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Dangerous Border-Collision bifurcations of a piecewise-smooth map
In this paper we study the dangerous border-collision
bifurcations [8] which recently have been numerically
found on piecewise smooth maps characterized by
non-differentiability on some surface in the phase space. The
striking feature of such bifurcations is characterized by exhibiting
a stable fixed point before and after the critical bifurcation
point, but the unbounded behavior of orbits at the critical
bifurcation point.
We consider a specific variable space in order to do an analytical
investigation of such bifurcations and prove the stability of fixed
points. We also extend these bifurcation phenomena for the fixed
points to the multiple coexisting attractors.