Sliding in a piecewise-smooth dynamical system with a hold-on effect

•We study a piecewise smooth hybrid (hold-on) dynamical system.•The hold-on term introduces new discontinuity induced behavior to the system.•We suggest an approach to explain and describe this behavior.•We examine different structural models of the system to demonstrate the new effect.

In this paper, we study a piecewise-smooth dynamical system of a Filippov type that has a specific discontinuity in the form of a hold-on term. The system resembles a driven dry-friction oscillator with the difference that the magnitude of the friction depends on the value of a local maximum of the oscillator displacement. Due to the hold-on term, the definition of the sliding region is not trivial. Along with a sliding region that is found analytically and is valid for any orbits, there exists a sliding region that we name ‘virtual’ because it is specific for each particular orbit. The existence of the virtual sliding region is explained by the specific discontinuity — the hold-on term — and the behavior associated with the sliding region and its boundaries can be considered as a new type of sliding-associated behavior.