Qualitative theory of two-dimensional polynomial dynamical systems: Problems, approaches, conjectures

DOI10.1016/S0362-546X(97)00199-5zbMath0955.34019WikidataQ123340051 ScholiaQ123340051MaRDI QIDQ4377203

Valery A. Gaiko

Publication date: 13 February 2001

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

limit cyclespolynomial vector fieldseparatrix cycles

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) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items

Global bifurcations of limit and separatrix cycles in a generalized Liénard system, Global-in-time existence of unbounded separatrices and blow-up time of solutions for Liénard systems whose restoring force is an odd power function, Limit cycles of quadratic systems, HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS, Wintner-Perko termination principle, parameters rotating a field, and limit-cycle problem, Global analysis of planar neural networks, A quadratic system with two parallel straight-line-isoclines

Cites Work

• Quadratic vector fields in the plane have a finite number of limit cycles
• Keeping track of limit cycles
• Hilbert's 16th problem for quadratic vector fields
• Limit-cycles and rotated vector fields
• Separatrix and Limit Cycles of Quadratic Systems and Dulac's Theorem
• Elementary graphics of cyclicity 1 and 2
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