Limit Cycle Problem for Quadratic System with some Applications of a Class I
This paper is part of a wider study limit cycle problems of a class and planar system; we study the existence of limit cycle for polynomial planar system. In this paper, we present a proof of a result on the existence of limit cycle of the Quadratic System:
Cherkas and L. Zhilevich, Some criteria for the absence of limit cycle and for the existence of a single limit cycle, Differential Equations,(1977).
Cherkas, Estimation of the number of limit cycles of autonomous systems, Differential Equations, 13 (1977).
Chicone and M. Jacobs, Bifurcation of limit cycles from quadratic isochrones, J. Dif. Eq. 91 (1991).
Ling, a concrete example of the existence of four limit cycles for plane quadratic systems, Sci. Sinica, (1980).
Llibre J. and Dana Schlomiuk, The geometry of quadratic differential systems with a weak focus of third order, Condition J. of Math, (2004).
Perko L., Differential Equations and Dynamical systems. Third Edition. Springer, New York, (2001).
Yan-Qian Y et al., Theory of Limit Cycles, Trans. Math. Mono, A.M. Soc. V 66, 1986.