Nonlinear behaviors as well as the mechanism in a piecewise-linear dynamical system with two time scales

Kiss, A.M., Marx, B., Mourot, G., Schutz, G., Ragot, J.: State estimation of two-time scale multiple models. Application to wastewater treatment plant. Control Eng. Pract. 19, 1354–1362 (2011)

Kess, M., Brning, C., Engel, V.: Multiple time scale population transfer-dynamics in coupled electronic states. Chem. Phys. 442, 26–30 (2014)

Abobda, L.T., Woafo, P.: Subharmonic and bursting oscillations of a ferromagnetic mass fixed on a spring and subjected to an AC electromagnet. Commun. Nonlinear Sci. Numer. Simul. 17, 3082–3091 (2012)

Courbage, M., Maslennikov, O.V., Nekorkin, V.I.: Synchronization in time-discrete model of two electrically coupled spike-bursting neurons. Chaos Solitons Fractals 45, 645–659 (2012)

Bi, Q.S.: The mechanism of bursting phenomena in BZ chemical reaction with multiple time scales. Sci. China Ser. E 10, 2820–2830 (2012)

Simo, H., Woafo, P.: Bursting oscillations in electromechanical systems. Mech. Res. Commun. 38, 537–541 (2011)

Izhikevich, E.: Neural excitability, spiking and bursting. Int. J. Bifurc. Chaos 10, 1171–1266 (2000)

Gaiko, V.A.: Multiple limit cycle bifurcations of the FitzHugh–Nagumo neuronal model. Nonlinear Anal. Theory Methods Appl. 74, 7532–7542 (2011)

Li, X.H., Bi, Q.S.: Cusp bursting and slow-fast analysis with two slow parameters in photosensitive Belousov–Zhabotinsky reaction. Chin. Phys. Lett. 30, 070503 (2013)

Yang, Z.Q., Lu, Q.S., Gu, H.G., Ren, W.: Integer multiple spiking in the stochastic Chay model and its dynamical generation mechanism. Phys. Lett. A 299, 499–506 (2002)

Rasmussen, A., Wyller, J., Vik, J.O.: Relaxation oscillations in spruce–budworm interactions. Nonlinear Anal. Real World Appl. 12, 304–319 (2011)

Watts, M., Tabak, J., Zimliki, C., Sherman, A., Bertram, R.: Slow variable dominance and phase resetting in phantom bursting. J. Theor. Biol. 276, 218–228 (2011)

Han, A.J., Jiang, B., Bi, Q.S.: Symmetric bursting of focus-focus type in the controlled Lorenz system with two time scales. Phys. Lett. A 373, 3643–3649 (2009)

Bi, Q.S., Zhang, Z.D.: Bursting phenomena as well as the bifurcation mechanism in controlled Lorenz oscillator with two time scales. Phys. Lett. A 375, 1183–1190 (2011)

Han, X.J., Bi, Q.S.: Bursting oscillations in Duffing’s equation with slowly changing external forcing. Commun. Nonlinear Sci. Numer. Simul. 16, 4146–4152 (2011)

Yi, G.S., Wang, J., Wei, X.L., Deng, B., Li, H.Y., Han, C.X.: Dynamic analysis of Hodgkins three classes of neurons exposed to extremely low-frequency sinusoidal induced electric field. Appl. Math. Comput. 231, 100–110 (2014)

Grgoire-Lacoste, F., Jacquemet, V., Vinet, A.: Bifurcations, sustained oscillations and torus bursting involving ionic concentrations dynamics in a canine atrial cell model. Math. Biosci. 250, 10–25 (2014)

Medetov, M., Weiß, R.G., Zhanabaev, Z.Z., Zaks, M.A.: Numerically induced bursting in a set of coupled neuronal oscillators. Commun. Nonlinear Sci. Numer. Simul. 20, 1090–1098 (2015)

Goussis, D.A.: The role of slow system dynamics in predicting the degeneracy of slow invariant manifolds: the case of vdP relaxation–oscillations. Phys. D 48, 16–32 (2013)

Bi, Q.S., Zhang, R., Zhang, Z.D.: Bifurcation mechanism of bursting oscillations in parametrically excited dynamical system. Appl. Math. Comput. 243, 482–491 (2014)

Li, X.H., Bi, Q.S.: Forced bursting and transition mechanism in CO oxidation with three time scales. Chin. Phys. B 22, 040504 (2013)

Arts, J.C., Llibre, J., Medrado, J.C., Teixeira, M.A.: Piecewise linear differential systems with two real saddles. Math. Comput. Simul. 95, 13–22 (2014)

Zhang, C., Bi, Q.S., Han, X.J., Zhang, Z.D.: On two-parameter bifurcation analysis of switched system composed of Duffing and van der Pol oscillators. Commun. Nonlinear Sci. Numer. Simul. 19, 750–757 (2014)

Zhang, Z.D., Li, Y.Y., Bi, Q.S.: Routes to bursting in a periodically driven oscillator. Phys. Lett. A 377, 975–980 (2013)

Chen, Z.Y., Zhang, X.F., Bi, Q.S.: Bifurcations and chaos of coupled electrical circuits. Nonlinear Anal. Real World Appl. 9, 1158–1168 (2008)

Mkaouar, H., Boubaker, O.: Chaos synchronization for master slave piecewise linear systems: application to Chuas circuit. Commun. Nonlinear Sci. Numer. Simul. 17, 1292–1302 (2012)

Baptista, M.S., Caldas, I.L.: Type-II intermittency in the driven double scroll circuit. Phys. D 132, 325–338 (1999)

Ontanon-Garcia, L.J., Jimenez-Lopez, E., Campos-Canton, E., Basin, M.: A family of hyperchaotic multi-scroll attractors in $$R^n$$ R n . Appl. Math. Comput. 233, 522–533 (2014)

Trejo-Guerra, R., Tlelo-Cuautle, E., Jimenez-Fuentes, J.M., Sanchez-Lopez, C., Munoz-Pacheco, J.M., Espinosa-Flores-Verdad, G., Rocha-Perez, J.M.: Integrated circuit generating 3- and 5-scroll attractors. Commun. Nonlinear Sci. Numer. Simul. 17, 4328–4335 (2012)

Leine, R.I., Campen, D.H.: Bifurcation phenomena in non-smooth dynamical systems. Eur. J. Mech. A Solids 25, 595–616 (2006)