Coexistence of centers and limit cycles in polynomial systems

DOI10.1216/rmjm/1022009285zbMath0981.34018OpenAlexW2059272391MaRDI QIDQ5928696

Robert E. Kooij, André Zegeling

Publication date: 1 April 2001

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/VOL30-2/CONT30-2/CONT30-2.html

zbMATH Keywords

limit cyclepolynomial systemsingular point of center type

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (1)

Liénard limit cycles enclosing period annuli, or enclosed by period annuli

Cites Work

• Bifurcations of limit cycles forming compound eyes in the cubic system
• Reversible systems
• Rotated vector fields and the global behavior of limit cycles for a class of quadratic systems in the plane
• Algebraic invariant curves and the integrability of polynomial systems
• The classification of reversible cubic systems with center
• Remarks on ``The classification of reversible cubic systems with center
• Cubic Lienard equations with linear damping
• On the uniqueness of limit cycles surrounding one or more singularities for Liénard equations
• Mathematical problems
• Polynomial systems: a lower bound for the Hilbert numbers
• THE ORIGIN OF LIMIT CYCLES UNDER PERTURBATION OF THE EQUATIONdw/dz= -R_z/R_w, WHERER(z,w) IS A POLYNOMIAL
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