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A coupled system composed of two nonlinear circuit systems is investigated. In this paper, the existence condition and the analytical expressions of equilibrium in higher-dimensional system are derived, and the co-dimension 1 and co-dimension 2 bifurcations of equilibrium are also studied. Furthermore, the complicated bifurcations are obtained through the continuation of limit cycles. It may lead to various dynamical behaviors such as periodic motion, chaos, etc., for the interaction of two subsystems with periodic motions under different coupling parameters. Using the qualitative analysis of equilibrium before and after coupling, the relation between the discontinuity of bifurcation diagram and occurrence of neutral saddle in the case of weak coupling is presented.
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Keywords:
- nonlinear circuit /
- coupling /
- equilibrium /
- bifurcation
[1] Rand R H, Holmes P J 1980 Int. J. Nonlin. Mech. 15 387
[2] Maccari A 2001 Int. J. Nonlin. Mech. 36 335
[3] Soto M S, Tischendorf C 2005 Appl. Numer. Math. 53 471
[4] Rasmussen J, Mosekilde E, Reick C 1996 Math. Comput. Simu. 40 247
[5] Rogister F, Pieroux D, Sciamanna M, Mégret P, Blondel M 2002 Opt. Commun. 207 295
[6] Wen G L, Xu D L 2004 Phys. Lett. A 321 24
[7] Yu H J, Liu Y Z 2005 Acta Phys. Sin. 54 3029 (in Chinese) [于洪洁, 刘延柱 2005 物理学报 54 3029]
[8] Bi Q S 2004 Int. J. Nonlin. Mech. 39 33
[9] Bi Q S 2004 Int. J. Bifur. Chaos 14 337
[10] Chen Z Y, Bi Q S 2010 Acta Phys. Sin. 59 7669 (in Chinese) [陈章耀, 毕勤胜 2010 物理学报 59 7669]
[11] Liu Y Q, Xu P 2008 Control Theory Appl. 25 139 (in Chinese) [刘永强, 徐鹏 2008 控制理论与应用 25 139]
[12] Chen L L, Zhao J P, Chen H L 2003 Chin. J. Appl. Mech. 20 70 (in Chinese) [陈玲莉, 赵建平, 陈花玲 2003 应用力学学报 20 70]
[13] Li Q H, Xi J Z, Hua C C 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 769
[14] Zhang X F, Chen Z Y, Bi Q S 2009 Acta Phys. Sin. 58 2963 (in Chinese) [张晓芳, 陈章耀, 毕勤胜 2009 物理学报 58 2963]
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[1] Rand R H, Holmes P J 1980 Int. J. Nonlin. Mech. 15 387
[2] Maccari A 2001 Int. J. Nonlin. Mech. 36 335
[3] Soto M S, Tischendorf C 2005 Appl. Numer. Math. 53 471
[4] Rasmussen J, Mosekilde E, Reick C 1996 Math. Comput. Simu. 40 247
[5] Rogister F, Pieroux D, Sciamanna M, Mégret P, Blondel M 2002 Opt. Commun. 207 295
[6] Wen G L, Xu D L 2004 Phys. Lett. A 321 24
[7] Yu H J, Liu Y Z 2005 Acta Phys. Sin. 54 3029 (in Chinese) [于洪洁, 刘延柱 2005 物理学报 54 3029]
[8] Bi Q S 2004 Int. J. Nonlin. Mech. 39 33
[9] Bi Q S 2004 Int. J. Bifur. Chaos 14 337
[10] Chen Z Y, Bi Q S 2010 Acta Phys. Sin. 59 7669 (in Chinese) [陈章耀, 毕勤胜 2010 物理学报 59 7669]
[11] Liu Y Q, Xu P 2008 Control Theory Appl. 25 139 (in Chinese) [刘永强, 徐鹏 2008 控制理论与应用 25 139]
[12] Chen L L, Zhao J P, Chen H L 2003 Chin. J. Appl. Mech. 20 70 (in Chinese) [陈玲莉, 赵建平, 陈花玲 2003 应用力学学报 20 70]
[13] Li Q H, Xi J Z, Hua C C 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 769
[14] Zhang X F, Chen Z Y, Bi Q S 2009 Acta Phys. Sin. 58 2963 (in Chinese) [张晓芳, 陈章耀, 毕勤胜 2009 物理学报 58 2963]
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