Nonradial entire solutions for Liouville systems

We consider the following system of Liouville equations: $$\l\{\bll-\D u_1=2e^{u_1}+\mu e^{u_2}&\tx{in }\R^2\\-\D u_2=\mu e^{u_1}+2e^{u_2}&\tx{in }\R^2\\ \int_{\R^2}e^{u_1}<+\infty,\ \int_{\R^2}e^{u_2}<+\infty.\ \earr\r.$$ We show the existence of at least $n-\left[\frac n3\right]$ global branches of nonradial solutions bifurcating from $u_1(x)=u_2(x)=U(x)=\log\fr{64}{(2+\mu)\l(8+|x|^2\r)^2}$ at the values $\mu=-2\fr{n^2+n-2}{n^2+n+2}$ for any $n\in\N$.