polynomial systems
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2022 ◽  
Vol 309 ◽  
pp. 13-31
Stefano Barbero ◽  
Emanuele Bellini ◽  
Carlo Sanna ◽  
Javier Verbel

2022 ◽  
Vol 0 (0) ◽  
Hamadi Jerbi ◽  
Thouraya Kharrat ◽  
Fehmi Mabrouk

Abstract In this paper, we study the stabilization problem of a class of polynomial systems of odd degree in dimension three. The constructed stabilizing feedback is homogeneous and guarantee the homogeneity of the closed loop system.mynotered In the end of the paper, we show the efficiency of such a study in the local stabilization of nonlinear systems affine in control.

2022 ◽  
pp. 1154-1203
Jun-Ting Hsieh ◽  
Pravesh K. Kothari

2021 ◽  
Vol 31 (14) ◽  
Meilan Cai ◽  
Maoan Han

In this paper, we consider the bifurcation problem of limit cycles for a class of piecewise smooth cubic systems separated by the straight line [Formula: see text]. Using the first order Melnikov function, we prove that at least [Formula: see text] limit cycles can bifurcate from an isochronous cubic center at the origin under perturbations of piecewise polynomials of degree [Formula: see text]. Further, the maximum number of limit cycles bifurcating from the center of the unperturbed system is at least [Formula: see text] if the origin is the unique singular point under perturbations.

Lixiu Wang ◽  
Weikun Shan ◽  
Huiyuan Li ◽  
Zhimin Zhang

In this paper, we propose an [Formula: see text]-conforming quadrilateral spectral element method to solve quad-curl problems. Starting with generalized Jacobi polynomials, we first introduce quasi-orthogonal polynomial systems for vector fields over rectangles. [Formula: see text]-conforming elements over arbitrary convex quadrilaterals are then constructed explicitly in a hierarchical pattern using the contravariant transform together with the bilinear mapping from the reference square onto each quadrilateral. It is worth noting that both the simplest rectangular and quadrilateral spectral elements possess only 8 degrees of freedom on each physical element. In the sequel, we propose our [Formula: see text]-conforming quadrilateral spectral element approximation based on the mixed weak formulation to solve the quad-curl equation and its eigenvalue problem. Numerical results show the effectiveness and efficiency of our method.

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Amor Menaceur ◽  
Mohamed Abdalla ◽  
Sahar Ahmed Idris ◽  
Ibrahim Mekawy

In light of the previous recent studies by Jaume Llibre et al. that dealt with the finite cycles of generalized differential Kukles polynomial systems using the first- and second-order mean theorem such as (Nonlinear Anal., 74, 1261–1271, 2011) and (J. Dyn. Control Syst., vol. 21, 189–192, 2015), in this work, we provide upper bounds for the maximum number of limit cycles bifurcating from the periodic orbits of Hamiltonian system using the averaging theory of first order.

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