A necessary and sufficient condition on algebraic limit cycles of a hybrid van der Pol-Rayleigh oscillator

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Invariant manifolds for ordinary differential equations (34C45)

Cites Work

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Integrability of dynamical systems: algebra and analysis
Invariant algebraic curves and rational first integrals of holomorphic foliations in \(\mathbb C P(2)\)
The 16th Hilbert problem on algebraic limit cycles
The limit cycle of the van der Pol equation is not algebraic
On ``relaxation-oscillations.
Mathematische Probleme. Vortrag, gehalten auf dem internationalen Mathematiker-Congress zu Paris 1900.
Invariant algebraic curves of large degree for quadratic system
Algebraic limit cycles of degree 4 for quadratic systems
Novel algebraic aspects of Liouvillian integrability for two-dimensional polynomial dynamical systems
Quadratic planar differential systems with algebraic limit cycles via quadratic plane Cremona maps
Global dynamics of hybrid van der Pol-Rayleigh oscillators
Non-existence, existence, and uniqueness of limit cycles for a generalization of the van der Pol-Duffing and the Rayleigh-Duffing oscillators
On the number of limit cycles of a class of Liénard-Rayleigh oscillators
On the 16th Hilbert problem for algebraic limit cycles
Qualitative theory of planar differential systems
Perturbation Analysis of the Limit Cycle of the Free van der Pol Equation
The Periodic Solution of Van Der Pol's Equation
Asymptotic behaviour and expansions of solutions of an ordinary differential equation
The method of Puiseux series and invariant algebraic curves
Algebraic limit cycles in polynomial systems of differential equations

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