Noise in nonsmooth dynamical systems

This article-based thesis comprises a collection of four articles, each of which constitutes a chapter, written and formatted in pre-print manuscript form. The general aim underlying these articles is to understand how noise affects the dynamics of nonsmooth dynamical systems. Nonsmooth dynamical systems arise naturally when modelling systems in engineering and applied sciences and are characterised by sudden changes in system properties. Examples of naturally arising nonsmooth systems include mechanical systems involving impacts or friction, economic or sociological systems with decision thresholds, switching electronic systems and climate systems with sharp ice-cap boundaries. The dynamical systems resulting from these models exhibit several unique behaviours including new types of bifurcations called discontinuity induced bifurcations, which can be considered the hallmark of nonsmooth systems. A level of noise or randomness is also ubiquitous in real-world systems and has been shown to have significant nontrivial effects on smooth but nonlinear systems close to bifurcation points. As a result, it is both interesting an important to understand the effects of noise on the unique dynamics possible in nonsmooth systems