Constructing linear families from parameter-dependent nonlinear dynamics

Abstract

Generating families of linear models from nonlinear parameter-dependent equations requires explicit analytical characterization of the equilibrium surface. Doing so in terms of the original system parameters is generally not possible. Introducing an alternative parameterization, we propose an efficient method for computing local linear parameter-dependent families. Although local, these families can be constructed anywhere, specifically around bifurcation points where other methods fail.