Summary
An extension of a collocation based periodic orbit continuation framework developed for piecewise-smooth delay differential equations is presented, to incorporate neutral delayed terms in the problem formulation. Numerical difficulties arising from the consequent disappearance of the natural smoothing property of delay differential equations are discussed in detail, along with mesh improvement approaches which may help mitigate this issue. The capabilities of the extended continuation framework are demonstrated on a low-degree-of-freedom traffic dynamics model, where driver behaviour is modelled with the help of piecewise-smooth controllers, which also take reaction delays into account.
