Kukles revisited: Advances in computing techniques

DOI10.1016/j.camwa.2010.09.034zbMath1207.68449OpenAlexW2013766837MaRDI QIDQ630663

Jane M. Pearson, Noel G. Lloyd

Publication date: 19 March 2011

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2010.09.034

zbMATH Keywords

resultantsnonlinear differential equationscomputer algebrakukles systemmodular calculations

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

Related Items (20)

Integrability conditions for complex kukles systems ⋮ Solution of center-focus problem for a class of cubic systems ⋮ On the limit cycles of a class of Kukles type differential systems ⋮ Homogeneous-like generalized cubic systems ⋮ Integrability Conditions for Complex Homogeneous Kukles Systems ⋮ Analytic integrability of cubic-linear planar polynomial differential systems ⋮ Kukles systems of degree three with global centers ⋮ A complete classification on the center-focus problem of a generalized cubic Kukles system with a nilpotent singular point ⋮ On the Gröbner basis of the ideal of Lyapunov quantities of the Kukles system ⋮ Nine limit cycles around a weak focus in a class of three-dimensional cubic Kukles systems ⋮ CENTERS FOR THE KUKLES HOMOGENEOUS SYSTEMS WITH EVEN DEGREE ⋮ Globally asymptotically stable equilibrium points in Kukles systems ⋮ Center conditions for generalized polynomial Kukles systems ⋮ Analytic Integrability of Two Lopsided Systems ⋮ Global Phase Portraits for a Planar ℤ2-Equivariant Kukles Systems of Degree 3 ⋮ Global Phase Portraits for the Kukles Systems of Degree 3 with ℤ2-Reversible Symmetries ⋮ Symbolic computation for the qualitative theory of differential equations ⋮ Centers for the Kukles homogeneous systems with odd degree ⋮ Integrability and limit cycles in cubic Kukles systems with a nilpotent singular point ⋮ Nondegenerate centers for Abel polynomial differential equations of second kind

Uses Software

• Fermat
• REDUCE

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Limit cycles for the kukles system
• Algorithmic derivation of isochronicity conditions
• REDUCE and the bifurcation of limit cycles
• Limit cycles of a predator-prey model with intratrophic predation
• Computing centre conditions for certain cubic systems
• Multipolynomial resultant algorithms
• Intratrophic predation in simple predator-prey models
• Fast computation of the Bézout and Dixon resultant matrices
• Linearization of isochronous centers
• Space saving calculation of symbolic resultants
• Heuristics to accelerate the Dixon resultant
• On the conditions of Kukles for the existence of a Centre
• Isochronous Centers in Planar Polynomial Systems
• On the Paper of Jin and Wang Concerning the conditions for a Centre in certain Cubic Systems
• Bifurcation of limit cycles and integrability of planar dynamical systems in complex form
• The centres in the reduced Kukles system
• Algorithmic Derivation of Centre Conditions

This page was built for publication: Kukles revisited: Advances in computing techniques