Algebraic limit cycles for quadratic polynomial differential systems [PDF]
Discrete & Continuous Dynamical Systems - B, 2018 AbstractAlgebraic limit cycles in quadratic polynomial differential systems started to be studied in 1958, and a few years later the following conjecture appeared: quadratic polynomial differential systems have at most one algebraic limit cycle. We prove that a quadratic polynomial differential system having an invariant algebraic curve with at most ...
Llibre, Jaume, Valls, Clàudia
exaly +14 more sources
Planar chemical reaction systems with algebraic and non-algebraic limit cycles. [PDF]
J Math BiolAbstract The Hilbert number H(n) is defined as the maximum number of limit cycles of a planar autonomous system of ordinary differential equations (ODEs) with right-hand sides containing polynomials of degree at most $$n \in {{\mathbb {N}}}$$ n
Craciun G, Erban R.
europepmc +6 more sources
The cubic polynomial differential systems with two circles as algebraic limit cycles [PDF]
Advanced Nonlinear Studies, 2017 In this paper we characterize all cubic polynomial differential systems in the plane having two circles as invariant algebraic limit cycles.The first author is partially supported by a MINECO grant number MTM2014-53703-P, and an AGAUR (Generalitat de ...
Giné, Jaume +2 more
core +9 more sources
Polynomial differential systems with explicit non-algebraic limit cycles
Electronic Journal of Differential Equations, 2012 Up to now all the examples of polynomial differential systems for which non-algebraic limit cycles are known explicitly have degree at most 5. Here we show that already there are polynomial differential systems of degree at least exhibiting explicit ...
Rebiha Benterki, Jaume Llibre
doaj +3 more sources
Coexistence of algebraic and non-algebraic limit cycles for quintic polynomial differential systems
Electronic Journal of Differential Equations, 2017 In the work by Gine and Grau [11], a planar differential system of degree nine admitting a nested configuration formed by an algebraic and a non-algebraic limit cycles explicitly given was presented.
Ahmed Bendjeddou, Rachid Cheurfa
doaj +2 more sources
Algebraic Limit Cycles Bifurcating from Algebraic Ovals of Quadratic Centers [PDF]
International Journal of Bifurcation and Chaos, 2018 In the integrability of polynomial differential systems it is well known that the invariant algebraic curves play a relevant role. Here we will see that they can also play an important role with respect to limit cycles.In this paper, we study quadratic polynomial systems with an algebraic periodic orbit of degree [Formula: see text] surrounding a ...
Jaume Llibre, Yun Tian
openaire +7 more sources
Application of modelling approaches of twin-screw compressors: thermodynamic investigation and reduced-order model identification [PDF]
E3S Web of Conferences, 2021 Refrigeration is an essential part of the food chain. It is used in all stages of the chain, from industrial food processing to final consumption at home.
Di Mattia Edoardo +3 more
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Algebraic Limit Cycles in Piecewise Linear Differential Systems [PDF]
International Journal of Bifurcation and Chaos, 2018 This paper is devoted to study the algebraic limit cycles of planar piecewise linear differential systems. In particular, we present examples exhibiting two explicit hyperbolic algebraic limit cycles, as well as some one-parameter families with a saddle-node bifurcation of algebraic limit cycles.
Claudio A. Buzzi +2 more
openaire +8 more sources
Global algebraic Poincaré–Bendixson annulus for the Rayleigh equation
Electronic Journal of Qualitative Theory of Differential Equations, 2023 We consider the Rayleigh equation $\ddot{x} + \lambda (\dot{x}^2/3-1)\dot{x} +x=0$ depending on the real parameter $\lambda$ and construct a Poincaré–Bendixson annulus $\mathcal{A}_\lambda$ in the phase plane containing the unique limit cycle $\Gamma_ ...
Alexander Grin, Klaus Schneider
doaj +1 more source
On limit cycles of piecewise differential systems formed by arbitrary linear systems and a class of quadratic systems [PDF]
Mathematica Bohemica, 2023 We study the continuous and discontinuous planar piecewise differential systems separated by a straight line and formed by an arbitrary linear system and a class of quadratic center.
Aziza Berbache
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