On the Double-Zero Bifurcation of Jerk Systems

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.

On a Family of Hamilton–Poisson Jerk Systems

“…Despite their simple form, jerk systems provide examples of chaotic behavior (see, e.g., [2][3][4]). Bifurcations in the dynamics of jerk systems are also analyzed (see, e.g., [5][6][7][8]).…”