Linearization

Abstract

Decoupling and linearization of dynamical models given by differential or difference equations are very successful and frequently used simplification concepts in applied sciences. On the one hand, provided a system can be decoupled, due to possibly different growth rates, each part might be approached using methods more suitable for a subsystem than for the whole problem. On the other hand, linearization includes the advantage that linear equations are mathematically wellunderstood and problems can be approached on an analytical level. Indeed, the basic reason why such linear models oftentimes yield a realistic and successful description of real nonlinear problems, is the Hartman–Grobman theorem.