Symmetries in Timed Continuous Petri Nets

The dynamics of timed continuous Petri nets under infinite server semantics can be expressed by a piecewise linear system with polyhedral regions. In this paper we establish connections between the qualitative behavior of the dynamics of the continuous marking and the net structure. In particular, Petri nets with symmetries are addressed where symmetry is understood as a permutation symmetry of the nodes. It is shown that such a symmetry leads to a permutation of the regions and equivariant dynamics.