Results 171 to 180 of about 2,719 (189)

Coexistence of algebraic and non-algebraic limit cycles, explicitly given, using Riccati equations

Nonlinearity, 2006
We give a family of planar polynomial differential systems whose limit cycles can be explicitly described using polar coordinates. Moreover, we characterize the multiplicity of each one of the limit cycles whenever they exist. The given family of planar polynomial differential systems can have at most two limit cycles, counted with multiplicity.As an ...
Jaume Giné, Maite Grau
openaire   +1 more source

Limit cycles bifurcated from some reversible quadratic centres with a non-algebraic first integral

Nonlinearity, 2012
We study the cyclicity of period annuli of some reversible non-Hamiltonian quadratic systems under quadratic perturbations. In general, the first integral, which we study, is non-algebraic. Via estimating the number of zeros of the associated Abelian integral (first order Melnikov function), we show that the cyclicity is 2.
openaire   +1 more source

EXPLICIT NON-ALGEBRAIC LIMIT CYCLES OF A CLASS OF POLYNOMIAL SYSTEMS

Far East Journal of Applied Mathematics, 2015
Ahmed Bendjeddou, Rachid Boukoucha
openaire   +1 more source

On the cubic Kukles systems with an algebraic limit cycle of degree two

Journal of Mathematical Analysis and Applications, 2023
Yulin Zhao
exaly  

Number of Limit Cycles for Planar Systems with Invariant Algebraic Curves

Qualitative Theory of Dynamical Systems, 2023
Armengol Gasull, Hector Giacomini, Gasull Armengol   +2 more
exaly  

Algebraic limit cycles of degree 4 for quadratic systems

Journal of Differential Equations, 2004
Jaume Llibre
exaly  

Classification of quadratic systems admitting the existence of an algebraic limit cycle

Bulletin Des Sciences Mathematiques, 2007
Jaume Llibre, Grzegorz Świrszcz
exaly  

On the uniqueness of algebraic limit cycles for quadratic polynomial differential systems with two pairs of equilibrium points at infinity

Geometriae Dedicata, 2017
Claudia Valls, Jaume Llibre, Valls Claudia   +2 more
exaly  

Algebraic limit cycles for quadratic polynomial differential systems

Discrete and Continuous Dynamical Systems - Series B, 2018
Claudia Valls, Jaume Llibre
exaly  

Rational Lyapunov Functions and Stable Algebraic Limit Cycles

IEEE Transactions on Automatic Control, 2014
Emmanuel Moulay
exaly