On Hopf Cyclicity of Planar Systems

By Maoan Han. 2000

80 citations recorded by the source corpus.

We investigate the maximal number of limit cycles which appear under perturbations in Hopf bifurcations by using the first-order Melnikov function with multiple parameters.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4bf1b990e4385c793aada06849a590d579b78690

Citations in the corpus

• Hilbert's 16th Problem and bifurcations of Planar Polynomial Vector Fields (2003, unknown): “(42) When the condition (41) does not hold [Han, 2000], proved that (i) For each fixed a = (a 1 , a 2 , a 3 ) ∈ R 3 , there exists ε * (a) > 0 such that system (42) has at most two limit cycles near the origin for all 0 |ε| ε * (a).”