English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

This paper concerns stochastic perturbations of piecewise-smooth ODE systemsrelevant for vibro-impacting dynamics, where impact events constitute theprimary source of randomness. Such systems are characterised by the existenceof switching manifolds that divide the phase space into regions where thesystem is smooth. The initiation of impacts is captured by a grazingbifurcation, at which a periodic orbit describing motion without impactsdevelops a tangential intersection with a switching manifold. Oscillatorydynamics near regular grazing bifurcations are described by piecewise-smoothmaps involving a square-root singularity, known as Nordmark maps. We considerthree scenarios where coloured noise only affects impacting dynamics, andderive three two-dimensional stochastic Nordmark maps with the noise appearingin different nonlinear or multiplicative ways, depending on the source of thenoise. Consequently the stochastic dynamics differs between the three noisesources, and is fundamentally different to that of a Nordmark map with additivenoise. This critical dependence on the nature of the noise is illustrated witha prototypical one-degree-of-freedom impact oscillator.

The influence of localised randomness on regular grazing bifurcations with applications to impacting dynamics