Some aspects of modeling and analysis of complex biological systems using time Petri nets

Models of complex biological systems can be built using different types of Petri nets. Qualitative nets, for example, can be successfully used to obtain a model of such a system and on its basis a structure-based analysis can be performed. Time is an important factor influencing a whole biological system behaviour and in many cases it should be considered during building a model of such a system. In this paper various types of time Petri nets have been described and methods for studying corresponding models have been discussed. In particular, an algorithm using time parameters to enhance t-invariants based analysis is proposed. This algorithm allows for calculation of the minimal and maximal numbers of tokens (respectively, for an optimistic and pessimistic case) in particular places necessary to assure that all transitions from a given t-invariant support will be able to fire. Additionally, to address the problem of the proper assignment of time values to transitions, the known methods for calculation and evaluation of such time parameters based on the net structure have also been discussed.