English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we study limit cycle bifurcations for a kind of non-smoothpolynomial differential systems by perturbing a piecewise linear Hamiltoniansystem with a center at the origin and a homoclinic loop around the origin. Byusing the first Melnikov function of piecewise near-Hamiltonian systems, wegive lower bounds of the maximal number of limit cycles in Hopf and homoclnicbifurcations, and derive an upper bound of the number of limit cycles thatbifurcate from the periodic annulus between the center and the homoclinic loopup to the first order in. In the case when the degree of perturbing terms islow, we obtain a precise result on the number of zeros of the first Melnikovfunction.

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