Chaotic Dynamics, Stability, and Bifurcations

Abstract

In the previous chapters it was shown how the behavior of material systems can be described by mathematical models represented by ordinary differential equations. In particular, Chapters 3 and 6 showed that the equilibrium configurations can be identified by looking for those values of u = (u ₁ …, u _n ) for which the right-hand side of the system of evolution equations

$$ \frac{{du}}{{dt}} = f\left( u \right) $$

(8.1.1)

vanishes, and we learned how to distinguish stable from unstable equilibrium points.