Qualitative dynamics of chemical reaction networks: an investigation using partial tropical equilibrations

The paper formalizes the partial tropical equilibration constraints (27)–(29), proves the solution set is a polyhedral complex built from finite choices of minima, and defines the associated tropically truncated system E′; it also gives the Tyson-cell-cycle reduced model obtained at total tropical equilibration. The candidate independently reconstructs the same encoding of minima into affine constraints, the branch/complex structure, and E′, and on the Tyson model derives exactly the reduced system reported in the paper. Minor differences (ε* chosen as 0.1 instead of 1/11, and using closures for strict inequalities) do not affect correctness and are consistent with the paper’s implementation and robustness remarks. Key statements and the final reduced model match the paper’s results.