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Based on Lyapunov stability theory, optimal control principle and step design methodology, nonlinear feedback controller and optimal controller are designed, in which the nonlinear feedback controller makes the trajectory error between two neuron systems tend to zero, and the optimal controller makes the spent energy meet minimum, which is spent in the process of synchronizing. In this paper, the uncertain cable model is taken as an example to illustrate the full-order optimal synchronization of two neurons. The uncertain cable model and the uncertain Hindmarsh-Rose (HR) model are taken to illustrate the reduced-order optimal synchronization of two neurons. In addition, the unknown parameters are identified successfully. Numerical Simulation results show the effectiveness of the strategy further.
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Keywords:
- optimal synchronization /
- full-order and reduced-order /
- step design /
- neurons
[1] Chay T R 1985 Physica D 16 233
[2] Thompson C J, Bardos D C, Yang Y S, Joyner K H 1999 Chaos, Solitons and Fractals 10 1825
[3] Hindmarsh J L, Rose R M 1984 P. Roy. Soc. Lond. B Biol. 221 87
[4] Glass L 1995 Chaos in Neural Systems (Cambridge: MIT) p186
[5] Roelfsema P R, Engel A K, K? nig P, Singer W 1997 Nature 385 157
[6] Steriade M,McCormick D A, Sejnowski T J 1993 Science 262 679
[7] Meister M, Wong R O, Baylor D A, Shatz C J 1991 Science 252 939
[8] Kreiter A K, Singer W 1996 J. Neurosci. 16 2381
[9] Shuai J W, Durand D M 1999 Phys. Lett. A 264 289
[10] Bennett M V L, Verselis V K 1992 Semin. Cell Biol. 3 29
[11] Liu Y J,WangW, Tong S C, Liu Y S 2010 IEEE Trans. Syst. Man Cybern. Syst. Hum. 40 170
[12] Liu Y J, Wen G X, Tong S C 2011 IEEE Trans. Neural Network 22 1162
[13] Zhang H G, Ma T D, Yu W, Fu J 2008 Chin. Phys. B 17 3616
[14] Liu Y J, Zheng Y Q 2009 Nonlin. Dyn. 57 431
[15] Wang Z S, Zhang H G, Wang Z L 2006 Acta Phys. Sin. 55 2687 (in Chinese)[王占山, 张化光, 王智良 2006 55 2687]
[16] Dhamala M, Jirsa V K, Ding M 2004 Phys. Rev. Lett. 92 074104
[17] Wang Q Y, Lu Q S, Chen G R, Guo D 2006 Phys. Lett. A 356 17
[18] Cornejo-Pérez O, Femat R 2005 Chaos, Solitons and Fractals 25 43
[19] Zhang H G, Xie Y H, Wang Z L, Zheng C D 2007 IEEE Trans. Neural Network. 18 1841
[20] Song Y, Chen Z Q, Yuan Z Z 2007 Chin. J. Chem. Eng. 15 539
[21] Che Y Q, Wang J, Zhou S S, Deng B 2009 Chaos, Solitons and Fractals 40 1333
[22] Wang Q Y, Lua Q S, Chen G R, Guo D H 2006 Phys. Lett. A 356 17
[23] Awad E G 2006 Chaos, Solitons and Fractals 27 345
[24] Terman D, Kopell N, Bose A 1998 Physica D 117 241
[25] Schäfer C, Rosenblum M G, Abel H H, Kurths J R 1999 Phys. Rev. E 60 857
[26] Bartsch R, Kantelhardt J W, Penzel T, Havlin S 2007 Phys. Rev. Lett. 98 054102 060508-6
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[1] Chay T R 1985 Physica D 16 233
[2] Thompson C J, Bardos D C, Yang Y S, Joyner K H 1999 Chaos, Solitons and Fractals 10 1825
[3] Hindmarsh J L, Rose R M 1984 P. Roy. Soc. Lond. B Biol. 221 87
[4] Glass L 1995 Chaos in Neural Systems (Cambridge: MIT) p186
[5] Roelfsema P R, Engel A K, K? nig P, Singer W 1997 Nature 385 157
[6] Steriade M,McCormick D A, Sejnowski T J 1993 Science 262 679
[7] Meister M, Wong R O, Baylor D A, Shatz C J 1991 Science 252 939
[8] Kreiter A K, Singer W 1996 J. Neurosci. 16 2381
[9] Shuai J W, Durand D M 1999 Phys. Lett. A 264 289
[10] Bennett M V L, Verselis V K 1992 Semin. Cell Biol. 3 29
[11] Liu Y J,WangW, Tong S C, Liu Y S 2010 IEEE Trans. Syst. Man Cybern. Syst. Hum. 40 170
[12] Liu Y J, Wen G X, Tong S C 2011 IEEE Trans. Neural Network 22 1162
[13] Zhang H G, Ma T D, Yu W, Fu J 2008 Chin. Phys. B 17 3616
[14] Liu Y J, Zheng Y Q 2009 Nonlin. Dyn. 57 431
[15] Wang Z S, Zhang H G, Wang Z L 2006 Acta Phys. Sin. 55 2687 (in Chinese)[王占山, 张化光, 王智良 2006 55 2687]
[16] Dhamala M, Jirsa V K, Ding M 2004 Phys. Rev. Lett. 92 074104
[17] Wang Q Y, Lu Q S, Chen G R, Guo D 2006 Phys. Lett. A 356 17
[18] Cornejo-Pérez O, Femat R 2005 Chaos, Solitons and Fractals 25 43
[19] Zhang H G, Xie Y H, Wang Z L, Zheng C D 2007 IEEE Trans. Neural Network. 18 1841
[20] Song Y, Chen Z Q, Yuan Z Z 2007 Chin. J. Chem. Eng. 15 539
[21] Che Y Q, Wang J, Zhou S S, Deng B 2009 Chaos, Solitons and Fractals 40 1333
[22] Wang Q Y, Lua Q S, Chen G R, Guo D H 2006 Phys. Lett. A 356 17
[23] Awad E G 2006 Chaos, Solitons and Fractals 27 345
[24] Terman D, Kopell N, Bose A 1998 Physica D 117 241
[25] Schäfer C, Rosenblum M G, Abel H H, Kurths J R 1999 Phys. Rev. E 60 857
[26] Bartsch R, Kantelhardt J W, Penzel T, Havlin S 2007 Phys. Rev. Lett. 98 054102 060508-6
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