On a Family of Hamilton–Poisson Jerk Systems

Cristian Lăzureanu () and Jinyoung Cho
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Cristian Lăzureanu: Department of Mathematics, Politehnica University Timişoara, P-ta Victoriei 2, 300006 Timişoara, Romania
Jinyoung Cho: Department of Mathematics, Politehnica University Timişoara, P-ta Victoriei 2, 300006 Timişoara, Romania

Mathematics, 2024, vol. 12, issue 8, 1-12

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.

Keywords: jerk systems; Hamilton–Poisson systems; stability; periodic orbits; homoclinic and heteroclinic orbits (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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