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Since most of the work relevant to the control of Chen system is based on the same time scale, and the results associated with the coupled systems with two time scales are mainly for the cases with only one slow variable, in this paper we investigate the dynamical evolution of the Chen system with the controller described by Duffing oscillator on a slow time scale, which implies two slow variables may be involved in the coupled vector field. Different types of bursting oscillations such as the symmetric fold/fold bursting, symmetric fold/Hopf bursting, symmetric homoclinic/homoclinic bursting, and mechanism are presented, revealing that the mutual influence between the two slow variables may cause the bursting behaviors similar to those in the periodic excited systems.
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Keywords:
- Chen system /
- bursting /
- bifurcation /
- fast-slow effect
[1] Hadef S, Boukabou A 2014 J. Franklin Inst. 351 2728
[2] Smaoui N, Karouma A, Zribi M 2011 Commun. Nonlinear Sci. Numer. Simul. 16 3279
[3] Alhajaj A, Dowell N M, Shah N 2013 Energy Procedia 37 2552
[4] Powathil G G, Gordon K E, Hill L A, Chaplain M A 2012 J. Theor. Biol. 308 1
[5] Bridge J, Mendelowitz L, Rand R, Sah S, Verdugo A 2009 Commun. Nonlinear Sci. Numer. Simul. 14 1598
[6] Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[7] Gyorgui L 1992 Field R J. Nature 355 808
[8] Shen J H, Zhou Z Y 2013 Commun. Nonlinear Sci. Numer. Simul. 18 2213
[9] Shinizu K, Sekikawa M, Inaba N 2011 Phys. Lett. A 375 1566
[10] Han X J, Jiang B, Bi Q S 2009 Phys. Lett. A 373 3643
[11] Shi M, Wang Z H 2014 Commun. Nonlinear Sci. Numer. Simul. 19 1956
[12] Wang Q Y, Aleksandra M, MAtjaz P, Lu Q S 2011 Chin. Phys. B 20 040504
[13] L Y B, Shi X, Zheng Y H 2013 Chin. Phys. B 22 040505
[14] Wang M J, Zeng Y C, Chen G H, He J 2011 Acta Phys. Sin. 60 010509(in Chinese)[王梦蛟, 曾以成, 陈光辉, 贺娟 2011 60 010509]
[15] Zhang X F, Chen Z Y, Bi Q S 2010 Acta Phys. Sin. 59 3802(in Chinese)[张晓芳, 陈章耀, 毕勤胜 2010 59 3802]
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[1] Hadef S, Boukabou A 2014 J. Franklin Inst. 351 2728
[2] Smaoui N, Karouma A, Zribi M 2011 Commun. Nonlinear Sci. Numer. Simul. 16 3279
[3] Alhajaj A, Dowell N M, Shah N 2013 Energy Procedia 37 2552
[4] Powathil G G, Gordon K E, Hill L A, Chaplain M A 2012 J. Theor. Biol. 308 1
[5] Bridge J, Mendelowitz L, Rand R, Sah S, Verdugo A 2009 Commun. Nonlinear Sci. Numer. Simul. 14 1598
[6] Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[7] Gyorgui L 1992 Field R J. Nature 355 808
[8] Shen J H, Zhou Z Y 2013 Commun. Nonlinear Sci. Numer. Simul. 18 2213
[9] Shinizu K, Sekikawa M, Inaba N 2011 Phys. Lett. A 375 1566
[10] Han X J, Jiang B, Bi Q S 2009 Phys. Lett. A 373 3643
[11] Shi M, Wang Z H 2014 Commun. Nonlinear Sci. Numer. Simul. 19 1956
[12] Wang Q Y, Aleksandra M, MAtjaz P, Lu Q S 2011 Chin. Phys. B 20 040504
[13] L Y B, Shi X, Zheng Y H 2013 Chin. Phys. B 22 040505
[14] Wang M J, Zeng Y C, Chen G H, He J 2011 Acta Phys. Sin. 60 010509(in Chinese)[王梦蛟, 曾以成, 陈光辉, 贺娟 2011 60 010509]
[15] Zhang X F, Chen Z Y, Bi Q S 2010 Acta Phys. Sin. 59 3802(in Chinese)[张晓芳, 陈章耀, 毕勤胜 2010 59 3802]
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