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This paper concerns two-dimensional Filippov systems --- ordinarydifferential equations that are discontinuous on one-dimensional switchingmanifolds. In the situation that a stable focus transitions to an unstablefocus by colliding with a switching manifold as parameters are varied, a simplesufficient condition for a unique local limit cycle to be created isestablished. If this condition is violated, three nested limit cycles may becreated simultaneously. The result is achieved by constructing a Poincar\'e mapand generalising analytical arguments that have been employed for continuoussystems. Necessary and sufficient conditions for the existence ofpseudo-equilibria (equilibria of sliding motion on the switching manifold) arealso determined. For simplicity only piecewise-linear systems are considered.

Hopf-like boundary equilibrium bifurcations involving two foci in Filippov systems