Center conditions for a polynomial differential system

Садовский, А. П.; Shcheglova, Tatiana

doi:10.1134/s001226611302002x

Cited by 6 publications

(2 citation statements)

References 3 publications

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“…Over the past couple decades, various kinds of techniques and algorithms have been developed, and extensive analyses have been consequently produced. Some results about center-focus problem for polynomial differential systems are presented in [13][14][15][16]. About the topic of discontinuous systems, there are also a lot of literatures; see, for example, [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Existence of Center for Planar Differential Systems with Impulsive Perturbations

2015

Advances in Mathematical Physics

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We present a method that uses successor functions in ordinary differential systems to address the “center-focus” problem of a class of planar systems that have an impulsive perturbation. By deriving solution formulae for impulsive systems, several interesting criteria for distinguishing between the center and the focus of linear and nonlinear planar systems with state-dependent impulsions are established. The conditions describing the stability of the focus of the considered models are also given. The computing methods presented here are more convenient for determining the center of impulsive systems than those in the literature. Numerical examples are given to show the effectiveness of the theoretical results.

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Section: Introductionmentioning

confidence: 99%

Existence of Center for Planar Differential Systems with Impulsive Perturbations

2015

Advances in Mathematical Physics

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“…The authors show that the center variety of system (11) consists of four components. Finally, in [25] are given 16 center conditions of the differential systeṁ…”

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confidence: 99%

Center conditions for generalized polynomial Kukles systems

Giné¹

2017

CPAA

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In this paper we study the center problem for certain generalized Kukles systemṡ x = y,ẏ = P 0 (x) + P 1 (x)y + P 2 (x)y 2 + P 3 (x)y 3 , where P i (x) are polynomials of degree n, P 0 (0) = 0 and P 0 (0) < 0. Computing the focal values and using modular arithmetics and Gröbner bases we find the center conditions for such systems when P 0 is of degree 2 and P i for i = 1, 2, 3 are of degree 3 without constant terms. We also establish a conjecture about the center conditions for such systems.

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Integrability and limit cycles in cubic Kukles systems with a nilpotent singular point

2019

Nonlinear Dyn

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Center conditions for a polynomial differential system

Abstract: We obtain 16 center conditions for a polynomial differential system with 27 parameters.

Cited by 6 publications

References 3 publications

Existence of Center for Planar Differential Systems with Impulsive Perturbations

Existence of Center for Planar Differential Systems with Impulsive Perturbations

Center conditions for generalized polynomial Kukles systems

Integrability and limit cycles in cubic Kukles systems with a nilpotent singular point

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