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拓展和改变Lorenz混沌系统的非线性函数,构建一个新的具有光滑二次函数的自治混沌系统,系统包含3个系统变量乘积的非线性函数项和5个平衡点,详细讨论了平衡点的性质并计算了分形维数.利用分岔图和Lyapunov指数谱对系统随参数变化的情况进行分析后得出,系统会发生倍周期分岔.用数字信号处理芯片对混沌系统进行硬件实现,实验结果表明理论分析的正确性以及系统具有较为复杂的动力学行为.
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关键词:
- 混沌系统 /
- 分岔图 /
- Lyapunov指数 /
- 数字信号处理
Developing and changing nonlinear function of Lorenz chaotic system, a new autonomous chaotic system is generated which contains three smooth quadratic terms of system variables and five equilibriums. The characteristics of five equilibriums are discussed and a fractal dimension is calculated. The features of chaotic system are analyzed in detail using bifurcation diagram and Lyapunov exponent. The period doubling bifurcation of the system can occus. The chaotic system is realized based on digital signal processing. Experimental result shows the effectiveness and feasibility of the theoretical analysis and verifies the behaviors of various attractors.-
Keywords:
- chaotic system /
- bifurcation diagram /
- Lyapunov exponents /
- digital signal processing
[1] Lorenz E N 1963 J. Atmos. Sci. 20 130
[2] Elwakil A S, zguz S, Kennedy M P 2002 IEEE Trans. Circuits Syst.Ⅰ 49 527
[3] Miranda R, Stone E 1993 Phys. Lett. A 178 105
[4] Liu W B, Chen G R 2003 Int. J. Bifur. Chaos 13 261
[5] Chen G R, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[6] Lü J H, Chen G 2002 Int. J. Bifur. Chaos 12 659
[7] Lü J H, Chen G, Cheng D 2004 Int. J. Bifur. Chaos 14 1507
[8] Qi G Y, Chen G R, Du S Z, Chen Z Q, Yuan Z Z 2005 Physica A 352 295
[9] Liu C X, Liu T, Liu L, Liu K 2004 Chaos Solitons Fract. 22 1031
[10] Liu L, Su Y C, Liu C X 2007 Chin. Phys. 16 1897
[11] Wang F Z, Qi G Y, Chen Z Q, Zhang Y H, Yuan Z Z 2006 Acta Phys. Sin. 55 4005 (in Chinese) [王繁珍、 齐国元、 陈 增强、 张宇辉、 袁著祉 2006 55 4005] 〖12] Wang G Y, Qiu S S, Xu Z Y 2006 Acta Phys. Sin. 55 3295 (in Chinese) [王光义、 丘水生、 许志益 2006 55 3295]
[12] Wang G Y, Qiu S S, Li H W, Li C F, Zheng Y 2006 Chin. Phys. 15 2872
[13] Wang F Z, Chen Z Q, Wu W J, Yuan Z Z 2007 Chin. Phys. 16 3238
[14] Cai G L, Tan Z H, Zhou W H, Tu W T 2007 Acta Phys. Sin. 56 6230 (in Chinese) [蔡国梁、 谭振海、 周维怀、 涂文桃 2007 56 6230]
[15] Liu Y Z, Jiang C S, Lin C S 2007 Acta Phys. Sin. 56 5131 (in Chinese) [刘扬正、 姜长生、 林长圣 2007 56 5131]
[16] Shilnikov L P 1994 Int. J. Bifur. Chaos 4 489
[17] Long M, Qiu S S 2007 Chin. Phys. 16 2254
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[1] Lorenz E N 1963 J. Atmos. Sci. 20 130
[2] Elwakil A S, zguz S, Kennedy M P 2002 IEEE Trans. Circuits Syst.Ⅰ 49 527
[3] Miranda R, Stone E 1993 Phys. Lett. A 178 105
[4] Liu W B, Chen G R 2003 Int. J. Bifur. Chaos 13 261
[5] Chen G R, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[6] Lü J H, Chen G 2002 Int. J. Bifur. Chaos 12 659
[7] Lü J H, Chen G, Cheng D 2004 Int. J. Bifur. Chaos 14 1507
[8] Qi G Y, Chen G R, Du S Z, Chen Z Q, Yuan Z Z 2005 Physica A 352 295
[9] Liu C X, Liu T, Liu L, Liu K 2004 Chaos Solitons Fract. 22 1031
[10] Liu L, Su Y C, Liu C X 2007 Chin. Phys. 16 1897
[11] Wang F Z, Qi G Y, Chen Z Q, Zhang Y H, Yuan Z Z 2006 Acta Phys. Sin. 55 4005 (in Chinese) [王繁珍、 齐国元、 陈 增强、 张宇辉、 袁著祉 2006 55 4005] 〖12] Wang G Y, Qiu S S, Xu Z Y 2006 Acta Phys. Sin. 55 3295 (in Chinese) [王光义、 丘水生、 许志益 2006 55 3295]
[12] Wang G Y, Qiu S S, Li H W, Li C F, Zheng Y 2006 Chin. Phys. 15 2872
[13] Wang F Z, Chen Z Q, Wu W J, Yuan Z Z 2007 Chin. Phys. 16 3238
[14] Cai G L, Tan Z H, Zhou W H, Tu W T 2007 Acta Phys. Sin. 56 6230 (in Chinese) [蔡国梁、 谭振海、 周维怀、 涂文桃 2007 56 6230]
[15] Liu Y Z, Jiang C S, Lin C S 2007 Acta Phys. Sin. 56 5131 (in Chinese) [刘扬正、 姜长生、 林长圣 2007 56 5131]
[16] Shilnikov L P 1994 Int. J. Bifur. Chaos 4 489
[17] Long M, Qiu S S 2007 Chin. Phys. 16 2254
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