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In this paper, backstepping and adaptive dynamical sliding mode control is used to achieve chaos synchronization of coupled FitzHugh-Nagumo (FHN) neurons. The proposed controller consists of a combination of dynamical sliding mode control and adaptive backstepping technique. Based on a new switching function, the combined algorithm yields a design of dynamical sliding mode control law, which can realize chaos synchronization of coupled FHN neurons with uncertain parameters. It is shown that the proposed approach can effectively remove the chattering characteristic of the system, so that the intrinsic dynamics of neurons can avoid to be destroyed. Furthermore, it has rapid control performance. The simulation results have demonstrated the effectiveness of the control scheme.
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Keywords:
- adaptive /
- dynamical sliding mode control /
- FitzHugh-Nagumo neuron /
- chaos synchronization
[1] Manyakov N V, Van Hulle M M 2008 Chaos 18 037130
[2] Elson R C, Selverston A I, Huerta R, Rulkov N F, Rabinovich M I, Abarbanel H D I 1998 Phys. Rev. Lett. 81 5692
[3] Gray C M, König P, Engel A K, Singer W 1989 Nature 338 334
[4] Fell J, Fernández G, Klaver P, Elger C E, Fries P 2003 Brain Res. Rev. 42 265
[5] Wang Q Y, Lu Q S, Chen G R, Guo D H 2006 Phys. Lett. A 356 17
[6] Singer W 1993 Annu. Rev. Physiol. 55 349
[7] MacKay W A 1997 Trends Cogn. Sci. 1 176
[8] Cornejo-Pérez O C, Femat R 2005 Chaos Solitons Fract. 25 43
[9] Wang J, Deng B, Fei X Y 2006 Chaos Solitons Fract. 29 182
[10] Che Y Q, Wang J, Tsang K M, Chan W L 2010 Nonlinear Anal. Real World Appl. 11 1096
[11] Che Y Q, Wang J, Zhou S S, Deng B 2009 Chaos Solitons Fract. 40 1333
[12] Sira-Ramírez H, Llanes-Santiago O 1993 Proceeding of the 32nd IEEE Conference on Decision and Control San Antonio, America, December 15-17, 1993 p1422
[13] Li C H, Sun Y, Luo Q 2009 Computer Engineering and Design 30 185 (in Chinese) [李春华, 孙约, 罗琦 2009 计算机工程与设计 30 185]
[14] Chen D Y, Liu Y X, Ma X Y, Zhang R F 2011 Chin. Phys. B 20 120506
[15] Chao H M, Hu Y M 2001 Control and Decision 16 565 (in Chinese) [晁红敏, 胡跃明 2001 控制与决策 16 565]
[16] Huang L L, Qi X 2013 Acta Phys. Sin. 62 080507 (in Chinese) [黄丽莲, 齐雪 2013 62 080507]
[17] L L, Li Y S, Wei L L, Yu M, Zhang M 2012 Acta Phys. Sin. 61 120504 (in Chinese) [吕翎, 李雨珊, 韦琳玲, 于淼, 张檬 2012 61 120504]
[18] Cao H F, Zhang R X 2011 Acta Phys. Sin. 60 050510 (in Chinese) [曹鹤飞, 张若洵 2011 60 050510]
[19] L L, Yu M, Wei L L, Zhang M, Li Y S 2012 Chin. Phys. B 21 100507
[20] Chen D Y, Zhang R F, Ma X Y, Wang J 2012 Chin. Phys. B 21 120507
[21] Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[22] FitzHugh R 1961 Biophys. J. 1 445
[23] Thompson C J, Bardos D C, Yang Y S, Joyner K H 1999 Chaos Solitons Fract. 10 1825
[24] Wang J, Deng B, Tsang K M 2004 Chaos Solitons Fract. 22 469
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[1] Manyakov N V, Van Hulle M M 2008 Chaos 18 037130
[2] Elson R C, Selverston A I, Huerta R, Rulkov N F, Rabinovich M I, Abarbanel H D I 1998 Phys. Rev. Lett. 81 5692
[3] Gray C M, König P, Engel A K, Singer W 1989 Nature 338 334
[4] Fell J, Fernández G, Klaver P, Elger C E, Fries P 2003 Brain Res. Rev. 42 265
[5] Wang Q Y, Lu Q S, Chen G R, Guo D H 2006 Phys. Lett. A 356 17
[6] Singer W 1993 Annu. Rev. Physiol. 55 349
[7] MacKay W A 1997 Trends Cogn. Sci. 1 176
[8] Cornejo-Pérez O C, Femat R 2005 Chaos Solitons Fract. 25 43
[9] Wang J, Deng B, Fei X Y 2006 Chaos Solitons Fract. 29 182
[10] Che Y Q, Wang J, Tsang K M, Chan W L 2010 Nonlinear Anal. Real World Appl. 11 1096
[11] Che Y Q, Wang J, Zhou S S, Deng B 2009 Chaos Solitons Fract. 40 1333
[12] Sira-Ramírez H, Llanes-Santiago O 1993 Proceeding of the 32nd IEEE Conference on Decision and Control San Antonio, America, December 15-17, 1993 p1422
[13] Li C H, Sun Y, Luo Q 2009 Computer Engineering and Design 30 185 (in Chinese) [李春华, 孙约, 罗琦 2009 计算机工程与设计 30 185]
[14] Chen D Y, Liu Y X, Ma X Y, Zhang R F 2011 Chin. Phys. B 20 120506
[15] Chao H M, Hu Y M 2001 Control and Decision 16 565 (in Chinese) [晁红敏, 胡跃明 2001 控制与决策 16 565]
[16] Huang L L, Qi X 2013 Acta Phys. Sin. 62 080507 (in Chinese) [黄丽莲, 齐雪 2013 62 080507]
[17] L L, Li Y S, Wei L L, Yu M, Zhang M 2012 Acta Phys. Sin. 61 120504 (in Chinese) [吕翎, 李雨珊, 韦琳玲, 于淼, 张檬 2012 61 120504]
[18] Cao H F, Zhang R X 2011 Acta Phys. Sin. 60 050510 (in Chinese) [曹鹤飞, 张若洵 2011 60 050510]
[19] L L, Yu M, Wei L L, Zhang M, Li Y S 2012 Chin. Phys. B 21 100507
[20] Chen D Y, Zhang R F, Ma X Y, Wang J 2012 Chin. Phys. B 21 120507
[21] Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[22] FitzHugh R 1961 Biophys. J. 1 445
[23] Thompson C J, Bardos D C, Yang Y S, Joyner K H 1999 Chaos Solitons Fract. 10 1825
[24] Wang J, Deng B, Tsang K M 2004 Chaos Solitons Fract. 22 469
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