Iterative approximation of limit cycles for a class of Abel equations

DOI10.1016/j.physd.2008.05.011zbMath1160.34025OpenAlexW1991679586MaRDI QIDQ1000704

Hebertt Sira-Ramírez, Josep M. Olm, Enric Fossas

Publication date: 10 February 2009

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2008.05.011

zbMATH Keywords

limit cycleanalytical approximationAbel equation

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Dynamical systems in control (37N35) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (19)

Phase portraits of the complex Abel polynomial differential systems ⋮ Estimating the Attraction Domain for the Boost Inverter ⋮ 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 ⋮ Generalized Weierstrass integrability of the Abel differential equations ⋮ Stable inversion of Abel equations: application to tracking control in DC-DC nonminimum phase boost converters ⋮ Limit cycles of Abel equations of the first kind ⋮ Stability of singular limit cycles for Abel equations ⋮ Periodic solutions with nonconstant sign in Abel equations of the second kind ⋮ A functional iterative approach to the tracking control of nonminimum phase switched power converters ⋮ On the rational limit cycles of Abel equations ⋮ Rational limit cycles of Abel equations ⋮ A geometric criterion for equation \(\dot{x} = \sum\nolimits_{i = 0}^m a_i(t) x^i\) having at most \(m\) isolated periodic solutions ⋮ On the Number of Limit Cycles in Generalized Abel Equations ⋮ Rational limit cycles on Bernoulli and Riccati equations ⋮ Generalized Weierstrass integrability for the complex differential equations \(\frac{dy}{dx}=a(x)y^4+b(x)y^3+c(x)y^2+d(x)y+e(x)\) ⋮ Rational limit cycles on generalized Bernouilli polynomial equations ⋮ On the number of limit cycles in piecewise smooth generalized Abel equations with two asymmetric zones

Cites Work

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• Mathematical problems for the next century
• Asymptotic tracking in DC-to-DC nonlinear power converters
• Exact analytic solutions of unsolvable classes of first and second order nonlinear ODEs I: Abel's equations
• Exact analytic solutions of unsolvable classes of first- and second-order nonlinear ODEs (Part II: Emden--Fowler and relative equations)
• Galerkin method and approximate tracking in a non-minimum phase bilinear system
• DC-to-AC power conversion on a ‘boost’ converter
• Limit Cycles for a Class of Abel Equations
• Stable inversion for nonlinear nonminimum-phase time-varying systems
• Flatness and defect of non-linear systems: introductory theory and examples

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