Discontinuity Induced Bifurcations in Timed Continuous Petri Nets

In this contribution the dynamics of timed continuous Petri nets with infinite server semantics under variation of firing rates are studied. The systems are described by continuous piecewise linear systems with polyhedral regions. It is well known that the throughput of such systems may change discontinuously by variation of a firing rate. We identify these jumps in the throughput with discontinuity induced bifurcations. They occur when the steady state marking, that depends on the firing rate, hits a boundary between regions of the piecewise linear system and loses hyperbolicity. Such bifurcations affect the robustness of the system with respect to a variation of firing rates and are thus critical for control problems.