Linear recursion formulas of quantities of singular point and applications.

DOI10.1016/S0096-3003(02)00835-4zbMath1053.65051OpenAlexW2091738011MaRDI QIDQ1415271

Haibo Chen, Yi-rong Liu

Publication date: 3 December 2003

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0096-3003(02)00835-4

zbMATH Keywords

numerical examplenormal formsingular pointcomputer algebra systemsplanar autonomous systems

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (13)

Small limit cycles bifurcating from fine focus points in quartic order \(Z_{3}\)-equivariant vector fields ⋮ Center conditions and bifurcation of limit cycles at degenerate singular points in a quintic polynomial differential system ⋮ On the equivalence of singular point quantities and the integrability of a fine critical singular point ⋮ Isolated periodic wave trains and local critical wave lengths for a nonlinear reaction-diffusion equation ⋮ On the new solutions of the generalized Burgers-Huxley equation ⋮ The equivalence between singular point quantities and Liapunov constants on center manifold ⋮ Calculation of singular point quantities at infinity for a type of polynomial differential systems ⋮ Bifurcation at the equator for a class of quintic polynomial differential system ⋮ Hopf bifurcation for a class of three-dimensional nonlinear dynamic systems ⋮ A cubic polynomial system with seven limit cycles at infinity ⋮ Symbolic computation of limit cycles associated with Hilbert's 16th problem ⋮ Isolated periodic wave solutions arising from Hopf and Poincaré bifurcations in a class of single species model ⋮ Limit periodic travelling wave solution of a model for biological invasions

Uses Software

• Mathematica

Cites Work

• Unnamed Item
• Ljapunov approach to multiple Hopf bifurcation
• An explicit expression of the first Lyapunov and period constants with applications
• Saddle quantities and applications

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