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The inner equation for generic analytic unfoldings of the Hopf-zero singularity
1. | Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain |
[1] |
Freddy Dumortier, Santiago Ibáñez, Hiroshi Kokubu, Carles Simó. About the unfolding of a Hopf-zero singularity. Discrete and Continuous Dynamical Systems, 2013, 33 (10) : 4435-4471. doi: 10.3934/dcds.2013.33.4435 |
[2] |
Isaac A. García, Claudia Valls. The three-dimensional center problem for the zero-Hopf singularity. Discrete and Continuous Dynamical Systems, 2016, 36 (4) : 2027-2046. doi: 10.3934/dcds.2016.36.2027 |
[3] |
Radosław Kurek, Paweł Lubowiecki, Henryk Żołądek. The Hess-Appelrot system. Ⅲ. Splitting of separatrices and chaos. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 1955-1981. doi: 10.3934/dcds.2018079 |
[4] |
Yimei Li, Jiguang Bao. Semilinear elliptic system with boundary singularity. Discrete and Continuous Dynamical Systems, 2020, 40 (4) : 2189-2212. doi: 10.3934/dcds.2020111 |
[5] |
Sébastien Court. Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part II: The nonlinear system.. Evolution Equations and Control Theory, 2014, 3 (1) : 83-118. doi: 10.3934/eect.2014.3.83 |
[6] |
Sébastien Court. Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part I: The linearized system.. Evolution Equations and Control Theory, 2014, 3 (1) : 59-82. doi: 10.3934/eect.2014.3.59 |
[7] |
Jaume Llibre, Ernesto Pérez-Chavela. Zero-Hopf bifurcation for a class of Lorenz-type systems. Discrete and Continuous Dynamical Systems - B, 2014, 19 (6) : 1731-1736. doi: 10.3934/dcdsb.2014.19.1731 |
[8] |
Paweł Lubowiecki, Henryk Żołądek. The Hess-Appelrot system. I. Invariant torus and its normal hyperbolicity. Journal of Geometric Mechanics, 2012, 4 (4) : 443-467. doi: 10.3934/jgm.2012.4.443 |
[9] |
Xun Cao, Weihua Jiang. Double zero singularity and spatiotemporal patterns in a diffusive predator-prey model with nonlocal prey competition. Discrete and Continuous Dynamical Systems - B, 2020, 25 (9) : 3461-3489. doi: 10.3934/dcdsb.2020069 |
[10] |
Xin Zhong. Singularity formation to the two-dimensional non-barotropic non-resistive magnetohydrodynamic equations with zero heat conduction in a bounded domain. Discrete and Continuous Dynamical Systems - B, 2020, 25 (3) : 1083-1096. doi: 10.3934/dcdsb.2019209 |
[11] |
Xiang-Ping Yan, Wan-Tong Li. Stability and Hopf bifurcations for a delayed diffusion system in population dynamics. Discrete and Continuous Dynamical Systems - B, 2012, 17 (1) : 367-399. doi: 10.3934/dcdsb.2012.17.367 |
[12] |
Min Hu, Tao Li, Xingwu Chen. Bi-center problem and Hopf cyclicity of a Cubic Liénard system. Discrete and Continuous Dynamical Systems - B, 2020, 25 (1) : 401-414. doi: 10.3934/dcdsb.2019187 |
[13] |
Xiaoling Zou, Dejun Fan, Ke Wang. Stationary distribution and stochastic Hopf bifurcation for a predator-prey system with noises. Discrete and Continuous Dynamical Systems - B, 2013, 18 (5) : 1507-1519. doi: 10.3934/dcdsb.2013.18.1507 |
[14] |
Pau Martín, David Sauzin, Tere M. Seara. Resurgence of inner solutions for perturbations of the McMillan map. Discrete and Continuous Dynamical Systems, 2011, 31 (1) : 165-207. doi: 10.3934/dcds.2011.31.165 |
[15] |
Kerioui Nadjah, Abdelouahab Mohammed Salah. Stability and Hopf bifurcation of the coexistence equilibrium for a differential-algebraic biological economic system with predator harvesting. Electronic Research Archive, 2021, 29 (1) : 1641-1660. doi: 10.3934/era.2020084 |
[16] |
Xiaoyuan Chang, Junjie Wei. Stability and Hopf bifurcation in a diffusive predator-prey system incorporating a prey refuge. Mathematical Biosciences & Engineering, 2013, 10 (4) : 979-996. doi: 10.3934/mbe.2013.10.979 |
[17] |
Qi An, Weihua Jiang. Spatiotemporal attractors generated by the Turing-Hopf bifurcation in a time-delayed reaction-diffusion system. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 487-510. doi: 10.3934/dcdsb.2018183 |
[18] |
Hongyong Zhao, Daiyong Wu. Point to point traveling wave and periodic traveling wave induced by Hopf bifurcation for a diffusive predator-prey system. Discrete and Continuous Dynamical Systems - S, 2020, 13 (11) : 3271-3284. doi: 10.3934/dcdss.2020129 |
[19] |
Zuolin Shen, Junjie Wei. Hopf bifurcation analysis in a diffusive predator-prey system with delay and surplus killing effect. Mathematical Biosciences & Engineering, 2018, 15 (3) : 693-715. doi: 10.3934/mbe.2018031 |
[20] |
Guido Schneider, Matthias Winter. The amplitude system for a Simultaneous short-wave Turing and long-wave Hopf instability. Discrete and Continuous Dynamical Systems - S, 2021 doi: 10.3934/dcdss.2021119 |
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