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A nonlinear circuit model with periodic switching is established. The fold bifurcation and Hopf bifurcation sets of the subsystems are derived via the analysis of the relevant equilibrium points as well as the stabilities. Complex dynamical behaviors caused by periodic switching in various equilibrium states of subsystems are investigated. The results show that there exist two types of destabilizing cases, i.e., period-doubling bifurcation and saddle-node bifurcation, in the variation of periodic solution to the switching system with parameter, leading to different forms of chaotic oscillations correspondingly. Furthermore, by analyzing the the phase trajectory and its corresponding bifurcation, the mechanisms for different types of oscillations are presented, which can explain some phenomena of the switched dynamical system.
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Keywords:
- periodic switching /
- period-doubling bifurcation /
- saddle-node bifurcation /
- chaos
[1] Wyczalek F A 2001 IEEE Aero. El. Sys. Mag. 16 15
[2] Varaiya P P 1993 IEEE Trans. Automat. Contr. 38 195
[3] Wang Y B, Han Z J, Luo Z W 1997 Contr. Deci. 12 403
[4] Shi Y Q 2001 Proceedings of ICII Beijing International Conferences on Info-tech and Info-net Beijing, China, October 29, 2001 p85
[5] Hiskens I A 2001 Proceedings of the 40th IEEE Conference on Decision and Control Orlando, USA, December 4–7, 2001 p774
[6] Ueta T, Kawakami H 2002 International Symposium on Circuits and Systems (Japan: Toskushima) pII–544
[7] Zhang Z D, Bi Q S 2011 Proceedings of the 13th of the National Nonlinear Vibration Tianjin, China p167
[8] Xie G M, Wang L 2005 J. Math. Anal. Appl. 305 277
[9] Branicky M S 1998 IEEE Trans. Automat. Contr. 43 475
[10] Cheng D, Guo L, Lin Y, Wang Y 2005 IEEE Trans. Automat. Contr. 50 661
[11] Wu T Y, Zhang Z D, Bi Q S 2012 Acta Phys. Sin. 61 070502 (in Chinese) [吴天一, 张正娣, 毕勤胜 2012 物理学报 61 070502]
[12] Yu Y, Zhang C, Han X J, Bi Q S 2012 Acta Phys. Sin. 61 200507 (in Chinese) [余跃, 张春, 韩修静, 毕勤胜 2012 物理学报 61 200507]
[13] Zhang C, Yu Y, Han X J, Bi Q S 2012 Chin. Phys. B 21 100501
[14] Sun C C, Xu Q C, Sui Y 2013 Chin. Phys. B 22 030507
[15] Dong X P, Ma G L 2004 J. Hefei Univ. Technol. 27 10 (in Chinese) [董学平, 马国梁 2004 合肥工业大学学报 27 10]
[16] Wang R M, Guan Z H, Liu X Z 2004 Syst. Engineer. Electron. 26 1 (in Chinese) [王仁明, 关治洪, 刘新芝 2004 系统工程与电子技术 26 1]
[17] Nishiuchi Y, Ueta T, Kawakami H 2006 Chaos Solition. Fract. 27 941
[18] Kousaka T, Ueta T, Ma Y, Kawakami H 2006 Chaos Solition. Fract. 27 1019
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[1] Wyczalek F A 2001 IEEE Aero. El. Sys. Mag. 16 15
[2] Varaiya P P 1993 IEEE Trans. Automat. Contr. 38 195
[3] Wang Y B, Han Z J, Luo Z W 1997 Contr. Deci. 12 403
[4] Shi Y Q 2001 Proceedings of ICII Beijing International Conferences on Info-tech and Info-net Beijing, China, October 29, 2001 p85
[5] Hiskens I A 2001 Proceedings of the 40th IEEE Conference on Decision and Control Orlando, USA, December 4–7, 2001 p774
[6] Ueta T, Kawakami H 2002 International Symposium on Circuits and Systems (Japan: Toskushima) pII–544
[7] Zhang Z D, Bi Q S 2011 Proceedings of the 13th of the National Nonlinear Vibration Tianjin, China p167
[8] Xie G M, Wang L 2005 J. Math. Anal. Appl. 305 277
[9] Branicky M S 1998 IEEE Trans. Automat. Contr. 43 475
[10] Cheng D, Guo L, Lin Y, Wang Y 2005 IEEE Trans. Automat. Contr. 50 661
[11] Wu T Y, Zhang Z D, Bi Q S 2012 Acta Phys. Sin. 61 070502 (in Chinese) [吴天一, 张正娣, 毕勤胜 2012 物理学报 61 070502]
[12] Yu Y, Zhang C, Han X J, Bi Q S 2012 Acta Phys. Sin. 61 200507 (in Chinese) [余跃, 张春, 韩修静, 毕勤胜 2012 物理学报 61 200507]
[13] Zhang C, Yu Y, Han X J, Bi Q S 2012 Chin. Phys. B 21 100501
[14] Sun C C, Xu Q C, Sui Y 2013 Chin. Phys. B 22 030507
[15] Dong X P, Ma G L 2004 J. Hefei Univ. Technol. 27 10 (in Chinese) [董学平, 马国梁 2004 合肥工业大学学报 27 10]
[16] Wang R M, Guan Z H, Liu X Z 2004 Syst. Engineer. Electron. 26 1 (in Chinese) [王仁明, 关治洪, 刘新芝 2004 系统工程与电子技术 26 1]
[17] Nishiuchi Y, Ueta T, Kawakami H 2006 Chaos Solition. Fract. 27 941
[18] Kousaka T, Ueta T, Ma Y, Kawakami H 2006 Chaos Solition. Fract. 27 1019
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