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
Bifurcation of Limit Cycles from Quadratic Centers
β Scribed by D.S. Shafer; A. Zegeling
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 837 KB
- Volume
- 122
- Category
- Article
- ISSN
- 0022-0396
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β¦ Synopsis
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 Press. Inc.
π SIMILAR VOLUMES
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
A combination of analytical and numerical work is done to analyze bifurcation of limit cycles from non-Hamiltonian codimension-three quadratic centers. The winding curve C C of cyclicity-three separatrix cycles, qualitatively located in earlier 3 Ε½ . Ε½ . Ε½ . work, is determined numerically. Evidenc
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