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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.
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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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