A Note on the Number of Limit Cycles in Certain Two-Dimensional Systems
From MaRDI portal
Publication:4193771
DOI10.1112/jlms/s2-20.2.277zbMath0407.34027OpenAlexW2000562084MaRDI QIDQ4193771
Publication date: 1979
Published in: Journal of the London Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1112/jlms/s2-20.2.277
Related Items (55)
A new approach to fuzzy sets: application to the design of nonlinear time series, symmetry-breaking patterns, and non-sinusoidal limit-cycle oscillations ⋮ An index theorem and Bendixson's negative criterion for certain differential equations of higher dimension ⋮ Periodic solutions of linear, Riccati, and Abel dynamic equations ⋮ Uniqueness of limit cycles for quadratic vector fields ⋮ Rational Periodic Solutions on Some Generalized Abel Equations ⋮ Word problems related to derivatives of the displacement map ⋮ Multiplicity of limit cycles and analytic \(m\)-solutions for planar differential systems ⋮ Limit cycles of vector fields of the form \(X(v)=Av+f(v)Bv\) ⋮ Limit cycles of a class of polynomial vector fields in the plane ⋮ Periodic orbits in complex Abel equations ⋮ A new uniqueness criterion for the number of periodic orbits of Abel equations ⋮ Hausdorff dimension estimates for invariant sets of time-dependent vector fields ⋮ Rational solutions of Abel trigonometric polynomial differential equations ⋮ A uniqueness criterion of limit cycles for planar polynomial systems with homogeneous nonlinearities ⋮ Non-existence and uniqueness of limit cycles for planar polynomial differential systems with homogeneous nonlinearities ⋮ Limit cycles of polynomial systems with homogeneous non-linearities ⋮ Estimate for the number of limit cycles of Abel equation via a geometric criterion on three curves ⋮ Counting configurations of limit cycles and centers ⋮ Stability of singular limit cycles for Abel equations revisited ⋮ Periodic solutions of a quartic nonautonomous equation ⋮ Periodic solutions for equation \(\dot x = A(t)x^m + B(t)x^n + C(t)x^l\) with \(A(t)\) and \(B(t)\) changing signs ⋮ Geometrical conditions for the stability of orbits in planar systems ⋮ Upper bounds of limit cycles in Abel differential equations with invariant curves ⋮ Bifurcation values for a family of planar vector fields of degree five ⋮ Characterization of the existence of non-trivial limit cycles for generalized Abel equations ⋮ Stability of singular limit cycles for Abel equations ⋮ Limit cycles of a class of polynomial systems ⋮ On the number of limit cycles of some systems on the cylinder ⋮ Effectiveness of the Bendixson-Dulac theorem ⋮ Center cyclicity for some nilpotent singularities including the ℤ2-equivariant class ⋮ Limit cycles of polynomial differential equations with quintic homogeneous nonlinearities ⋮ Abel-like differential equations with a unique limit cycle ⋮ Global dynamics of a two-patch SIS model with infection during transport ⋮ Fixed and moving limit cycles for Liénard equations ⋮ Alien limit cycles in Abel equations ⋮ The nondegenerate center problem and the inverse integrating factor ⋮ Bifurcation diagram and stability for a one-parameter family of planar vector fields ⋮ Limit cycles for cubic systems with a symmetry of order 4 and without infinite critical points ⋮ On the limit cycles surrounding a diagonalizable linear node with homogeneous nonlinearities ⋮ On the rational limit cycles of Abel equations ⋮ Limit cycles of planar system defined by the sum of two quasi-homogeneous vector fields ⋮ 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 study and application of limit cycles of a kind of piecewise smooth equation ⋮ Some theorems on the existence, uniqueness, and nonexistence of limit cycles for quadratic systems ⋮ Rational limit cycles on Bernoulli and Riccati equations ⋮ Uniqueness of the limit cycles for complex differential equations with two monomials ⋮ Rational limit cycles on generalized Bernouilli polynomial equations ⋮ Criteria on the existence of limit cycles in planar polynomial differential systems ⋮ Bifurcation of a periodic orbit from infinity in planar piecewise linear vector fields ⋮ A new criterion for controlling the number of limit cycles of some generalized Liénard equations ⋮ Some Applications of the Extended Bendixson-Dulac Theorem ⋮ Unnamed Item ⋮ On a class of complete polynomial vector fields in the plane ⋮ Bounding the number of cycles of O.D.E.s in 𝐑ⁿ
This page was built for publication: A Note on the Number of Limit Cycles in Certain Two-Dimensional Systems
