Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
758232 | Communications in Nonlinear Science and Numerical Simulation | 2014 | 16 Pages |
•Studying bifurcation of limit cycles related to Hilbert’s 16th problem.•Showing the existence of 12 limit cycles around a singular point in a planar cubic system.•This is the best result so far for planar cubic systems around a singular point.
In this paper, we prove the existence of 12 small-amplitude limit cycles around a singular point in a planar cubic-degree polynomial system. Based on two previously developed cubic systems in the literature, which have been proved to exhibit 11 small-amplitude limit cycles, we applied a different method to show 11 limit cycles. Moreover, we show that one of the systems can actually have 12 small-amplitude limit cycles around a singular point. This is the best result so far obtained in cubic planar vector fields around a singular point.