Weak-foci of high order and cyclicity

DOI10.1007/s12346-016-0189-9zbMath1396.34018OpenAlexW2291077683MaRDI QIDQ1697717

Haihua Liang, Joan Torregrosa

Publication date: 20 February 2018

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/169466

zbMATH Keywords

polynomial systemcyclicityLyapunov quantitiesweak-focus order

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (2)

Local stability and Hopf bifurcations analysis of the Muthuswamy-Chua-Ginoux system ⋮ Center Conditions and Bifurcation of Limit Cycles Created from a Class of Second-Order ODEs

Uses Software

• PARI/GP

Cites Work

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• Planar real polynomial differential systems of degree \(n> 3\) having a weak focus of high order
• Higher order limit cycle bifurcations from non-degenerate centers
• Parallelization of the Lyapunov constants and cyclicity for centers of planar polynomial vector fields
• Cyclicity versus center problem
• Lower bounds for the Hilbert number of polynomial systems
• On the structure of Poincaré-Lyapunov constants for the weak focus of polynomial vector fields
• On a Żołądek theorem
• Center problem for systems with two monomial nonlinearities
• On the focus order of planar polynomial differential equations
• A method of constructing cycles without contact around a weak focus
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• A new approach to the computation of the Lyapunov constants
• Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation
• Centennial History of Hilbert's 16th Problem
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• Eleven small limit cycles in a cubic vector field
• Polynomial systems: a lower bound for the Hilbert numbers
• A Quartic System with Twenty-Six Limit Cycles
• The CD45 Case Revisited

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