Scaling invariants and symmetry reduction of dynamical systems

Scalings form a class of group actions that have theoretical and practical importance. A scaling is accurately described by a matrix of integers. Tools from linear algebra over the integers are exploited to compute their invariants, rational sections (a.k.a. global cross-sections), and offer an algorithmic scheme for the symmetry reduction of dynamical systems. A special case of the symmetry reduction algorithm applies to reduce the number of parameters in physical, chemical or biological models. Keywords Group actions * Rational invariants * Matrix normal form * Model reduction * Dimensional analysis * Symmetry reduction * Equivariant moving frame Mathematics Subject Classification 08-04 * 12-04 * 14L30 * 15-04
1 Introduction Consider the following predator-prey model: [dn/dt] = n(r(1 - n/K) - k[p/n + d]), [dp/dt] = sp(1 - h[p/n]) which has six parameters, r, h, K, s, k, [...]