✦ LIBER ✦

Limit cycles bifurcate from centers of discontinuous quadratic systems

✍ Scribed by Xingwu Chen; Zhengdong Du

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 391 KB
Volume: 59
Category: Article
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2010.04.019

No coin nor oath required. For personal study only.

✦ Synopsis

a b s t r a c t Like for smooth quadratic systems, it is important to determine the maximum order of a fine focus and the cyclicity of discontinuous quadratic systems. Previously, examples of discontinuous quadratic systems with five limit cycles bifurcated from a fine focus of order 5 have been constructed. In this paper we construct a class of discontinuous quadratic systems with a fine focus of order 9. In addition, by using a method similar to that developed by C. Christopher for smooth systems, which allows one to estimate the cyclicity just from the lower order terms of Lyapunov constants, we show that the cyclicity of discontinuous quadratic systems is at least 9, thus improving on previous results.

📜 SIMILAR VOLUMES

Bifurcation of Limit Cycles from Quadrat

Bifurcation of Limit Cycles from Quadratic Centers

✍ D.S. Shafer; A. Zegeling 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 837 KB

Bifurcation of limit cycles from the class \(Q_{3}^{N H}\) of quadratic systems possessing centers is investigated. Bifurcation diagrams for various systems in this class are constructed, and are used to locate systems possessing a period annulus whose closure has cyclicity three. "1995 Acidenic Pre

Limit cycles of quadratic systems

✍ Valery A. Gaiko 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 266 KB

In this paper, the global qualitative analysis of planar quadratic dynamical systems is established and a new geometric approach to solving Hilbert's Sixteenth Problem in this special case of polynomial systems is suggested. Using geometric properties of four field rotation parameters of a new canon

Bifurcation of Limit Cycles in a Particu

Bifurcation of Limit Cycles in a Particular Class of Quadratic Systems with Two Centers

✍ W.T. Vanhorssen; R.E. Kooij 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 861 KB

Within the class of quadratic perturbations we show analytically or numerically how many limit cycles can be bifurcated at first order out of the periodic orbits nested around the centre point in \((0,0)\) or nested around the centre point in \((0,1 / n)\) of the quadratic system \(\dot{x}=-y+n y^{2

Weak Focus, Limit Cycles, and Bifurcatio

Weak Focus, Limit Cycles, and Bifurcations for Bounded Quadratic Systems

✍ C.Z. Li; J. Llibre; Z.F. Zhang 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 781 KB

We study the bounded quadratic systems with either two weak foci or a weak focus of order 2. From the first case we obtain (1,1)-configuration of limit cycles, and in the second case we prove that there is no limit cycle surrounding the weak focus of order 2. Also, we unfold the bounded quadratic sy

Bifurcation of limit cycles from a two-d

Bifurcation of limit cycles from a two-dimensional center inside

✍ Jaume Llibre; Amar Makhlouf 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 385 KB

Uniqueness of Algebraic Limit Cycles for

Uniqueness of Algebraic Limit Cycles for Quadratic Systems

✍ Javier Chavarriga; Hector Giacomini; Jaume Llibre 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 102 KB

We know five different families of algebraic limit cycles in quadratic systems, one of degree 2 and four of degree 4. Moreover, if there are other families of algebraic limit cycles for quadratic systems, then their degrees must be larger than 4. It is known that if a quadratic system has an algebra