### Mathematical definition

In the MATCONT / CL_MATCONT toolbox Hopf curves are computed by minimally extended defining systems, cf. [22] §4.3.4. The Hopf curve is defined by the following system

| (61)

with the unknowns and where is obtained by solving

| (62)

where has eigenvalues , and are chosen such that the matrix in (62) is nonsingular. and are auxiliary variables that can be adapted. This method is implemented in the curve definition file `hopf.m`.