Stability of singular limit cycles for Abel equations

DOI10.3934/dcds.2015.35.1873zbMath1312.34080OpenAlexW1973824721MaRDI QIDQ484412

Yong-Cai Geng, Sumit K. Garg

Publication date: 7 January 2015

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2015.35.1873

zbMATH Keywords

limit cycleperiodic solutionAbel equationclosed solution

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonlinear ordinary differential equations and systems (34A34) Stability of solutions to ordinary differential equations (34D20) Periodic orbits of vector fields and flows (37C27) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (10)

Rational Periodic Solutions on Some Generalized Abel Equations ⋮ Centers and limit cycles for a family of Abel equations ⋮ Rational solutions of Abel trigonometric polynomial differential equations ⋮ Periodic solutions of Abel equations with jumps ⋮ Stability of singular limit cycles for Abel equations revisited ⋮ Hilbert number for a family of piecewise nonautonomous equations ⋮ Anti-periodic solutions of Abel differential equations with state dependent discontinuities ⋮ Rational limit cycles of Abel equations ⋮ Rational limit cycles on Bernoulli and Riccati equations ⋮ Rational limit cycles on generalized Bernouilli polynomial equations

Cites Work

• Periodic solutions with nonconstant sign in Abel equations of the second kind
• Relativistic dissipative cosmological models and Abel differential equation
• Construction of exact parametric or closed form solutions of some unsolvable classes of nonlinear ODEs (Abel's nonlinear ODEs of the first kind and relative degenerate equations)
• A new uniqueness criterion for the number of periodic orbits of Abel equations
• Iterative approximation of limit cycles for a class of Abel equations
• On the number of solutions of the equation \(\sum^n_{j=0}a_j(t)x^j,0\leq t\leq 1\), for which \(x(0)=x(1)\)
• Existence of periodic solutions with nonconstant sign in a class of generalized Abel equations
• The number of periodic solutions of polynomial differential equations
• Abel-like differential equations with no periodic solutions
• Limit-cycles and rotated vector fields
• Limit Cycles for a Class of Abel Equations
• Qualitative Tools for Studying Periodic Solutions and Bifurcations as Applied to the Periodically Harvested Logistic Equation
• A Note on the Number of Limit Cycles in Certain Two-Dimensional Systems
• Non-autonomous equations related to polynomial two-dimensional systems
• LIMIT CYCLES FOR GENERALIZED ABEL EQUATIONS
• LIMIT CYCLES FOR SOME ABEL EQUATIONS HAVING COEFFICIENTS WITHOUT FIXED SIGNS
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Stability of singular limit cycles for Abel equations