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**On flow switching bifurcations in discontinuous dynamical systems.**
*(English)*
Zbl 1102.37014

Summary: The sliding dynamics on the separation boundary is discussed based on the set-valued vector field theory. From vector fields in the neighborhood of a specific separation boundary, the passability of the flow from the one domain into another one is further discussed. The switching bifurcation conditions from the passable boundary to the non-passable boundary are developed. The sliding flow fragmentation on the separation boundary surface is also presented. The normal vector product field function is introduced to determine the switching bifurcation and sliding fragmentation.

### MSC:

37C10 | Dynamics induced by flows and semiflows |

34A36 | Discontinuous ordinary differential equations |

37G99 | Local and nonlocal bifurcation theory for dynamical systems |

34C23 | Bifurcation theory for ordinary differential equations |

### Keywords:

discontinuous dynamic systems; switching bifurcation; sliding fragmentation; normal vector field product function
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\textit{A. C. J. Luo}, Commun. Nonlinear Sci. Numer. Simul. 12, No. 1, 100--116 (2007; Zbl 1102.37014)

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### References:

[1] | Luo, A. C.J., A theory for non-smooth dynamic systems on the connectable domains, Commun Nonlinear Sci Numer Simul, 10, 1-55 (2005) · Zbl 1065.34007 |

[2] | Fillippov, A. F., Differential equations with discontinuous righthand sides (1988), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0664.34001 |

[3] | Aubin, J. P.; Cellina, A., Differential inclusions (1984), Springer-Verlag: Springer-Verlag Berlin · Zbl 0538.34007 |

[4] | Luo ACJ, Gegg BC. An analytical prediction of sliding motions along discontinuous boundary in non-smooth dynamical systems. Nonlinear Dynam, in press.; Luo ACJ, Gegg BC. An analytical prediction of sliding motions along discontinuous boundary in non-smooth dynamical systems. Nonlinear Dynam, in press. · Zbl 1181.70029 |

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