Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop
By Li Feng, Maoan Han, Valery G. Romanovski. 2011
99 citations recorded by the source corpus.
Abstract In this paper, we study limit cycle bifurcations for a kind of non-smooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with the center at the origin and a homoclinic loop around the origin. By using the first Melnikov function of piecewise near-Hamiltonian systems, we give lower bounds of the maximal number of limit cycles in Hopf and homoclinic bifurcations, and derive an upper bound of the number of limit cycles that bifurcate from the periodic annulus between the center and the homoclinic loop up to the first order in e . In the case when the degree of perturbing terms is low, we obtain a precise result on the number of zeros of the first Melnikov function.
Subfields: Biochemistry, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/93543a4b89c88b2b5db243feac536a3d50237424
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In Biochemistry
In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- Bifurcation of limit cycles from generalized homoclinic loops in planar piecewise smooth systems (2013, methodology): “In [19,21], homoclinic bifurcations are discussed for piecewise smooth differential systems by using extended Melnikov methods.”
- Bifurcation of limit cycles in piecewise smooth systems via Melnikov function (2015, methodology): “This theorem has also many applications to Hopf bifurcation and homoclinic and heteroclinic bifurcations, see [4,10,11,14] for instance.”