Nonlinear dynamics with applications

Using logarithmic norms and logarithmic Lipschitz constants, we shall demonstrate how qualitative and quantitative insight into the behavior of dynamical systems of the form \( \dot{\textit{u}} = \textit{F} (\textit{u}) \) can be gained. The focus is on how these tools can be used to analyze some important aspects of the wide variety of phenomena that occur in nonlinear dynamics. One example is to characterize stiffness, explaining why special computational methods are necessary in the presence of strong dissipation.