-
Previous Article
A theorem on chaotic dynamics and its application to differential delay equations
- PROC Home
- This Issue
-
Next Article
A method, with applications, for analyzing co-registered EEG and MRI data
Normal form of Duffing-van der Pol oscillator under nonautonomous parametric perturbations
| 1. | Institut für Mathematik, Universität Augsburg, 86135 Augsburg, Germany |
- Abstract
- Related Papers
Under a Creative Commons license
| [1] |
Zhaosheng Feng. Duffing-van der Pol-type oscillator systems. Discrete & Continuous Dynamical Systems - S, 2014, 7 (6) : 1231-1257. doi: 10.3934/dcdss.2014.7.1231 |
| [2] |
Zhaoxia Wang, Hebai Chen. A nonsmooth van der Pol-Duffing oscillator (I): The sum of indices of equilibria is $ -1 $. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021096 |
| [3] |
Zhaoxia Wang, Hebai Chen. A nonsmooth van der Pol-Duffing oscillator (II): The sum of indices of equilibria is $ 1 $. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021101 |
| [4] |
Zhaosheng Feng, Guangyue Gao, Jing Cui. Duffing--van der Pol--type oscillator system and its first integrals. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1377-1391. doi: 10.3934/cpaa.2011.10.1377 |
| [5] |
Vivi Rottschäfer. Multi-bump patterns by a normal form approach. Discrete & Continuous Dynamical Systems - B, 2001, 1 (3) : 363-386. doi: 10.3934/dcdsb.2001.1.363 |
| [6] |
Todor Mitev, Georgi Popov. Gevrey normal form and effective stability of Lagrangian tori. Discrete & Continuous Dynamical Systems - S, 2010, 3 (4) : 643-666. doi: 10.3934/dcdss.2010.3.643 |
| [7] |
Dario Bambusi, A. Carati, A. Ponno. The nonlinear Schrödinger equation as a resonant normal form. Discrete & Continuous Dynamical Systems - B, 2002, 2 (1) : 109-128. doi: 10.3934/dcdsb.2002.2.109 |
| [8] |
Virginie De Witte, Willy Govaerts. Numerical computation of normal form coefficients of bifurcations of odes in MATLAB. Conference Publications, 2011, 2011 (Special) : 362-372. doi: 10.3934/proc.2011.2011.362 |
| [9] |
Letizia Stefanelli, Ugo Locatelli. Kolmogorov's normal form for equations of motion with dissipative effects. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2561-2593. doi: 10.3934/dcdsb.2012.17.2561 |
| [10] |
John Burke, Edgar Knobloch. Normal form for spatial dynamics in the Swift-Hohenberg equation. Conference Publications, 2007, 2007 (Special) : 170-180. doi: 10.3934/proc.2007.2007.170 |
| [11] |
Majid Gazor, Mojtaba Moazeni. Parametric normal forms for Bogdanov--Takens singularity; the generalized saddle-node case. Discrete & Continuous Dynamical Systems, 2015, 35 (1) : 205-224. doi: 10.3934/dcds.2015.35.205 |
| [12] |
Svetlana Bunimovich-Mendrazitsky, Yakov Goltser. Use of quasi-normal form to examine stability of tumor-free equilibrium in a mathematical model of bcg treatment of bladder cancer. Mathematical Biosciences & Engineering, 2011, 8 (2) : 529-547. doi: 10.3934/mbe.2011.8.529 |
| [13] |
Kazuyuki Yagasaki. Existence of finite time blow-up solutions in a normal form of the subcritical Hopf bifurcation with time-delayed feedback for small initial functions. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021151 |
| [14] |
Xiaoqin P. Wu, Liancheng Wang. Hopf bifurcation of a class of two coupled relaxation oscillators of the van der Pol type with delay. Discrete & Continuous Dynamical Systems - B, 2010, 13 (2) : 503-516. doi: 10.3934/dcdsb.2010.13.503 |
| [15] |
Boris Anicet Guimfack, Conrad Bertrand Tabi, Alidou Mohamadou, Timoléon Crépin Kofané. Stochastic dynamics of the FitzHugh-Nagumo neuron model through a modified Van der Pol equation with fractional-order term and Gaussian white noise excitation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (7) : 2229-2243. doi: 10.3934/dcdss.2020397 |
| [16] |
Leszek Gasiński, Piotr Kalita. On dynamic contact problem with generalized Coulomb friction, normal compliance and damage. Evolution Equations & Control Theory, 2020, 9 (4) : 1009-1026. doi: 10.3934/eect.2020049 |
| [17] |
Songsong Lu, Hongqing Wu, Chengkui Zhong. Attractors for nonautonomous 2d Navier-Stokes equations with normal external forces. Discrete & Continuous Dynamical Systems, 2005, 13 (3) : 701-719. doi: 10.3934/dcds.2005.13.701 |
| [18] |
David Iglesias-Ponte, Juan Carlos Marrero, David Martín de Diego, Edith Padrón. Discrete dynamics in implicit form. Discrete & Continuous Dynamical Systems, 2013, 33 (3) : 1117-1135. doi: 10.3934/dcds.2013.33.1117 |
| [19] |
Luigi Chierchia, Gabriella Pinzari. Planetary Birkhoff normal forms. Journal of Modern Dynamics, 2011, 5 (4) : 623-664. doi: 10.3934/jmd.2011.5.623 |
| [20] |
Giuseppe Gaeta, Sebastian Walcher. Higher order normal modes. Journal of Geometric Mechanics, 2020, 12 (3) : 421-434. doi: 10.3934/jgm.2020026 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]