The limit cycle of the van der Pol equation is not algebraic
From MaRDI portal
Publication:1343703
DOI10.1006/jdeq.1995.1008zbMath0816.34023OpenAlexW2044392679MaRDI QIDQ1343703
Publication date: 30 January 1995
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jdeq.1995.1008
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Abstract differential equations (12H20)
Related Items (61)
Estimate for the amplitude of the limit cycle of the Liénard equation ⋮ Liouvillian integrability versus Darboux polynomials ⋮ The method of Puiseux series and invariant algebraic curves ⋮ A note on: ``Relaxation oscillators with exact limit cycles ⋮ Explicit non-algebraic limit cycles for polynomial systems ⋮ Unnamed Item ⋮ Limit cycles of generalized Liénard equations ⋮ The stable limit cycles: a synchronization phenomenon ⋮ Formal Weierstrass integrability for a Liénard differential system ⋮ Unnamed Item ⋮ Auxiliary functions as Koopman observables: data-driven analysis of dynamical systems via polynomial optimization ⋮ Unnamed Item ⋮ Unnamed Item ⋮ The hyperelliptic limit cycles of the Liénard systems ⋮ LIMIT CYCLES AND PHASE PORTRAIT FOR A CLASS OF DIFFERENTIAL SYSTEMS ⋮ On a classification of polynomial differential operators with respect to the type of first integrals ⋮ Realization problems for limit cycles of planar polynomial vector fields ⋮ Integrability and limit cycles for a class of multi-parameter differential systems with unstable node point ⋮ Balancing at the edge of excitability: implications for cell movement ⋮ Darboux integrability and the inverse integrating factor. ⋮ Number and amplitude of limit cycles emerging from topologically equivalent perturbed centers. ⋮ A class of planar differential systems with explicit expression for two limit cycles ⋮ Unnamed Item ⋮ Generalized cofactors and nonlinear superposition principles ⋮ On the Lyapunov type inequality ⋮ The homotopy analysis method and the Liénard equation ⋮ Birational Geometry of Foliations Associated to Simple Derivations ⋮ Semi-invariants and their use for stability analysis of planar systems ⋮ Seeking Darboux polynomials ⋮ Approximating the amplitude and form of limit cycles in the weakly nonlinear regime of Liénard systems ⋮ Unnamed Item ⋮ GLOBAL CLF STABILIZATION OF SYSTEMS WITH POINT-DISSIPATIVE FREE DYNAMICS VIA ADMISSIBLE CONTROLS: CHAOS CONTROL OF A CHUA'S SYSTEM ⋮ Liénard systems and the second part of Hilbert's sixteenth problem ⋮ Algebraic invariant curves for the Liénard equation ⋮ On some open problems in planar differential systems and Hilbert's 16th problem ⋮ Periodic solutions of multi-degree-of-freedom strongly nonlinear coupled van der Pol oscillators by homotopy analysis method ⋮ Liouvillian integrability of some quadratic Liénard polynomial differential systems ⋮ Liouvillian first integrals for Liénard polynomial differential systems ⋮ Resolution of the Poincaré problem and nonexistence of algebraic limit cycles in family (I) of Chinese classification ⋮ Invariant algebraic curves for the cubic Liénard system with linear damping ⋮ Accurate approximate analytical solutions for multi-degree-of-freedom coupled van der Pol-Duffing oscillators by homotopy analysis method ⋮ Blow-up method to compute necessary conditions of integrability for planar differential systems ⋮ A topological method for finding invariant sets of continuous systems ⋮ A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems ⋮ Invariant algebraic curves and hyperelliptic limit cycles of Liénard systems ⋮ Phase portraits of the quadratic polynomial Liénard differential systems ⋮ On the number of hyperelliptic limit cycles of Liénard systems ⋮ On the Liénard system with two isoclines ⋮ On the nonexistence of Liouvillian first integrals for generalized Liénard polynomial differential systems ⋮ Stable hyperbolic limit cycles for a class of differential systems ⋮ Bounding Extreme Events in Nonlinear Dynamics Using Convex Optimization ⋮ Two non algebraic limit cycles of a class of polynomial differential systems with non-elementary equilibrium point ⋮ The limit cycles of Liénard equations in the strongly nonlinear regime ⋮ Global dynamics of hybrid van der Pol-Rayleigh oscillators ⋮ DARBOUXIAN INTEGRABILITY OF POLYNOMIAL VECTOR FIELDS WITH SPECIAL EMPHASIS ON THE TWO-DIMENSIONAL SURFACES ⋮ Transcendental limit cycles via the structure of arbitrary degree invariant algebraic curves of polynomial planar vector fields ⋮ 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 ⋮ A new criterion for controlling the number of limit cycles of some generalized Liénard equations ⋮ Puiseux integrability of differential equations ⋮ Non-algebraic limit cycles in Holling type III zooplankton-phytoplankton models
This page was built for publication: The limit cycle of the van der Pol equation is not algebraic