On Hopf and Fold Bifurcations of Jerk Systems - Cristian Lăzureanu; Jinyoung Cho (Mathematics, 2023)
In this paper we consider a jerk system <semantics><mover accent="true">x˙</mover>=y,<mover accent="true">y˙</mover>=z,<mover accent="true">z˙</mover>=j(x,y,z,α),</semantics> where j is an arbitrary smooth function and <semantics>α</semantics> 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.