Preservation of Takens-Bogdanov bifurcations for delay differential equations by Euler discretization
DOI10.1007/s10884-014-9354-5zbMath1322.34082arXiv1202.4337OpenAlexW1977860785MaRDI QIDQ487951
Publication date: 23 January 2015
Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1202.4337
delay differential equationTakens-Bogdanov bifurcationforward Euler methodpreservation under discretization
Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Computational methods for bifurcation problems in dynamical systems (37M20) Numerical bifurcation problems (65P30) Bifurcation theory of functional-differential equations (34K18)
Related Items (2)
Cites Work
- Discretizing dynamical systems with generalized Hopf bifurcations
- Preservation of homoclinic orbits under discretization of delay differential equations
- Preservation of oscillations of the Runge-Kutta method for equation \(x'(t)+ax(t)+a_1x([t - 1)=0\)]
- Periodic orbits of delay differential equations under discretization
- A numerical \(C^{1}\)-shadowing result for retarded functional differential equations
- On manifolds of connecting orbits in discretizations of dynamical systems
- Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
- Normal forms for retarded functional differential equations and applications to Bogdanov-Takens singularity
- Numerical Hopf bifurcation for a class of delay differential equations
- Homoclinic orbits and Hopf bifurcations in delay differential systems with T-B singularity
- Discretizing dynamical systems with Hopf-Hopf bifurcations
- Normal forms near critical points for differential equations and maps
- DISCRETIZING BIFURCATION DIAGRAMS NEAR CODIMENSION TWO SINGULARITIES
- Width of the Homoclinic Zone in the Parameter Space for Quadratic Maps
- Consistency of local dynamics and bifurcation of continuous-time dynamical systems and their numerical discretizations
- Numerical Methods for Delay Differential Equations
- Discretization of homoclinic orbits, rapid forcing and “invisible” chaos
- Invariant circles in the Bogdanov-Takens bifurcation for diffeomorphisms
- A Hopf bifurcation theorem for difference equations approximating a differential equation
- Numerical Methods for Ordinary Differential Equations
- Unstable manifolds for RFDEs under discretization: The Euler method
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Preservation of Takens-Bogdanov bifurcations for delay differential equations by Euler discretization
