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Aiming at the parameter identification problem in chaotic systems, we propose the quantum particle swarm optimization algorithm based on the swarm intelligence particle swarm optimization. The test functions show that the method has good global optimization. Then the method is applied to the parameter identification problem of the chaotic system. We transform the parameter identification problem into the optimization in the multi-dimensional function space. Through research on the balance board thermal convection in a typical chaotic Lorenz system, the proposed method has been compared with the basic algorithm and the genetic algorithm. Simulation results show that the proposed algorithm is effective, and is very important to the development of chaos theory.
[1] Edward O, Celso G, James A 1990 Phys. Rev. Lett. 64 1196
[2] Wang X Y, Meng J 2009 Acta Phys. Sin. 58 3780 (in Chinese) [王兴元, 孟娟 2009 58 3780]
[3] Li N, Li J F, Liu Y P, Ma J 2008 Acta Phys. Sin. 57 1404 (in Chinese) [李农, 李建芬, 刘宇平, 马健 2008 57 1404]
[4] Huang L L, Feng R P, Wang M 2004 Phys. Lett. A 2 271
[5] Wang C C, Su J P 2003 Chaos Solitons and Fractals 2 275
[6] Chen S H, Hu J, Wang C P, Lu J H 2004 Phys. Lett. A 150
[7] Poznyak A S, Yu W, Sanchez E N 1999 IEEE Trans. Circ. Syst. 12 1491
[8] Zhao J C, Zhang Q J, Lu J A 2011 Chin. Phys. B 20 050507
[9] Wang J Y, Huang D X 2008 Acta Phys. Sin. 57 2755 (in Chinese) [王钧炎, 黄德先 2008 57 2755]
[10] Dai D,Ma X K, Li F C, You R 2002 Acta Phys. Sin. 51 2459 (in Chinese) [戴栋, 马西奎, 李富才, 尤勇 2002 51 2459]
[11] Kenndy J, Eberhart R C 1995 IEEE International Conference on Neural Networks Perth, Australian, November 27-December 1,1995 p1942
[12] Sun J, Fang W 2011 Quantum-behaved particle swarm optimization principle and its application (Beijing: Tsinghua University Press) p33 (in Chinese) [孙俊, 方伟 2011 量子行为粒子群优化原理及其应用 (北京: 清华大学出版社) 第33页]
[13] Wen S H, Wang Z, Liu F C 2009 Acta Phys. Sin. 58 3753 (in Chinese) [温淑焕, 王哲, 刘福才 2009 58 3753]
[14] Coelho L S 2008 Chaos Solitons and Fractals 5 1409
[15] Liu C H, Zhang Y J, Zhang J, Wu J H 2011 Acta Phys. Sin. 60 019501 (in Chinese) [刘朝华, 张英杰, 章兢, 吴建辉 2011 60 019501]
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[1] Edward O, Celso G, James A 1990 Phys. Rev. Lett. 64 1196
[2] Wang X Y, Meng J 2009 Acta Phys. Sin. 58 3780 (in Chinese) [王兴元, 孟娟 2009 58 3780]
[3] Li N, Li J F, Liu Y P, Ma J 2008 Acta Phys. Sin. 57 1404 (in Chinese) [李农, 李建芬, 刘宇平, 马健 2008 57 1404]
[4] Huang L L, Feng R P, Wang M 2004 Phys. Lett. A 2 271
[5] Wang C C, Su J P 2003 Chaos Solitons and Fractals 2 275
[6] Chen S H, Hu J, Wang C P, Lu J H 2004 Phys. Lett. A 150
[7] Poznyak A S, Yu W, Sanchez E N 1999 IEEE Trans. Circ. Syst. 12 1491
[8] Zhao J C, Zhang Q J, Lu J A 2011 Chin. Phys. B 20 050507
[9] Wang J Y, Huang D X 2008 Acta Phys. Sin. 57 2755 (in Chinese) [王钧炎, 黄德先 2008 57 2755]
[10] Dai D,Ma X K, Li F C, You R 2002 Acta Phys. Sin. 51 2459 (in Chinese) [戴栋, 马西奎, 李富才, 尤勇 2002 51 2459]
[11] Kenndy J, Eberhart R C 1995 IEEE International Conference on Neural Networks Perth, Australian, November 27-December 1,1995 p1942
[12] Sun J, Fang W 2011 Quantum-behaved particle swarm optimization principle and its application (Beijing: Tsinghua University Press) p33 (in Chinese) [孙俊, 方伟 2011 量子行为粒子群优化原理及其应用 (北京: 清华大学出版社) 第33页]
[13] Wen S H, Wang Z, Liu F C 2009 Acta Phys. Sin. 58 3753 (in Chinese) [温淑焕, 王哲, 刘福才 2009 58 3753]
[14] Coelho L S 2008 Chaos Solitons and Fractals 5 1409
[15] Liu C H, Zhang Y J, Zhang J, Wu J H 2011 Acta Phys. Sin. 60 019501 (in Chinese) [刘朝华, 张英杰, 章兢, 吴建辉 2011 60 019501]
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