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Articles, 4 records found
Articles 4 records found  
1.
26 p, 400.8 KB Melnikov functions of arbitrary order for piecewise smooth differential systems in Rn and applications / Chen, Xingwu (Sichuan University. Department of Mathematics) ; Li, Tao (Southwestern University of Finance and Economics. School of Economic Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we develop an arbitrary order Melnikov function to study limit cycles bifurcating from a periodic submanifold for autonomous piecewise smooth differential systems in R with two zones separated by a hyperplane. [...]
2022 - 10.1016/j.jde.2022.01.019
Journal of differential equations, Vol. 314 (March 2022) , p. 340-369  
Detailed record - Creative Commons
2.
13 p, 326.6 KB Cyclicity of (1,3)-switching FF type equilibria / Chen, Xingwu (Sichuan University. Department of Mathematics (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Weinian (Sichuan University. Department of Mathematics (China))
Hilbert's 16th Problem suggests a concern to the cyclicity of planar polynomial differential systems, but it is known that a key step to the answer is finding the cyclicity of center-focus equilibria of polynomial differential systems (even of order 2 or 3). [...]
2019 - 10.3934/dcdsb.2019153
Discrete and continuous dynamical systems. Series B, Vol. 24, Issue 12 (December 2019) , p. 6541-6552  
Detailed record -
3.
15 p, 328.5 KB Averaging approach to cyclicity of Hopf bifurcation in planar linear-quadratic polynomial discontinuous differential systems / Chen, Xingwu (Sichuan University (Xina). Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Weinian (Sichuan University (Xina). Department of Mathematics)
It is well known that the cyclicity of a Hopf bifurcation in continuous quadratic polynomial differential systems in \R^2 is 3. In contrast here we consider discontinuous differential systems in \R^2 defined in two half--planes separated by a straight line. [...]
2017 - 10.3934/dcdsb.2017203
Discrete and continuous dynamical systems. Series B, Vol. 22 Núm. 10 (2017) , p. 3953-3965  
Detailed record -
4.
17 p, 792.7 KB Restricted independence in displacement function for better estimation of cyclicity / Chen, Xingwu (Sichuan University (Xina). Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Wang, Zhaoxia (University of Electronic Science and Technology of China. School of Mathematical Sciences) ; Zhang, Weinian (Sichuan University (Xina). Department of Mathematics)
Since the independence of focal values is a sufficient condition to give a number of limit cycles arising from a center-focus equilibrium, in this paper we consider a restricted independence to a parametric curve, which gives a method not only to increase the lower bound for the cyclicity of the center-focus equilibrium but also to be available when those focal values are not independent. [...]
2017 - 10.1016/j.jde.2017.02.015
Journal of differential equations, Vol. 262 (2017) , p. 5773-5791  
Detailed record -

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