcation of Jerk Systems," Mathematics, MDPI, vol. 11(21), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4468-:d:1269357
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    References listed on IDEAS

    as
    1. Cristian Lăzureanu & Jinyoung Cho, 2023. "On Hopf and Fold Bifurcations of Jerk Systems," Mathematics, MDPI, vol. 11(20), pages 1-15, October.
    2. Weipeng Lyu & Shaolong Li & Zhenyang Chen & Qinsheng Bi, 2023. "Bursting Dynamics in a Singular Vector Field with Codimension Three Triple Zero Bifurcation," Mathematics, MDPI, vol. 11(11), pages 1-20, May.
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    1. Cristian Lăzureanu & Jinyoung Cho, 2023. "On Hopf and Fold Bifurcations of Jerk Systems," Mathematics, MDPI, vol. 11(20), pages 1-15, October.
    2. Cristian Lăzureanu & Jinyoung Cho, 2024. "On a Family of Hamilton–Poisson Jerk Systems," Mathematics, MDPI, vol. 12(8), pages 1-12, April.

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