On Saddle-Loop Bifurcations of Limit Cycles in Perturbations of Quadratic Hamiltonian Systems
β Scribed by E. Horozov; I.D. Iliev
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 653 KB
- Volume
- 113
- Category
- Article
- ISSN
- 0022-0396
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π SIMILAR VOLUMES
In this paper a class of quadratic systems is studied. By quadratic systems we mean autonomous quadratic vector fields in the plane. The class under consideration is class \(\mathrm{II}_{n=0}\) in the Chinese classification of quadratic systems. Bifurcation sets \(\delta=\delta^{*}(l, m)(m>2, l>0)\)
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