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Coexistence of algebraic and non-algebraic limit cycles, explicitly given, using Riccati equations
Nonlinearity, 2006We 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
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Coexistence of limit cycles and invariant algebraic curves for a Kukles system
Nonlinear Analysis: Theory, Methods & Applications, 2004This paper deals with the so-called Kukles systems, \[ \dot x=-y,\qquad \dot y=f(x,y), \] \(f\) being a polynomial of degree \(d.\) Firstly, the authors study the number and distribution of invariant straight lines that this type of systems can have.
Chavarriga, J. +3 more
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Homology for operator algebras. IV. On the regular classification of limits of 4-cycle algebras
1997According with the terminology and notations from the research notes ``Limit algebras'' [Pitman Research Notes in Math. 278, London (1993)] of the second author, the subject of the present paper is related to the 4-cycle algebras, that is a CSL-algebra whose reduced digraph is a 4-cycle, and to the regular direct systems of 4-cycle algebras with rigid ...
Power, Stephen C., Donsig, A. P.
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On the cubic Kukles systems with an algebraic limit cycle of degree two
Journal of Mathematical Analysis and Applications, 2023Yulin Zhao
exaly
Cubic planar differential systems with non-algebraic limit cycles enclosing a focus
International Journal of Dynamical Systems and Differential Equations, 2023exaly