Homogeneous eigenvalue analysis for complex homogeneous systems of degree (/spl lscr/, /spl lscr/)

In this paper, we analyze the stability of complex homogeneous systems of degree (/spl lscr/, /spl lscr/) by homogeneous eigenvalues. First, we define homogeneous eigenvalues and homogeneous eigenvectors for complex homogeneous systems of degree (/spl lscr/, /spl lscr/). Then, we obtain solutions on homogeneous eigenvectors. Convergence of the solutions depends not only on homogeneous eigenvalues but also on homogeneous eigenvectors. Moreover, solutions on homogeneous eigenvectors never vibrate. Hence, it may not be appropriate to assign complex analytic homogeneous systems to real analytic homogeneous systems in complex transformation.