Aziza Berbache

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

abstract:
For a given family of planar piecewise linear differential systems, it is a very difficult problem 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 by two regions separated by a straight line and having only one focus whose limit cycles can be explicitly described by using the first integrals. We show that these systems may have at most two explicit non-algebraic limit cycles.

Mathematics Subject Classification: 34C25, 34A36, 34C07

Key words and phrases: Discontinuous piecewise differential systems, first integrals, non-algebraic limit cycles