Editorial

Abstract

This issue is dedicated to nonsmooth dynamics, particularly the widening applications where dynamics is modelled by nonsmooth differential equations. The modeling of electrical or mechanical switches as nonsmooth can be traced throughout the (at least) 90-year history in which nondifferentiable terms, such as sign or step functions, have been turning up in differential equations. In recent decades, nonsmooth models have found increasing use in areas like contact mechanics, climate modeling, and the life sciences, among others, with a wealth of new theory and novel dynamical phenomena discovered along the way. Our aim here is to give just a partial snapshot of the current landscape of research topics in the field. We open with Paul Glendinning's article extending a classic phenomenon of nonlinear dynamics — a form of chaos introduced by Leonid Pavlovich Shilnikov — to nonsmooth systems. The scenario introduces a fundamental notion of nonsmooth dyamics, that of trajectories (in this case the crucial homoclinic orbit) that can ‘slide’ along a discontinuity. Shilnikov's scenario is moreover shown to occur naturally as an equilibrium hits a discontinuity, helping with a fundamental yet complex problem, namely that of extending the notion of boundary equilibrium bifurcations beyond systems of two variables.