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以典型的Duffing单边碰撞系统为研究对象,对系统中的混沌鞍进行了细致的分析.研究表明,系统的混沌鞍同样存在合并激变,合并激变是由连接两个混沌鞍的周期鞍的稳定流形与不稳定流形相切所诱发,相切使得边界上的混沌鞍与内部的混沌鞍发生碰撞而突然合并为一个较大的边界混沌鞍.混沌鞍的合并激变行为最终会诱导混沌吸引子的合并激变发生.
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关键词:
- Duffing碰撞系统 /
- 混沌鞍 /
- 周期鞍 /
- 稳定与不稳定流形
A computational investigation of chaotic saddles in a Duffing vibro-impact system is presented. Chaoctic saddle crisis is investigated in a duffing vibro-impact system considered. This crisis is due to the tangency of the stable and unstable manifolds of period saddle connecting two chaotic saddles. The threshold of tangency induces the merging crisis of chaotic saddle, that is, as the system parameter crosses the critical value, a larger boundary chaotic saddle appears due to the merging of two chaotic saddles located on the basin boundary and in the internal basin respectively. In fact, this chaotic saddle crisis is responsible for the merging crisis of chaotic attractors eventually.-
Keywords:
- Duffing virbo-impact system /
- chaotic saddle /
- period saddle /
- stable and unstable manifold
[1] Grebogi C, Ott E, Yorke J A 1983 Physica D 7 181
[2] Grebogi C, Ott E, Yorke J A 1986 Phys. Rev. Lett. 57 1284
[3] [4] [5] Hong L, Xu J X 2000 Acta Phys. Sin. 49 1228 (in Chinese) [洪 灵、 徐健学 2000 物理学报 49 1228]
[6] [7] Hong L, Xu J X 2001 Acta Phys. Sin. 50 612 (in Chinese) [洪灵、 徐健学 2001 物理学报 50 612]
[8] [9] Dai D, Ma X K, Li X F 2003 Acta Phys. Sin. 52 2729 (in Chinese) [戴 栋、 马西奎、 李小峰 2003 物理学报 52 2729]
[10] He Q, Xu W, Li S, Xiao Y Z 2008 Acta Phys. Sin. 57 743 (in Chinese) [贺 群、 徐 伟、 李 爽、 肖玉柱 2008 物理学报 57 743]
[11] [12] He Q, Xu W, Li S, Xiao Y Z 2008 Acta Phys. Sin. 57 4021 (in Chinese) [贺 群、 徐 伟、 李 爽、 肖玉柱 2008 物理学报 57 4021]
[13] [14] Nordmark A B 1991 J. Sound Vib. 2 279
[15] [16] [17] Dankowicz H, Nordmark A B 1999 Physica D 136 280
[18] [19] di Bernardo M, Budd C J, Champneys A R 2001 Phys. Rev. Lett. 86 2553
[20] Chin W, Ott E, Nusse H E, Grebogi C 1994 Phys. Rev. E 50 4427
[21] [22] [23] Virgin L N, Begley C J 1999 Physica D 130 43
[24] Feng J Q, Xu W, Niu Y J 2010 Acta Phys. Sin. 59 157 (in Chinese) [冯进钤、 徐 伟、 牛玉俊 2010 物理学报 59 157]
[25] [26] [27] Xu W, He Q, Li S 2007 Symposium on Dynamics and Control of Nonlinear Systems with Uncertainty (Vol.2, Part 2) (Dordrecht: Springer) p117
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[1] Grebogi C, Ott E, Yorke J A 1983 Physica D 7 181
[2] Grebogi C, Ott E, Yorke J A 1986 Phys. Rev. Lett. 57 1284
[3] [4] [5] Hong L, Xu J X 2000 Acta Phys. Sin. 49 1228 (in Chinese) [洪 灵、 徐健学 2000 物理学报 49 1228]
[6] [7] Hong L, Xu J X 2001 Acta Phys. Sin. 50 612 (in Chinese) [洪灵、 徐健学 2001 物理学报 50 612]
[8] [9] Dai D, Ma X K, Li X F 2003 Acta Phys. Sin. 52 2729 (in Chinese) [戴 栋、 马西奎、 李小峰 2003 物理学报 52 2729]
[10] He Q, Xu W, Li S, Xiao Y Z 2008 Acta Phys. Sin. 57 743 (in Chinese) [贺 群、 徐 伟、 李 爽、 肖玉柱 2008 物理学报 57 743]
[11] [12] He Q, Xu W, Li S, Xiao Y Z 2008 Acta Phys. Sin. 57 4021 (in Chinese) [贺 群、 徐 伟、 李 爽、 肖玉柱 2008 物理学报 57 4021]
[13] [14] Nordmark A B 1991 J. Sound Vib. 2 279
[15] [16] [17] Dankowicz H, Nordmark A B 1999 Physica D 136 280
[18] [19] di Bernardo M, Budd C J, Champneys A R 2001 Phys. Rev. Lett. 86 2553
[20] Chin W, Ott E, Nusse H E, Grebogi C 1994 Phys. Rev. E 50 4427
[21] [22] [23] Virgin L N, Begley C J 1999 Physica D 130 43
[24] Feng J Q, Xu W, Niu Y J 2010 Acta Phys. Sin. 59 157 (in Chinese) [冯进钤、 徐 伟、 牛玉俊 2010 物理学报 59 157]
[25] [26] [27] Xu W, He Q, Li S 2007 Symposium on Dynamics and Control of Nonlinear Systems with Uncertainty (Vol.2, Part 2) (Dordrecht: Springer) p117
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