Limit Cycles and Invariant Curves in a Class of Switching Systems with Degree Four

摘要

In this paper, a class of switching systems which have an invariant conic x~2 +cy~2 = 1,c ∈ R, is investigated.Half attracting invariant conic x~2 + cy~2 = 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.