NON-ALGEBRAIC LIMIT CYCLES FOR PARAMETRIZED PLANAR POLYNOMIAL SYSTEMS

DOI10.1142/S0129167X07003984zbMath1121.34036MaRDI QIDQ3435113

Khalil I. T. Al-Dosary

Publication date: 25 April 2007

Published in: International Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

polynomial planar systemnon-algebraic solution

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)

Related Items (14)

Unnamed Item ⋮ Unnamed Item ⋮ The hyperelliptic limit cycles of the Liénard systems ⋮ Integrability and limit cycles for a class of multi-parameter differential systems with unstable node point ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On the non-existence of periodic orbits for a class of two-dimensional Kolmogorov systems ⋮ Unnamed Item ⋮ A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems ⋮ On the dynamics of a class of rational Kolmogorov systems ⋮ Two non algebraic limit cycles of a class of polynomial differential systems with non-elementary equilibrium point ⋮ On the Dynamics of a Class of Kolmogorov Systems ⋮ A Class of Quintic Kolmogorov Systems with Explicit Non-algebraic Limit Cycle ⋮ Coexistence of limit cycles in a septic planar differential system enclosing a non-elementary singular point, using Riccati equation

Cites Work

• Equations de Pfaff algébriques
• A family of non-Darboux-integrable quadratic polynomial differential systems with algebraic solutions of arbitrarily high degree
• Generalized cofactors and nonlinear superposition principles
• The Poincaré problem in the nondicritical case

This page was built for publication: NON-ALGEBRAIC LIMIT CYCLES FOR PARAMETRIZED PLANAR POLYNOMIAL SYSTEMS