ERODE

Evaluation and reduction of stochastic reaction networks, differential equations, and Boolean networks

An all-in-one tool for the numerical solution, stochastic simulation, and minimization of dynamical systems with import/export options for a variety of third-party formats including SBML and Matlab. Main Features

Numerical solvers for differential equations

Supported through the Apache Commons Math library and through a Java porting of the SUNDIALS library.

Stochastic simulation of reaction networks

Gillespie's Direct Method, Gibson and Bruck's Next Reaction Method, tau-leaping.

Exact reduction of ordinary differential equations with polynomial derivatives

Forward equivalence produces a reduced model where every macro-variable represents the sum of variables in each block.
Backward equivalence ensures that all variables in a block have the same solution at all times points.

Exact reduction of stochastic reaction networks via network-to-network transformation

Species equivalence identifies a partition of the species of in a network and produces a reduced one where the marginal probability distribution of each macro-species corresponds to the probability distribution of the sum of the species in each block.

Exact reduction of ordinary differential equations with arbitrary nonlinearities backed by SMT

Forward differential equivalence and backward differential equivalence are generalizations of the forward and backward equivalences when the derivatives have rational expressions, minimum/maximum functions, etc.

Approximate reduction of ordinary differential equations with polynomial derivatives

ε-forward and ε-backward equivalence: relaxations of forward and backward equivalence where the macro-variables approximately represent the sum of original variables within some computable bound.

Exact reduction of differential algebraic equations with linear derivatives

Backward Invariance is a generalization of backward equivalence when the derivatives are linear and the differential equations are complemented by algebraic constraints (e.g., a constraint x1=x2+x3 implies that whatever value these 3 variables take, x1+x2 must always be equal to x1, constraining the space of admissible solutions).

Exact reduction of Boolean networks

Boolean backward equivalence: is a recasting of backward equivalence to Boolean networks. These are a popular qualitative model of biological models where variables and update functions are Boolean.