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The linear control and the anti-control of a class of chaotic systems with only one nonlinear term are studied. Based on the Routh- Hurwitz stability condition,the chaotic system is controlled and the stable state is reached. Then,the chaotic state is recovered through changing controlled coefficient and a new chaotic system follows. The basic dynamical behavior of the new chaotic system is investigated and numerical simulation shows the chaotic nature of this new system.
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Keywords:
- chaotic system /
- chaos control /
- bifurcation /
- Lyapunov exponents
[1] Lorenz E N 1963 J. Atmos. Sci. 20 130
[2] Chen G,Lai D 1998 Int. J. Bifurcation and chaos 8 1585
[3] Lü J,Chen G 2002 Int. J. Bifurcation and chaos 12 659
[4] Lü J,Chen G,Cheng D,Celikovsky S 2002 Int. J. Bifurcation and chaos 12 2917
[5] Wang J Z,Chen Z Q,Yuan Z Z 2006 Acta Phys. Sin. 55 3956 (in Chinese) [王杰智、陈增强、袁著祉 2006 物理学报 55 3956]
[6] Cai G L,Tan Z M,Zhou W H,Tu W T 2007 Acta Phys. Sin. 56 6230 (in Chinese) [蔡国梁、谭振梅、周维怀、涂文桃 2007 物理学报 56 6230]
[7] Liu C X,Liu L 2009 Chin. Phys. B 18 2188
[8] Zhou P,Wei J L,Chen X F 2009 Acta Phys. Sin. 58 5201 (in Chinese) [周 平、危丽佳、程雪峰 2009 物理学报 58 5201]
[9] Qi G,Chen G,Du S,Chen Z,Yuan Z 2005 Physica A 352 295
[10] Zhang L,Yu J N,Li Y 2007 Journal of Lanzhou Jiaotong University (Natural Sciences) 26 154 (in Chinese) [张 莉、俞建宁、李 阳 2007 兰州交通大学学报(自然科学版) 26 154]
[11] Tigan Gh 2005 Sci. Bull. Politehnica University of Timisoara,Tomul 50,Fascicola 1 61
[12] Yang Q,Zhang M,Chen G 2009 Nonlinear Anal. 10 1601
[13] Sprott J C 1994 Phys. Rev.E 50 647
[14] Zhang Z F,Ding T R,Huang W D 1985 Qualitative Theory of Differential Equations (Beijing:Science Press) (in Chinese) [张芷芬、丁同仁、黄文灶 1985 微分方程定性理论(北京:科学出版社)]
[15] Ma Z E,Zhou Y C 2001 Qualitative Theory of Ordinary Differential Equations and Stability Methods (Beijing:Science Press) (in Chinese) [马知恩、周义仓 2001 常微分方程定性与稳定性方法(北京:科学出版社)]
[16] Han M 2007 Prediction Theory and Method of Chaotic Time Series (Beijing:China Waterpower Press) (in Chinese) [韩 敏 2007 混沌时间序列预测理论与方法(北京:中国水利水电出版社)]
[17] Lü J H,Zhang S C 2001 Journal of Nonlinear Dynamics in Science and Technology 1 84 (in Chinese) [吕金虎、张锁春 2001 非线性动力学学报 1 84]
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[1] Lorenz E N 1963 J. Atmos. Sci. 20 130
[2] Chen G,Lai D 1998 Int. J. Bifurcation and chaos 8 1585
[3] Lü J,Chen G 2002 Int. J. Bifurcation and chaos 12 659
[4] Lü J,Chen G,Cheng D,Celikovsky S 2002 Int. J. Bifurcation and chaos 12 2917
[5] Wang J Z,Chen Z Q,Yuan Z Z 2006 Acta Phys. Sin. 55 3956 (in Chinese) [王杰智、陈增强、袁著祉 2006 物理学报 55 3956]
[6] Cai G L,Tan Z M,Zhou W H,Tu W T 2007 Acta Phys. Sin. 56 6230 (in Chinese) [蔡国梁、谭振梅、周维怀、涂文桃 2007 物理学报 56 6230]
[7] Liu C X,Liu L 2009 Chin. Phys. B 18 2188
[8] Zhou P,Wei J L,Chen X F 2009 Acta Phys. Sin. 58 5201 (in Chinese) [周 平、危丽佳、程雪峰 2009 物理学报 58 5201]
[9] Qi G,Chen G,Du S,Chen Z,Yuan Z 2005 Physica A 352 295
[10] Zhang L,Yu J N,Li Y 2007 Journal of Lanzhou Jiaotong University (Natural Sciences) 26 154 (in Chinese) [张 莉、俞建宁、李 阳 2007 兰州交通大学学报(自然科学版) 26 154]
[11] Tigan Gh 2005 Sci. Bull. Politehnica University of Timisoara,Tomul 50,Fascicola 1 61
[12] Yang Q,Zhang M,Chen G 2009 Nonlinear Anal. 10 1601
[13] Sprott J C 1994 Phys. Rev.E 50 647
[14] Zhang Z F,Ding T R,Huang W D 1985 Qualitative Theory of Differential Equations (Beijing:Science Press) (in Chinese) [张芷芬、丁同仁、黄文灶 1985 微分方程定性理论(北京:科学出版社)]
[15] Ma Z E,Zhou Y C 2001 Qualitative Theory of Ordinary Differential Equations and Stability Methods (Beijing:Science Press) (in Chinese) [马知恩、周义仓 2001 常微分方程定性与稳定性方法(北京:科学出版社)]
[16] Han M 2007 Prediction Theory and Method of Chaotic Time Series (Beijing:China Waterpower Press) (in Chinese) [韩 敏 2007 混沌时间序列预测理论与方法(北京:中国水利水电出版社)]
[17] Lü J H,Zhang S C 2001 Journal of Nonlinear Dynamics in Science and Technology 1 84 (in Chinese) [吕金虎、张锁春 2001 非线性动力学学报 1 84]
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