52 citations · 159 across the 19 of their papers we have counts for
6 papers · 2 filters
Smoothing tautologies, hidden dynamics, and sigmoid asymptotics for piecewise smooth systems
Mike R. Jeffrey
Switches in real systems take many forms, such as impacts, electronic relays, mitosis, and the implementation of decisions or control strategies. To understand what is lost, and wh…
The ghosts of departed quantities in switches and transitions
Mike R. Jeffrey
Transitions between steady dynamical regimes in diverse applications are often modelled using discontinuities, but doing so introduces problems of uniqueness. No matter how quickly…
Fast phase randomisation via two-folds
D. J. W. Simpson, M. R. Jeffrey
A two-fold is a singular point on the discontinuity surface of a piecewise-smooth vector field, at which the vector field is tangent to the discontinuity surface on both sides. If…
Fold singularities of nonsmooth and slow-fast dynamical systems -- equivalence by the hidden dynamics approach
Mike R. Jeffrey
The {\it two-fold singularity} has played a significant role in our understanding of uniqueness and stability in piecewise smooth dynamical systems. When a vector field is disconti…
Fold singularities of nonsmooth and slow-fast dynamical systems -- equivalence through regularization
Mike R. Jeffrey
The two-fold singularity has played a significant role in our understanding of uniqueness and stability in piecewise smooth dynamical systems. When a vector field is discontinuous…
Nonsmooth analogues of slow-fast dynamics -- pinching at a folded node
Mathieu Desroches, Mike R. Jeffrey
The folded node is a singularity associated with loss of normal hyperbolicity in systems where mixtures of slow and fast timescales arise due to singular perturbations. Canards are…