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Based on the classical Chua's circuit, a four-dimensional Generalized Chua's circuit with multiple interfaces is established by introducing feedback elements. For the appropriate condition, there exists a difference in order of magnitude between the variables of state and a fast-slow coupled system, thereby forming a fast- and slow-coupled system at time scale. Analyzing the equilibrium points and the characteristics of the fast subsystems, and combining the theory of Clarke differential inclusions, the singularities on the non-smooth boundaries are explored. Two types of periodic bursting phenomena for different conditions are presented. Fast-slow analysis is employed to explore the special cluster phenomenon while the system trajectory passes across multiple interfaces. The coexisting different bursting mechanisms for the case with multiple attractors are explored in detail, while the influence of non-smooth bifurcations on bursting behavior is revealed.
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Keywords:
- non-smooth bifurcation /
- multiple interfaces /
- bursting /
- fast-slow system
[1] Chiba H 2011 J. Differential Equations 250 112
[2] Both R, Finger W, Chaplain R A 1976 Biol. Cybernet. 23 1
[3] Rinzel J 1985 Ordinary and Partial Differential Equations (Berlin: Springer-Verlag) p304
[4] Izhikevich E M 2000 Int. J. Bifurcat. Chaos 10 1171
[5] Perc M, Marhl M 2003 Chaos, Solitons and Fractals 18 759
[6] Mease K D 2005 Appl. Math. Comput. 164 627
[7] Lashina E A, Chumakova N A, Chumakov G A, Boronin A I 2009 Chem. Eng. J. 154 82
[8] Wang H X, Wang Q Y, Lu Q S 2011 Chaos, Solitons and Fractals 44 667
[9] Sundarapandian V, Sundarapandian I 2012 Math. Comput. Modelling 55 1904
[10] Gao T G, Chen G R, Chen Z Q, Cang S J 2007 Phys. Lett. A 361 78
[11] Leine R I 2006 Physica D 223 121
[12] Ren H P, Li W C, Liu D 2010 Chin. Phys. B 19 030511
[13] Gámez-Guzmán L, Cruz-Hernández C, López-Gutiérrez R M, García-Guerrero E E 2009 Commun. Nonlinear Sci. Numer. Simul. 14 2765
[14] Mkaouar H, Boubaker O 2012 Commun. Nonlinear Sci. Numer. Simul. 17 1292
[15] Koliopanos C L, Kyprianidis I M, Stouboulos I N, Anagnostopoulos A N, Magafsa L 2003 Chaos, Solitons and Fractals 16 173
[16] Yu S M, Yu Z D 2008 Acta Phys. Sin. 57 6859 (in Chinese) [禹思敏, 禹之鼎 2008 57 6859]
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[1] Chiba H 2011 J. Differential Equations 250 112
[2] Both R, Finger W, Chaplain R A 1976 Biol. Cybernet. 23 1
[3] Rinzel J 1985 Ordinary and Partial Differential Equations (Berlin: Springer-Verlag) p304
[4] Izhikevich E M 2000 Int. J. Bifurcat. Chaos 10 1171
[5] Perc M, Marhl M 2003 Chaos, Solitons and Fractals 18 759
[6] Mease K D 2005 Appl. Math. Comput. 164 627
[7] Lashina E A, Chumakova N A, Chumakov G A, Boronin A I 2009 Chem. Eng. J. 154 82
[8] Wang H X, Wang Q Y, Lu Q S 2011 Chaos, Solitons and Fractals 44 667
[9] Sundarapandian V, Sundarapandian I 2012 Math. Comput. Modelling 55 1904
[10] Gao T G, Chen G R, Chen Z Q, Cang S J 2007 Phys. Lett. A 361 78
[11] Leine R I 2006 Physica D 223 121
[12] Ren H P, Li W C, Liu D 2010 Chin. Phys. B 19 030511
[13] Gámez-Guzmán L, Cruz-Hernández C, López-Gutiérrez R M, García-Guerrero E E 2009 Commun. Nonlinear Sci. Numer. Simul. 14 2765
[14] Mkaouar H, Boubaker O 2012 Commun. Nonlinear Sci. Numer. Simul. 17 1292
[15] Koliopanos C L, Kyprianidis I M, Stouboulos I N, Anagnostopoulos A N, Magafsa L 2003 Chaos, Solitons and Fractals 16 173
[16] Yu S M, Yu Z D 2008 Acta Phys. Sin. 57 6859 (in Chinese) [禹思敏, 禹之鼎 2008 57 6859]
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