Reduction of Algebraic Parametric Systems by Rectification of Their Affine Expanded Lie Symmetries

Abstract

Abstract. Lie group theory states that knowledge of a m-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by m the number of equations. We apply this principle by finding some affine derivations that induces expanded Lie point symmetries of considered system. By rewriting original problem in an invariant coordinates set for these symmetries, we reduce the number of involved parameters. We present an algorithm based on this standpoint whose arithmetic complexity is quasi-polynomial in input's size.

Scaling Invariants and Symmetry Reduction of Dynamical Systems

“…As illustrated in the above example scalings also give mathematical sense to rules of thumb applied to reduce the number of parameters in biological and physical models [20,17]. In this context, reduction by a scaling symmetry of a dynamical was previously studied with an algorithmic point of view in [11,16,24]. In this paper we go further in this direction than handled in the previous cited works.…”

Rational invariants of scalings from Hermite normal forms

“…A second use of scalings is that they give mathematical sense to the rule of thumb used to reduce the number of parameters in biological models [18,15]. This reduction by scaling symmetry of dynamical or polynomial systems was previously studied in [9,14,23].…”

Applying a Rigorous Quasi-Steady State Approximation Method for Proving the Absence of Oscillations in Models of Genetic Circuits

“…Last observe that one more parameter could be removed from the above system, the software [21] shows. The above reduction is however more convenient in this paper for it permits us to directly apply the results of [1].…”