Bifurcations in Timed Continuous Petri Nets

Abstract

This paper is concerned with the steady-state throughput changes due to firing rate variations in Timed Continuous Petri Nets (TCPN) under infinite server semantics. Jumps in this value (equivalently in the steady state marking) are bifurcations. It presents a novel structural characterization of bifurcations based on the P-semiflows and T-semiflows appearing in the TCPN configurations. In order to give this characterization, first strongly connected and conservative JF-TCPN (join free TCPN) are studied. Bifurcations are not possible in this class of nets. Afterwards, strongly connected and consistent CF-TCPN (choice free TCPN) are addressed. It is shown that this class of nets does not exhibit bifurcations. This kind of result is extended to topologically Equal-conflict nets when we vary the firing rates of transitions in conflict in the same proportion. Based on these results, bifurcations in MTS-TCPN (Mono-T-Semiflow TCPN) including non-equal conflicts and joins are addressed. The main result in this class of nets states that bifurcations appear when the places restricting the transition's flow in a certain configuration do not belong to the support of any net P-semiflow. Finally, this work presents a relationship between bifurcations and non monotonic throughput in this class of systems.