Two Explicit Non-Algebraic Crossing Limit Cycles for a Family of Piecewise Linear Systems

摘要

For a given family of planar piecewise linear differential systems, it is a very difficultproblem to determine an upper bound for the number of its limit cycles and its explicit expressions.In this paper, we give a family of planar discontinuous piecewise linear differential systems formed bytwo regions separated by a straight line and having only one focus whose limit cycles can be explicitlydescribed by using the first integrals. We show that these systems may have at most two explicitnon-algebraic limit cycles.