Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop

Details Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop

2011-09-29

arxiv.org/abs/1109.6476v1

Mathematics

Classical Analysis and ODEs

This paper was submitted to Nonlinear Analysis: Theory, Methods & Applications

Scientific paper

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 a 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 homoclnic 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. 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.

Affiliated with

Also associated with

No associations

Rating

Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-151679