The chaos phenomenon is observed in the extended Lornez system in four dimensional phase space. The trivial solution is calculated as a saddle. With seasonal varying effects, the Lornez shaped stable manifold of the zero solution is simulated which is two dimensional. The alike Lornez shaped stable manifold is also observed in a developed autonomous Lornez system in four dimensional phase space. The modified Lornez system has a singular attractor. The manifold is drawn by adopting the BVPs problem combined with time homogenous method. The two dimensional unstable manifold is deemed as the neighborhood of the attractor and drawn as a colorful picture. The modified Lornez system has a mirror symmetry structure.
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