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Upon the analysis of the equilibrium points as well as the stabilities in coupled Jerk systems, bifurcation sets in parameter space are derived, which divide the parameter space into several regions associated with different forms of dynamics. The dynamical evolution of the coupled system is investigated with the variation of different parameters and specially, the influence of the coupling strength on the dynamics of the system is explored in details. The mechanism of some nonlinear phenomena such as the coexistence of multiple behaviors as well as the sequence of period-doubling bifurcations are presented.
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Keywords:
- Jerk system /
- couple /
- bifurcation /
- coexistence
[1] Maccari A 2001 Int. J. Nonlin. Mech. 36 335
[2] Yu H J, Liu Y Z 2005 Acta Phy. Sin. 54 3029 (in Chinese)[于洪洁、刘延柱 2005 物理学报 54 3029]
[3] Liu M H, Yu S M 2006 Acta Phy. Sin. 55 5707 (in Chinese) [刘明华、禹思敏 2006 物理学报 55 5707 Sprott J C 2000 Amer. J. Phys. 68 758 〖5] Malasoma J M 2009 Chaos, Solitons and Fractals 39 533
[4] Chlouverakis K E, Sprott J C 2006 Chaos, Solitons and Fractals 28 739
[5] Maccari A 1998 Nonlinear Dynamics 15 329
[6] Liu Y 2009 Acta Phys. Sin. 58 0749 (in Chinese) [刘 勇 2009 物理学报 58 749]
[7] Roman A F, Alexander E H, Alexey A K 2006 Phys. Lett. A 358 301
[8] Agiza H N, Matouk A E 2006 Chaos, Solitons and Fractals 28 219
[9] Bi Q 2004 Int.l J. Nonlin. Mech. 39 33
[10] Bi Q 2004 Int. J. Bifur. Chaos 14 337
[11] Zhang Z D, Bi Q 2005 Int. J. Nonlin. Sci. Num. Simul. 6 81
[12] Zhang Z D, Bi Q 2005 Chaos, Solitons and Fractals 23 1185
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[1] Maccari A 2001 Int. J. Nonlin. Mech. 36 335
[2] Yu H J, Liu Y Z 2005 Acta Phy. Sin. 54 3029 (in Chinese)[于洪洁、刘延柱 2005 物理学报 54 3029]
[3] Liu M H, Yu S M 2006 Acta Phy. Sin. 55 5707 (in Chinese) [刘明华、禹思敏 2006 物理学报 55 5707 Sprott J C 2000 Amer. J. Phys. 68 758 〖5] Malasoma J M 2009 Chaos, Solitons and Fractals 39 533
[4] Chlouverakis K E, Sprott J C 2006 Chaos, Solitons and Fractals 28 739
[5] Maccari A 1998 Nonlinear Dynamics 15 329
[6] Liu Y 2009 Acta Phys. Sin. 58 0749 (in Chinese) [刘 勇 2009 物理学报 58 749]
[7] Roman A F, Alexander E H, Alexey A K 2006 Phys. Lett. A 358 301
[8] Agiza H N, Matouk A E 2006 Chaos, Solitons and Fractals 28 219
[9] Bi Q 2004 Int.l J. Nonlin. Mech. 39 33
[10] Bi Q 2004 Int. J. Bifur. Chaos 14 337
[11] Zhang Z D, Bi Q 2005 Int. J. Nonlin. Sci. Num. Simul. 6 81
[12] Zhang Z D, Bi Q 2005 Chaos, Solitons and Fractals 23 1185
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