等时中心组成的平面不连续分段微分系统的交叉极限环

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Dynamical Systems-An International Journal Pub Date : 2022-05-09 DOI:10.1080/14689367.2022.2122779

C. Buzzi, Yagor Romano Carvalho, J. Llibre

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引用次数: 0

摘要

近年来，由于在建模真实现象方面的丰富应用，人们对研究平面不连续分段微分系统越来越感兴趣。理解这些系统的动力学有许多困难。其中之一是研究它们的极限环。在本文中，我们研究了一类由直线分离的平面不连续分段微分系统的交叉极限环的最大数目，该系统由线性中心（因此是等时的）和具有齐次非线性的三次等时中心的组合形成。对于这类平面不连续分段微分系统，我们解决了第16个Hilbert问题的扩展，即我们提供了它们的最大交叉极限环数的上界。

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Crossing limit cycles of planar discontinuous piecewise differential systems formed by isochronous centres

These last years an increasing interest appeared in studying the planar discontinuous piecewise differential systems motivated by the rich applications in modelling real phenomena. The understanding of the dynamics of these systems has many difficulties. One of them is the study of their limit cycles. In this paper, we study the maximum number of crossing limit cycles of some classes of planar discontinuous piecewise differential systems separated by a straight line and formed by combinations of linear centres (consequently isochronous) and cubic isochronous centres with homogeneous nonlinearities. For these classes of planar discontinuous piecewise differential systems we solved the extension of the 16th Hilbert problem, i.e. we provide an upper bound for their maximum number of crossing limit cycles.

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来源期刊

Dynamical Systems-An International Journal 物理-力学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal: •Differential equations •Bifurcation theory •Hamiltonian and Lagrangian dynamics •Hyperbolic dynamics •Ergodic theory •Topological and smooth dynamics •Random dynamical systems •Applications in technology, engineering and natural and life sciences