Resolution of the Piecewise Smooth Visible–Invisible Two-Fold Singularity in $$\mathbb {R}^3$$ R 3 Using Regularization and Blowup-Reference-Cited by-同舟云学术

Resolution of the Piecewise Smooth Visible–Invisible Two-Fold Singularity in $$\mathbb {R}^3$$ R 3 Using Regularization and Blowup

Published:2018-10-12 Issue:2 Volume:29 Page:723-787
ISSN:0938-8974
Container-title:Journal of Nonlinear Science
language:en
Short-container-title:J Nonlinear Sci

Author:

Kristiansen K. Uldall^ORCID,Hogan S. J.^ORCID

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,General Engineering,Modelling and Simulation

Link

http://link.springer.com/content/pdf/10.1007/s00332-018-9502-x.pdf

Reference27 articles.

1. Brøns, M.: Private communication (2015)

2. Brøns, M., Krupa, M., Wechselberger, M.: Mixed mode oscillations due to the generalized canard phenomenon. In: Nagata, W., Sri Namachchivaya, N. (eds.) Bifurcation Theory and Spatio-Temporal Pattern Formation, Volume 49 of Fields Institute Communications, pp. 39–64. American Mathematical Society, Providence (2006)

3. Carr, J.: Applications of Centre Manifold Theory, vol. 35. Springer, New York (1981)

4. Colombo, A., Jeffrey, M.R.: Nondeterministic chaos, and the two-fold singularity in piecewise smooth flows. SIAM J. Appl. Dyn. Syst. 10(2), 423–451 (2011)

5. Desroches, M., Jeffrey, M.R.: Canards and curvature: nonsmooth approximation by pinching. Nonlinearity 24(5), 1655–1682 (2011)

Cited by 23 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Classification of Filippov Type 3 Singular Points in Planar Bimodal Piecewise Smooth Systems;SIAM Journal on Applied Dynamical Systems;2024-08-20

2. Sliding Cycles of Regularized Piecewise Linear Visible–Invisible Twofolds;Qualitative Theory of Dynamical Systems;2024-08-16

3. Revisiting the Kepler problem with linear drag using the blowup method and normal form theory;Nonlinearity;2024-02-09

4. The Painlevé paradox in three dimensions: resolution with regularization;Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences;2023-12

5. Blowup Analysis of a Hysteresis Model Based Upon Singular Perturbations;Journal of Nonlinear Science;2023-10-26