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The basin of attraction of the Liu system. (English) Zbl 1221.34145

Summary: By geometric analysis, the riddled property of the basin of attraction of the Liu attractor is discussed, and that any neighborhood of the Liu attractor contains repelled sets with positive Lebesgue measures is proved. Basing on analytic and numerical results, it is shown that the Liu attractor indeed has some unusual properties leading to a strange attractor in the sense of Milnor.

MSC:

34D20 Stability of solutions to ordinary differential equations
34D45 Attractors of solutions to ordinary differential equations
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
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