Crossing-sliding bifurcations in planar $\mathbb{Z}_2$-symmetric Filippov systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917151520063488 |
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| author | Chen, Xingwu Li, Jiahao Li, Tao |
| author_facet | Chen, Xingwu Li, Jiahao Li, Tao |
| contents | In this paper we investigate the crossing-sliding bifurcations of planar Filippov systems with $\mathbb{Z}_2$-symmetry. Such bifurcations are triggered by the perturbations of a critical crossing cycle and constitute an important class of discontinuity-induced bifurcations. By constructing transition maps and developing a decomposition theorem of functions to overcome the difficulty of describing bifurcation boundaries in multi-parameter settings, we systematically characterize the codimension-one and codimension-two bifurcation scenarios through the explicit statement of non-degenerate conditions and the presentation of the corresponding bifurcation diagrams. The asymptotic properties of all bifurcation curves are also derived. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_15336 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Crossing-sliding bifurcations in planar $\mathbb{Z}_2$-symmetric Filippov systems Chen, Xingwu Li, Jiahao Li, Tao Dynamical Systems In this paper we investigate the crossing-sliding bifurcations of planar Filippov systems with $\mathbb{Z}_2$-symmetry. Such bifurcations are triggered by the perturbations of a critical crossing cycle and constitute an important class of discontinuity-induced bifurcations. By constructing transition maps and developing a decomposition theorem of functions to overcome the difficulty of describing bifurcation boundaries in multi-parameter settings, we systematically characterize the codimension-one and codimension-two bifurcation scenarios through the explicit statement of non-degenerate conditions and the presentation of the corresponding bifurcation diagrams. The asymptotic properties of all bifurcation curves are also derived. |
| title | Crossing-sliding bifurcations in planar $\mathbb{Z}_2$-symmetric Filippov systems |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2512.15336 |