This paper initiates a novel approach to generate multi-wing butterfly attractor from the Liu chaotic system. The main idea is to increase the number of index-2 saddle-focus of chaotic system. By substitution of multi-segment quadratic function, the Liu′s chaotic system is designed to create many index-2 saddle-focus and generate multi-wing butterfly attractor. Theoretical analysis shows that every index-2 equilibrium point corresponds to unique wing in the butterfly attractor. The simulation demostrates the feasibility and effectiveness of the proposed method.
GAO Bingjian
,
GAO Bingjian
. Multi-wing Butterfly Attractor from a Modified Chaotic System[J]. Complex Systems and Complexity Science, 2016
, 13(1)
: 91
-94
.
DOI: 10.13306/j.1672-3813.2016.01.009
[1] Lorenz E N. Deterministic non-periodic flows[J].J Atmos Sci, 1963, 20: 130-141.
[2] Chen G R, Ueta T. Yet another chaotic attractor[J].Int J Bifur Chaos, 1999, 9(7): 1465-1466.
[3] Lü J H, Chen G R. A new chaotic attractor coined[J].Int J Bifur Chaos, 2002, 12(3): 659-661.
[4] 陈关荣,吕金虎. Lorenz系统族的动力学分析、控制与同步[M].北京:科学出版社,2003.
[5] Liu C X, Liu T, Liu L, et al. A new chaotic attractor[J].Chaos, Solitons and Fractals, 2004, 22 (3): 1031-1038.
[6] 王发强,刘崇新. Liu混沌系统的混沌分析及电路实验的研究[J].物理学报,2006, 55(10): 5061-5069.
Wang Faqiang, Liu Chongxin. Studies on Liu chaotic system and its experimental confirmation[J].Acta Phys Sin, 2006, 55(10): 5061-5069.
[7] Matsumoto T. A chaotic attractor from Chua’s circuit[J].IEEE Trans Circ Sym, 1984, 31(12): 1055-1058.
[8] Chua L O, Komuro M, Matsumoto T. The double scroll family[J].IEEE Trans Circ Sym, 1986, 33(11): 1072-1118.
[9] Suykens J A K, Vandewalle J. Generation of n-double scrolls (n=1; 2; 3; 4…)[J].IEEE Trans Circ Sym I, 1993, 40 (11): 861-867.
[10] Suykens J A K, Huang A, Chua L O. A family of n-scroll attractors from a generalized Chua’s circuit[J].Int J Electron Com, 1997,51(3): 131-138.
[11] Yalcin M E, Suykens J A K, Vandewalle J. Experimental confirmation of 3- and 5-scroll attractors from a generalized Chua’s circuit[J].IEEE Trans Circ Sym I, 2000, 47: 425-429.
[12] Miranda R, Stone E. The proto-Lorenz system[J].Physics Letters A, 1993, 178:105-113.
[13] Yu S M, Lü J H, Tang K S, et al. A general multi-scroll Lorenz system family and its realization via digital signal processors[J].Chaos, 2006, 16(3): 033126.
[14] Lü J H, Chen G R. Multi-scroll chaos generation: theories, methods and applications[J].Int J Bifur Chaos, 2006, 16 (4):775-858.
[15] Yu S M, Tang W K S, Lü J H, et al. Multi-wing butterfly attractors from the modified Lorenz systems[C]∥ Proceedings of the IEEE International Symposium on Circuits and Systems Seattle, USA, 2008: 768-771.
[16] Yu S M, Tang W K S, Lü J H, et al. Generating 2n-wing attractors from Lorenz-like systems[J].Int J Circ Theor Appl, 2010, 38: 243-258.
[17] 高秉建,陆君安,陈爱敏. 一个unified系统与Rössler系统的组合研究.物理学报, 2006, 55(9): 4450-4455.
Gao Bingjian, Lu Junan, Chen Aimin. A novel chaotic system via combining a unified system with Rössler system[J].Acta Phys Sin, 2006, 55(9): 4450-4455.
[18] Gao B J,Lu J A. Adaptive synchronization of hyperchaotic Lü system with uncertainty[J].Chin Phys, 2007, 16(3): 666-670.
