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
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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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Limit Cycles of Polynomially Integrable Piecewise Differential Systems
Axioms, 2023 In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides.
Belén García +3 more
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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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Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]
Adv Intell DiscovThis article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
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A class of nonlinear oscillators with non-autonomous first integrals and algebraic limit cycles
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, we present a class of autonomous nonlinear oscillators with non-autonomous first integral. We prove explicitly the existence of a global sink which is, under some conditions, an algebraic limit cycle.
Meryem Belattar +3 more
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On new results on extremal graph theory, theory of algebraic graphs, and their applications
Доповiдi Нацiональної академiї наук України, 2022 New explicit constructions of infinite families of finite small world graphs of large girth with well-defined projective limits which is an infinite tree are described.
V.O. Ustimenko
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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 0001
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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
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Algebraic limit cycles of planar cubic systems
Sibirskie Elektronnye Matematicheskie Izvestiya, 2020 Algebraic limit cycles of differential systems of the form \[\dot{x}=x+P_3(x,y),\quad \dot{y}=y+Q_3(x,y), \] where \(P_3(x,y)\) and \(Q_3(x,y)\) are homogeneous cubic polynomials, are studied. Note that the results of Theorem 1 were obtained much earlier in the monograph [\textit{V. N. Gorbuzov} and \textit{A. A.
Volokitin, E. P., Cheresiz, V. M.
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