Details:
Title  Limit cycle bifurcations from a nondegenerate center  Author(s)  Jaume Giné  Type  Article in Journal  Abstract  In this work we discuss the computational problems which appear in the computation of the Poincaré–Liapunov constants and the determination of their functionally independent number. Moreover, we calculate the minimum number of Bautin ideal generators which give the number of small limit cycles under certain hypothesis about the generators. In particular, we consider polynomial systems of the form x ˙ =  y + P n ( x , y ) , y ˙ = x + Q n ( x , y ) , where Pn and Qn are a homogeneous polynomial of degree n. We use center bifurcation rather than multiple Hopf bifurcations, used a previous work [19], to estimate the cyclicity of a unique singular point of focus–center type for n = 4, 5, 6, 7 and compare with the results given by the conjecture presented in [18].  Keywords  Poincaré–Liapunov constants, Limit cycles, Center problem, Groebner basis  ISSN  00963003 
URL 
http://www.sciencedirect.com/science/article/pii/S0096300310009720 
Language  English  Journal  Applied Mathematics and Computation  Volume  218  Number  9  Pages  4703  4709  Year  2012  Edition  0  Translation 
No  Refereed 
No 
