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On a Family of Hamilton–Poisson Jerk Systems

Author

Listed:
  • 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 Timşoara, Parvan Blv. 4, 300223 Timişoara, Romania
    These authors contributed equally to this work.)

  • Jinyoung Cho

    (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 Timşoara, Parvan Blv. 4, 300223 Timişoara, Romania
    These authors contributed equally to this work.)

Abstract

In this paper, we construct a family of Hamilton–Poisson jerk systems. We show that such a system has infinitely many Hamilton–Poisson realizations. In addition, we discuss the stability and we prove the existence of periodic orbits around nonlinearly stable equilibrium points. Particularly, we deduce conditions for the existence of homoclinic and heteroclinic orbits. We apply the obtained results to a family of anharmonic oscillators.

Suggested Citation

  • Cristian Lăzureanu & Jinyoung Cho, 2024. "On a Family of Hamilton–Poisson Jerk Systems," Mathematics, MDPI, vol. 12(8), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1260-:d:1380122
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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.
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