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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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Limit cycles bifurcated from some reversible quadratic centres with a non-algebraic first integral
Nonlinearity, 2012We 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.
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EXPLICIT NON-ALGEBRAIC LIMIT CYCLES OF A CLASS OF POLYNOMIAL SYSTEMS
Far East Journal of Applied Mathematics, 2015Ahmed Bendjeddou, Rachid Boukoucha
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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
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Rational Lyapunov Functions and Stable Algebraic Limit Cycles
IEEE Transactions on Automatic Control, 2014Emmanuel Moulay
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Global stability at a limit cycle of switched Boolean networks under arbitrary switching signals
Neurocomputing, 2014Fangfei Li
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The Limit Cycle of the van der Pol Equation Is Not Algebraic
Journal of Differential Equations, 1995exaly
Limit cycle for cubic system of Kolmogorov type with a conic algebraic trajectory
Acta Mathematicae Applicatae Sinica, 1989exaly