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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.
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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 49 1228]
[6] [7] Hong L, Xu J X 2001 Acta Phys. Sin. 50 612 (in Chinese) [洪灵、 徐健学 2001 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 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 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 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 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 49 1228]
[6] [7] Hong L, Xu J X 2001 Acta Phys. Sin. 50 612 (in Chinese) [洪灵、 徐健学 2001 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 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 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 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 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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