On Hopf and Fold Bifurcations of 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, 2023, vol. 11, issue 20, 1-15

Abstract: In this paper we consider a jerk system x ˙ = y , y ˙ = z , z ˙ = j ( x , y , z , α ) , where j is an arbitrary smooth function and α is a real parameter. Using the derivatives of j at an equilibrium point, we discuss the stability of that point, and we point out some local codim-1 bifurcations. Moreover, we deduce jerk approximate normal forms for the most common fold bifurcations.

Keywords: jerk systems; local stability; codim-1 bifurcations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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