Name
Abstract | ||
|---|---|---|
The dynamics of timed continuous Petri nets under infinite server semantics can be expressed in terms of a piecewise linear system with polyhedral regions. In this article, Petri nets with symmetries are considered where symmetry is understood as a permutation symmetry of the nodes. We establish connections between the qualitative dynamical behavior of the continuous marking and the symmetries. In particular, it is shown that such a symmetry leads to a permutation of the regions and to equivariant dynamics. This allows us to identify special flow-invariant sets which can be used for reductions to systems of smaller dimension. For general piecewise linear systems with polyhedral regions, it is shown that equivariant dynamics always implies a permutation of the regions. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1016/j.nahs.2010.05.005 | Nonlinear Analysis: Hybrid Systems |
Keywords | Field | DocType |
Continuous Petri nets,Piecewise linear systems,Symmetries,Equivariant dynamics | Discrete mathematics,Petri net,Equivariant map,Algebra,Permutation,Stochastic Petri net,Piecewise linear function,Homogeneous space,Semantics,Mathematics | Conference |
Volume | Issue | ISSN |
5 | 2 | 1751-570X |
Citations | PageRank | References |
2 | 0.47 | 8 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| albert r meyer | 1 | 3 | 0.86 |
| Michael Dellnitz | 2 | 174 | 20.34 |
| M. Hessel-von Molo | 3 | 2 | 0.47 |