## Module 1: Stochastic Simulator

When looking to analyse phenomenological bifurcations of stochastic chemical systems, sophisticated tools are required in order to be able to approximate the invariant distribution of the system. In particular, a suitable methods are required to restrain the exponential growth of the complexity for efficient solving the steady-state chemical Fokker-Planck equation.

Tensor-structured methods are included with the StoBifAn in this regard. These methods generalise the concept of separation of variables, where the conventional matrices and vectors are represented with some low-parametric tensor format. Thus, elementary algebraic operations can be done with such low-parametric representations. The package help users to assemble operators and solve the stationary problems by simply typing in the network structure and parameters. Note that this part relies on the TT-toolbox.

## Module 2: Multi-scale Computations

For chemical systems with more species than we can feasibly solve the steady-state Fokker Planck equation, numerical multiscale reductions can be used. The Constrained Multiscale Algorithm (CMA) allows us to approximate the dynamics of up to three slow species in the system by an effective SDE. Once the reduction has taken place, then adaptive FEMs can be used to solve for the invariant density of the slow variables. In the future we also hope to add tools to automatically identify suitable slow variables.

## Module 3: Bifurcation Analyser

Once the approximated invariant density (either of the full system, or of the reduced system) have been found over a range of reaction parameter values, then bifurcation analysis of the phenomological changes in the distributions can be undertaken. Tools exist for the identification of local maxima in the densities (corresponding to (meta-)stable states, and for the identification of toroidal features in the density where they might exist, indicating oscillations.

## Module 4: Parametric Analyser

With support from tensor data format, the StoBifAn has the power to solve the system with virtually all possible values of the unknown parameters simultaneously. The resulting data are stored in a tensor-structure that enables efficient manipulations. In this way, StoBifAn allows users to apply classic algorithms to conduct parametric analysis.

## Compatibility with SBML

The Systems Biology Markup Language (SBML), is a markup language for the description of models in systems biology, including biochemical networks. As such, we plan to generalise the tools within the SBAT in order to be able to read general biochemical networks. Currently the biochemical network models are hard-coded, but this functionality will be added soon.