AxiomsIn this paper, two classes of near-Hamiltonian systems with a nilpotent center are considered: the coexistence of algebraic limit cycles and small limit cycles.
Huimei Liu, Meilan Cai, Feng Li
doaj +4 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
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
doaj +1 more source
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
doaj +1 more source
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
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
doaj +1 more source
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
doaj +1 more source
Speed Oscillations of a Vehicle Rolling on a Wavy Road
Applied Sciences, 2021 Every driver knows that his car is slowing down or accelerating when driving up or down, respectively. The same happens on uneven roads with plastic wave deformations, e.g., in front of traffic lights or on nonpaved desert roads.
Walter V. Wedig
doaj +1 more source
Global bifurcation analysis of a rational Holling system [PDF]
Компьютерные исследования и моделирование, 2017 In this paper, we consider a quartic family of planar vector fields corresponding to a rational Holling system which models the dynamics of the populations of predators and their prey in a given ecological or biomedical system and which is a variation on
Valery Aleksandrovich Gaiko
doaj +1 more source
Quadratic systems with a symmetrical solution
Electronic Journal of Qualitative Theory of Differential Equations, 2018 In this paper we study the existence and uniqueness of limit cycles for so-called quadratic systems with a symmetrical solution: \begin{equation*} \begin{split} \frac{dx(t)}{dt}& = P_2(x,y) \equiv a_{00}+a_{10}x+a_{01}y+a_{20}x^2+a_{11}xy+a_{02}y^2 ...
Andre Zegeling, Robert Kooij
doaj +1 more source