Detecting Attractors in Biological Models with Uncertain Parameters

Digital Bifurcation Analysis of TCP Dynamics

“…The rest of this section gives a brief overview of the parallel algorithm for solving the tSCCs enumeration problem that we have developed in [1].…”

“…This makes our algorithm suitable for use in connection with various kinds of symbolic set representations. The reason for using a parallel algorithm is the necessity to deal with the high computational demands of the method as discussed in [1].…”

“…Of course, such choice cannot be made in advance. The paper [1] discusses the impact of several heuristics that try to approximate this choice.…”

“…One further key difference is that instead of choosing one starting vertex, we need to choose a set of starting vertices with disjoint parametrisation sets that together cover all parametrisations that are present in the currently explored parametrised subgraph. The reason for this, as well as a discussion on heuristics that allow choosing such sets efficiently, can be again found in [1].…”

“…In computer systems, the most typical attractors can be observed in the form of terminal strongly connected components (tSCCs) [38]. We have developed an efficient parallel algorithm for detecting tSCCs in parametrised graphs in [1], and we use this algorithm in our two case studies. We have already successfully applied the digital bifurcation analysis to several models from systems biology [4,5].…”