Comparison of invariant surfaces in multi-route reaction mechanisms

Anees Ur Rehman, M. Shahzad, Dipo Aldila

Research output: Contribution to journalArticlepeer-review


In dissipative systems of chemical kinetics, a general understanding of the idea of the slow invariant manifold (SIM) leads toward the various model reduction techniques (MRT). In this paper, the invariant surfaces are computed and compared for multi-route mechanisms. The slow invariant manifolds are constructed using the MRT such as Intrinsic Low Dimensional (ILDM), Symmetric Entropic Intrinsic Low Dimensional Manifold (SEILDM), Quasi Equilibrium Manifold, and Spectral Quasi Equilibrium Manifold (SQEM), which serve as initial approximations to SIM. With the use of graphical diagrams, the relationship between the eigenvalues and the solution points of the invariant surfaces is also addressed. The refinements of QEM and SQEM solutions are calculated by implementing the Method of Invariant Grid (MIG). The comparisons of MRT are given based on key factors such as accuracy, and size of the approximated manifolds. To compare MRT with respect to their computation time, the computational time analysis is also reported.

Original languageEnglish
Pages (from-to)1719-1737
Number of pages19
JournalReaction Kinetics, Mechanisms and Catalysis
Issue number4
Publication statusAccepted/In press - 2022


  • Graph theory
  • Invariant manifold
  • Mathematical modeling
  • Model reduction techniques
  • Reaction routes


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