Homoclinic-doubling and homoclinic-gluing bifurcations in the Takens-Bogdanov normal form with D4 symmetry
From MaRDI portal
Publication:4689227
DOI10.1063/1.5030692zbMath1397.37022OpenAlexW2890492950WikidataQ57120256 ScholiaQ57120256MaRDI QIDQ4689227
Mohamed Belhaq, Kwok Wai Chung, Bo-Wei Qin, Alejandro J. Rodríguez-Luis
Publication date: 15 October 2018
Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.5030692
Normal forms for dynamical systems (37G05) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Homoclinic and heteroclinic orbits for dynamical systems (37C29)
Related Items (10)
Study of a dynamical system with a strange attractor and invariant tori ⋮ High-Order Analysis of Canard Explosion in the Brusselator Equations ⋮ Computation of all the coefficients for the global connections in the \(\mathbb{Z}_2\)-symmetric Takens-Bogdanov normal forms ⋮ Study of a simple 3D quadratic system with homoclinic flip bifurcations of inward twist case \(\mathbf{C}_{\mathbf{in}}\) ⋮ High-order study of the canard explosion in an aircraft ground dynamics model ⋮ Analytical approximation of cuspidal loops using a nonlinear time transformation method ⋮ A nonlinear time transformation method to compute all the coefficients for the homoclinic bifurcation in the quadratic Takens-Bogdanov normal form ⋮ High-Order Analysis of Global Bifurcations in a Codimension-Three Takens–Bogdanov Singularity in Reversible Systems ⋮ High-Order Approximation of Heteroclinic Bifurcations in Truncated 2D-Normal Forms for the Generic Cases of Hopf-Zero and Nonresonant Double Hopf Singularities ⋮ Analytical approximation of the canard explosion in a van der Pol system with the nonlinear time transformation method
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Multi-symplectic method to simulate soliton resonance of \({(2+1)}\)-dimensional Boussinesq equation
- Analytics of heteroclinic bifurcation in a \(3:1\) subharmonic resonance
- On internal resonance of nonlinear vibrating systems with many degrees of freedom
- Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations
- Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields
- Analysis of Hopf and Takens-Bogdanov bifurcations in a modified van der Pol-Duffing oscillator
- A case study for homoclinic chaos in an autonomous electronic circuit. A trip from Takens-Bogdanov to Hopf-Sil'nikov
- Constructing dynamical systems having homoclinic bifurcation points of codimension two
- The existence of infinitely many homoclinic doubling bifurcations from some codimension 3 homoclinic orbits
- Asymptotics of homoclinic bifurcation in a three-dimensional system
- Homoclinic connections in strongly self-excited nonlinear oscillators: The Melnikov function and the elliptic Lindstedt-Poincaré method
- The Lorenz equations: bifurcations, chaos, and strange attractors
- Quantitative universality for a class of nonlinear transformations
- A bifurcation analysis of a simple electronic circuit
- Constructing explicit homoclinic solution of oscillators: an improvement for perturbation procedure based on nonlinear time transformation
- Takens-Bogdanov bifurcations of equilibria and periodic orbits in the Lorenz system
- Steady-state, self-oscillating and chaotic behavior of a PID controlled nonlinear servomechanism by using Bogdanov-Takens and Andronov-Poincaré-Hopf bifurcations
- Homoclinic and heteroclinic solutions of cubic strongly nonlinear autonomous oscillators by the hyperbolic perturbation method
- On the Heteroclinic Connections in the 1:3 Resonance Problem
- Takens–Bogdanov bifurcation of travelling-wave solutions in pipe flow
- AN ELLIPTIC PERTURBATION METHOD FOR CERTAIN STRONGLY NON-LINEAR OSCILLATORS
- Nonlinear periodic convection in double-diffusive systems
- TRAVELLING WAVES IN A CIRCULAR ARRAY OF CHUA’S CIRCUITS
- A strange attractor in the unfolding of an orbit-flip homoclinic orbit
- Driven synchronization in random networks of oscillators
- Chaos in the Takens–Bogdanov bifurcation withO(2) symmetry
- Numerical proof for chemostat chaos of Shilnikov's type
- Strange attractor in the unfolding of an inclination-flip homoclinic orbit
- ANALYTICAL APPROXIMATION OF HETEROCLINIC BIFURCATION IN A 1:4 RESONANCE
- KNEADINGS, SYMBOLIC DYNAMICS AND PAINTING LORENZ CHAOS
- Stability diagram for the forced Kuramoto model
- MULTIPARAMETRIC BIFURCATIONS IN AN ENZYME-CATALYZED REACTION MODEL
- MATCONT
- Global bifurcations in the Takens-Bogdanov normal form with \(D_4\) symmetry near the \(O(2)\) limit
- Death of period-doublings: Locating the homoclinic-doubling cascade
- Homoclinic-doubling cascades.
This page was built for publication: Homoclinic-doubling and homoclinic-gluing bifurcations in the Takens-Bogdanov normal form with D4 symmetry
