Centers of quasi-homogeneous polynomial planar systems

“…Smooth Quasi-homogeneous polynomial differential systems have been intensively studied by a great deal of authors from different views. We refer readers to see for example the integrability [2,17,19,21,29], the centers and limit cycles [1,15,18,24], the algorithm to compute quasi-homogeneous systems with a given degree [14], the characterization of centers or topological phase portraits for quasi-homogeneous equations of degrees 3-5 respectively [5,26,32] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Global dynamics and bifurcation of planar piecewise smooth quadratic quasi-homogeneous differential systems

Tang¹

2018

Discrete &Amp; Continuous Dynamical Systems - A

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In this paper we research global dynamics and bifurcations of planar piecewise smooth quadratic quasi-homogeneous but non-homogeneous polynomial differential systems. We present sufficient and necessary conditions for the existence of a center in piecewise smooth quadratic quasi-homogeneous systems. Moreover, the center is global and non-isochronous if it exists, which cannot appear in smooth quadratic quasi-homogeneous systems. Then the global structures of piecewise smooth quadratic quasi-homogeneous but non-homogeneous systems are studied. Finally we investigate limit cycle bifurcations of the piecewise smooth quadratic quasi-homogeneous center and give the maximal number of limit cycles bifurcating from the periodic orbits of the center by applying the Melnikov method for piecewise smooth near-Hamiltonian systems.

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“…The quasi-homogeneous (and in general nonhomogeneous) polynomial function is defined as follows, The quasi-homogeneous polynomial differential systems have been studied from many different point of view, one of these studies is the Centre, see for instance [1]; [2]; [3]; [4]. But up to now there was not an algorithm for constructing all the quasi-homogeneous polynomial differential systems for a given degree.…”

Section: Introductionmentioning

confidence: 99%

Period Monotonicity for Weight-Homogeneous Differential Systems

Al-Dosary

Abdullah

2017

International Journal of Mathematical Research

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Article HistoryIn this article, integrability, center, and monotonicity of associated period function forquasi-homogeneous vector fields are investigated. We are concerned with family of vector field given by sum, finite or infinite number of quasi-homogeneous polynomials not necessarily to be sharing the same weights. The investigation is done by utilizing method of computing focal values. As an application of the result, a particular family of (p, q)-quasi-homogeneous vector field is studied to find conditions for center, monotonicity and consequently an explicit form for the associated period function.

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Centers of quasi-homogeneous polynomial planar systems

Cited by 39 publications

References 18 publications

Geometric Criterium in the Center Problem

Geometric Criterium in the Center Problem

Global dynamics and bifurcation of planar piecewise smooth quadratic quasi-homogeneous differential systems

Period Monotonicity for Weight-Homogeneous Differential Systems

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