Bifurcations in Piecewise Smooth Systems
David Simpson
Applied Mathematics
A piecewise-smooth continuous dynamical system has a vector field that is
continuous but not everywhere differentiable. We consider the case when the
non-differentiable points lie on manifolds of dimension n-1, in an
n-dimensional phase space. If an equilibrium solution crosses such a manifold
as a system parameter is continuously varied, we expect the eigenvalues that
determine stability to jump discontinuously. In this talk I will describe the
resulting bifurcations unique to piecewise-smooth continuous systems and
identify discontinuous bifurcations in a mathematical model of yeast growth.