Abstract
In this paper, a class of switching systems which have an invariant conicx2+cy2=1,c∈R, is investigated. Half attracting invariant conicx2+cy2=1,c∈R, is found in switching systems. The coexistence of small-amplitude limit cycles, large amplitude limit cycles, and invariant algebraic curves under perturbations of the coefficients of the systems is proved.
Highlights
It is well known that the 16th problem stated in 1900 by D
As far as the maximal number of small-amplitude limit cycles which are bifurcated from an elementary center or focus is concerned, the best known result obtained by Bautin in 1952 [1] is M(2) = 3, where M(n) denotes the maximal number of small-amplitude limit cycles around a singular point with n being the degree of polynomials in the system
A cubic system was constructed by Lloyd and Pearson [2] to show 9 limit cycles with the aid of purely symbolic computation
Summary
It is well known that the 16th problem stated in 1900 by D. A class of switching systems which have an invariant conic x2 + cy2 = 1, c ∈ R, is investigated. The coexistence of small-amplitude limit cycles, large amplitude limit cycles, and invariant algebraic curves under perturbations of the coefficients of the systems is proved.
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