Noise-induced Strange Nonchaotic Attractors and Their Multifractal Properties
碩士 === 國立中興大學 === 物理學系所 === 94 === In this thesis, we discuss the periodic attractor which, after being added with noise, becomes a strange nonchaotic attractor. First, we present finite time Lyapunov exponents of strange nonchaotic attractors (SNAs). Then, we investigate an interesting phenomenon i...
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| Format: | Others |
| Language: | zh-TW |
| Published: |
2006
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| Online Access: | http://ndltd.ncl.edu.tw/handle/38859021118286700018 |
| Summary: | 碩士 === 國立中興大學 === 物理學系所 === 94 === In this thesis, we discuss the periodic attractor which, after being added with noise, becomes a strange nonchaotic attractor. First, we present finite time Lyapunov exponents of strange nonchaotic attractors (SNAs). Then, we investigate an interesting phenomenon in which the Lyapunov exponents of the system are smaller than those of the original periodic attractor when the added noise is small and below the threshold value. Finally, we study the singularity spectrum and generalized dimension of strange nonchaotic attractors. We find that: αmin and information dimension D1 become larger when the noise amplitude increases. Hausdorff dimension D0 is the same when we change the noise amplitude and the α(0) corresponding to Hausdorff dimension D0 decreases when the noise amplitude increases.
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