Gazor, Majid; Shoghi, Ahmad Normal forms of double Hopf oscillators with radial nonlinearities. (English) Zbl 1516.37056 Physica D 453, Article ID 133813, 30 p. (2023). MSC: 37G05 34C20 34C23 34H20 PDFBibTeX XMLCite \textit{M. Gazor} and \textit{A. Shoghi}, Physica D 453, Article ID 133813, 30 p. (2023; Zbl 1516.37056) Full Text: DOI
Xue, Miao; Gou, Junting; Xia, Yibo; Bi, Qinsheng Computation of the normal form as well as the unfolding of the vector field with zero-zero-Hopf bifurcation at the origin. (English) Zbl 07431522 Math. Comput. Simul. 190, 377-397 (2021). MSC: 37-XX 34-XX PDFBibTeX XMLCite \textit{M. Xue} et al., Math. Comput. Simul. 190, 377--397 (2021; Zbl 07431522) Full Text: DOI
Qin, B. W.; Chung, K. W.; Algaba, A.; Rodríguez-Luis, A. J. High-order approximation of heteroclinic bifurcations in truncated 2D-normal forms for the generic cases of Hopf-zero and nonresonant double Hopf singularities. (English) Zbl 1478.34067 SIAM J. Appl. Dyn. Syst. 20, No. 1, 403-437 (2021). Reviewer: Tao Li (Chengdu) MSC: 34E05 34E10 34C37 37M20 41A60 34C20 34C23 PDFBibTeX XMLCite \textit{B. W. Qin} et al., SIAM J. Appl. Dyn. Syst. 20, No. 1, 403--437 (2021; Zbl 1478.34067) Full Text: DOI
Algaba, A.; Fuentes, N.; Gamero, E.; García, C. Orbital normal forms for a class of three-dimensional systems with an application to Hopf-zero bifurcation analysis of Fitzhugh-Nagumo system. (English) Zbl 1433.34055 Appl. Math. Comput. 369, Article ID 124893, 21 p. (2020). MSC: 34C20 34C23 37G15 92C20 37G05 34C05 PDFBibTeX XMLCite \textit{A. Algaba} et al., Appl. Math. Comput. 369, Article ID 124893, 21 p. (2020; Zbl 1433.34055) Full Text: DOI
Mokhtari, Fahimeh On the representations and \(\mathbb{Z}_2\)-equivariant normal form for solenoidal Hopf-zero singularities. (English) Zbl 1415.37070 Physica D 386-387, 14-22 (2019). MSC: 37G05 37C80 34C20 PDFBibTeX XMLCite \textit{F. Mokhtari}, Physica D 386--387, 14--22 (2019; Zbl 1415.37070) Full Text: DOI arXiv
Gazor, Majid; Mokhtari, Fahimeh; Sanders, Jan A. Vector potential normal form classification for completely integrable solenoidal nilpotent singularities. (English) Zbl 1412.34131 J. Differ. Equations 267, No. 1, 407-442 (2019). MSC: 34C20 34C14 34C05 37J35 PDFBibTeX XMLCite \textit{M. Gazor} et al., J. Differ. Equations 267, No. 1, 407--442 (2019; Zbl 1412.34131) Full Text: DOI arXiv
Gazor, Majid; Kazemi, Mahsa Normal form analysis of \(\mathbb Z_2\)-equivariant singularities. (English) Zbl 1411.37063 Int. J. Bifurcation Chaos Appl. Sci. Eng. 29, No. 2, Article ID 1950015, 20 p. (2019). MSC: 37M20 37C80 37G05 PDFBibTeX XMLCite \textit{M. Gazor} and \textit{M. Kazemi}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 29, No. 2, Article ID 1950015, 20 p. (2019; Zbl 1411.37063) Full Text: DOI
Tian, Yun; Yu, Pei An explicit recursive formula for computing the normal forms associated with semisimple cases. (English) Zbl 1457.37066 Commun. Nonlinear Sci. Numer. Simul. 19, No. 7, 2294-2308 (2014). MSC: 37G05 37C15 37F75 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{P. Yu}, Commun. Nonlinear Sci. Numer. Simul. 19, No. 7, 2294--2308 (2014; Zbl 1457.37066) Full Text: DOI