The plasma parameter dependencies of the dynamics during the expansion of plasma are studied with the use of a versatile particle-in-cell simulation tailored to a plasma expansion experiment [Schr€ oder et al., J. Phys. D: Appl. Phys. 47, 055207 (2014); Schr€ oder et al., Phys. Plasmas 23, 013511 (2016)]. The plasma expansion into a low-density ambient plasma features a propagating ion front that is preceding a density plateau. It has been shown that the front formation is entangled with a wave-breaking mechanism, i.e., an ion collapse [Sack and Schamel, Plasma Phys. Controlled Fusion 27, 717 (1985); Sack and Schamel, Phys. Lett. A 110, 206 (1985)], and the launch of an ion burst [Schr€ oder et al., Phys. Plasmas 23, 013511 (2016)]. The systematic parameter study presented in this paper focuses on the influence on this mechanism its effect on the maximum velocity of the ion front and burst. It is shown that, apart from the well known dependency of the front propagation on the ion sound velocity, it also depends sensitively on the density ratio between main and ambient plasma density. The maximum ion velocity depends further on the initial potential gradient, being mostly influenced by the plasma density ratio in the source and expansion regions. The results of the study are compared with independent numerical studies.