A special type of codimension two bifurcation and unusual dynamics in a phase-modulated system with switched strategy |
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Authors: | Yongxiang Zhang Guanwei Luo |
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Institution: | 1.College of Science,Shenyang Agricultural University,Shenyang,China;2.Gansu Key Laboratory for System Dynamics and Reliability of Railway Transportation Equipment,Lanzhou Jiaotong University,Lanzhou,China |
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Abstract: | We investigate a new type of codimension two bifurcation and related dynamics in a phase-modulated system with switched strategy.
Two curves intersect at a point and are called the crisis–Hopf bifurcation. At the critical crisis–Hopf vertex, a boundary
crisis and Hopf bifurcation coincide. Metamorphosis of coexisting attractors can be observed in the vicinity of the vertex.
Another novelty is that we discover some sets of measure zero with riddled holes in the neighborhood of the bifurcation point.
These sets display some qualitative and quantitative features of riddled basins but they are essentially different from the
riddled basin. It may provide a more comprehensive picture for unusual dynamical features. |
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Keywords: | |
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