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Two Dimensional Stable and Unstable Manifolds in Modified Lornez System
Department of Mathematics, China Agricultural University, Beijing, China
- 1 Department of Mathematics, China Agricultural University, Beijing, China
International Journal of Modern Nonlinear Theory and Application·Volume 15 (2026)·Pages 52–62·Published 23 June 2026·DOI10.4236/ijmnta.2026.152006
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Abstract
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.
KeywordsModified Lornez SystemChaosTwo Dimensional Stable ManifoldLornez Shaped ManifoldTwo Dimensional Unstable Manifold
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