Hopf bifurcation for n variables

Local stability analysis and Hopf bifurcation for n variables 

The local stability analysis for a two-dimensional system has been given in some detail in chapter 3 and used frequently in later sections. The same general principles apply to any number of variables. Provided the perturbations imposed upon the stationary state are infinitesimal, the growth or decay for an n variable system will be governed by the sum of n exponential terms of the form e 1 1 with i = 1, n. 

---