Numerical Periodic Normalization for Codim 1 Bifurcations of Limit Cycles

DOI10.1137/040611306zbMath1103.34025arXiv1111.4445OpenAlexW1993534484MaRDI QIDQ5470887

Yuri A. Kuznetsov, Annick Dhooge, Willy Govaerts, Eusebius J. Doedel

Publication date: 2 June 2006

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.4445

zbMATH Keywords

limit cyclesnormal formsbifurcations

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Numerical investigation of stability of solutions to ordinary differential equations (65L07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Computational methods for bifurcation problems in dynamical systems (37M20)

Related Items (9)

Bifurcation Analysis of Bogdanov–Takens Bifurcations in Delay Differential Equations ⋮ Convergence analysis of a numerical method to solve the adjoint linearized periodic orbit equations ⋮ A Neural Mass Model with Direct and Indirect Excitatory Feedback Loops: Identification of Bifurcations and Temporal Dynamics ⋮ New features of the software M<scp>at</scp>C<scp>ont</scp>for bifurcation analysis of dynamical systems ⋮ On the stabilizing and destabilizing effects of damping in a non-conservative pin-disc system ⋮ Various closeness results in discretized bifurcations ⋮ Switching to nonhyperbolic cycles from codim 2 bifurcations of equilibria in ODEs ⋮ Switching to Nonhyperbolic Cycles from Codimension Two Bifurcations of Equilibria of Delay Differential Equations ⋮ Bifurcation analysis of an SIR model with logistic growth, nonlinear incidence, and saturated treatment

Uses Software

• ADOL-C
• MATCONT
• CL_MATCONT

This page was built for publication: Numerical Periodic Normalization for Codim 1 Bifurcations of Limit Cycles