Results 1 to 10 of about 350,644 (263)
Limit cycles and chaos in the hybrid atom-optomechanics system [PDF]
Scientific Reports, 2022 We consider atoms in two different periodic potentials induced by different lasers, one of which is coupled to a mechanical membrane via radiation pressure force.
Xingran Xu +2 more
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The algebraic curves of planar polynomial differential systems with homogeneous nonlinearities
Electronic Journal of Qualitative Theory of Differential Equations, 2021 We consider planar polynomial systems of ordinary differential equations of the form $\dot x = x + P_n(x,y)$, $\dot y = y + Q_n(x,y)$, where $P_n(x,y),\ Q_n(x,y)$ are homogeneous polynomials of degree $n$.
Vladimir Cheresiz, Evgenii Volokitin
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Rational limit cycles of Abel differential equations
Electronic Journal of Qualitative Theory of Differential Equations, 2023 We study the number of rational limit cycles of the Abel equation $x'=A(t)x^3+B(t)x^2$, where $A(t)$ and $B(t)$ are real trigonometric polynomials. We show that this number is at most the degree of $A(t)$ plus one.
José Luis Bravo +2 more
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Limit cycles in mass-conserving deficiency-one mass-action systems
Electronic Journal of Qualitative Theory of Differential Equations, 2022 We present some simple mass-action systems with limit cycles that fall under the scope of the Deficiency-One Theorem. All the constructed examples are mass-conserving and their stoichiometric subspace is two-dimensional.
Balázs Boros, Josef Hofbauer
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Rational Limit Cycles on Abel Polynomial Equations
Mathematics, 2020 In this paper we deal with Abel equations of the form d y / d x = A 1 ( x ) y + A 2 ( x ) y 2 + A 3 ( x ) y 3 , where A 1 ( x ) , A 2 ( x ) and A 3 ( x ) are real polynomials and A 3 ≢ 0 .
Claudia Valls
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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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Two Nested Limit Cycles in Two-Species Reactions
Mathematics, 2020 We search for limit cycles in the dynamical model of two-species chemical reactions that contain seven reaction rate coefficients as parameters and at least one third-order reaction step, that is, the induced kinetic differential equation of the reaction
Ilona Nagy +2 more
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Polynomial differential systems with hyperbolic algebraic limit cycles
Electronic Journal of Qualitative Theory of Differential Equations, 2020 For a given algebraic curve of degree $n$, we exhibit differential systems of degree greater than or equal $n$, by introducing functions which are solutions of certain partial differential equations.
Salah Benyoucef
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Third Order Melnikov Functions of a Cubic Center under Cubic Perturbations
Mathematics, 2022 In this paper, cubic perturbations of the integral system (1+x)2dH where H=(x2+y2)/2 are considered. Some useful formulae are deduced that can be used to compute the first three Melnikov functions associated with the perturbed system.
Yanwei Liu, Tonghua Zhang, Xia Liu
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Limit cycles in a Kolmogorov-type model
International Journal of Mathematics and Mathematical Sciences, 1990 In this paper, a Kolmogorov-type model, which includes the Gause-type model (Kuang and Freedman, 1988), the general predator-prey model (Huang 1988, Huang and Merrill 1989), and many other specialized models, is studied.
Xun-Cheng Huang
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