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By introducing the electrical controlling circuit composed of inductance and capacitance, a fourth order model of generalized Chuas circuit with fast-slow effect has been established for certain parameter conditions. The conditions for fold bifurcation as well as Hopf bifurcation of the fast subsystem are investigated with the variation of the slow variable. Furthermore, the dynamical evolution of the entire system is explored, in which the fast-slow effect existing in the system is focused. Two types of bursting phenomenon, namely, the symmetric fold/fold and fold/Hopf periodic bursters, as well as their mechanism, are presented, which discloses the difference between the two burstings from the view point of bifurcation.
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Keywords:
- generalized Chuas circuit /
- bursting /
- quiescent state /
- spiking
[1] ［1］Chua L O, Lin G N 1990 IEEE Trans. Circ. Syst. 37 885
[2] ［2］Feng C W, Cai L, Kang Q 2008 Acta Phys. Sin. 57 6155 (in Chinese)［冯朝文、蔡理、康强 2008 物理学报 57 6155］
[3] ［3］Luo X S, Wang B H, Chen G R, Jiang P Q, Fang J Q, Quan H J 2002 Acta Phys. Sin. 51 0988（in Chinese）［罗晓曙、汪秉宏、陈关荣、蒋品群、方锦清、全宏俊 2002 物理学报 51 0988］
[4] ［4］Zhang C X, Yu S M 2009 Acta Phys. Sin. 58 120（in Chinese）［张朝霞、禹思敏 2009 物理学报 58 120］
[5] ［5］Stouboulos I N, Miliou A N, Valaristos A P, Kyprianidis I M, Anagnostopoulos A N 2007 Chaos Soliton. Fract. 33 1256
[6] ［6 ］Hartley T T, Mossayebi F 1989 Proc. Am. Contr. Conf. Pittsburgh 419
[7] ［7］Hassan S, Aria A 2008 Math. Comput. Simul. 79 233
[8] ［8］Yassen M T 2003 Appl. Math. Comput. 135 113
[9] ［9］Thongchai B, Piyapong N 2007 Math. Comput. Simul. 75 37
[10] ］Jun J Y, Jui S L, The L L 2008 Chaos Soliton. Fract. 36 45
[11] ］Yang Z Q, Lu Q H 2008 Sci. Chin. Ser. G 51 687
[12] ］Izhikevich E M 2000 Int. J. Bifur. Chaos 10 1171
[13] ］Gukenheimer J, Holmes P 1983 Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Field (New York: Springer)
[14] ］Kuznetsov Y A 1998 Elements of Applied Bifurcation Theory (New York: Springer Verlag)
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[1] ［1］Chua L O, Lin G N 1990 IEEE Trans. Circ. Syst. 37 885
[2] ［2］Feng C W, Cai L, Kang Q 2008 Acta Phys. Sin. 57 6155 (in Chinese)［冯朝文、蔡理、康强 2008 物理学报 57 6155］
[3] ［3］Luo X S, Wang B H, Chen G R, Jiang P Q, Fang J Q, Quan H J 2002 Acta Phys. Sin. 51 0988（in Chinese）［罗晓曙、汪秉宏、陈关荣、蒋品群、方锦清、全宏俊 2002 物理学报 51 0988］
[4] ［4］Zhang C X, Yu S M 2009 Acta Phys. Sin. 58 120（in Chinese）［张朝霞、禹思敏 2009 物理学报 58 120］
[5] ［5］Stouboulos I N, Miliou A N, Valaristos A P, Kyprianidis I M, Anagnostopoulos A N 2007 Chaos Soliton. Fract. 33 1256
[6] ［6 ］Hartley T T, Mossayebi F 1989 Proc. Am. Contr. Conf. Pittsburgh 419
[7] ［7］Hassan S, Aria A 2008 Math. Comput. Simul. 79 233
[8] ［8］Yassen M T 2003 Appl. Math. Comput. 135 113
[9] ［9］Thongchai B, Piyapong N 2007 Math. Comput. Simul. 75 37
[10] ］Jun J Y, Jui S L, The L L 2008 Chaos Soliton. Fract. 36 45
[11] ］Yang Z Q, Lu Q H 2008 Sci. Chin. Ser. G 51 687
[12] ］Izhikevich E M 2000 Int. J. Bifur. Chaos 10 1171
[13] ］Gukenheimer J, Holmes P 1983 Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Field (New York: Springer)
[14] ］Kuznetsov Y A 1998 Elements of Applied Bifurcation Theory (New York: Springer Verlag)
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