Louiza Baymout, Rebiha Benterki
abstract:
Due to the wide interdisciplinary use of discontinuous piecewise differential
systems and the main role of the periodic solutions in understanding and
explaining many natural phenomena, scientists developed many methods and tools
for studying the periodic solutions of such differential systems, like the
averaging theory of given order. In this paper, by using the averaging theory up
to seven-order for computing the periodic solutions of discontinuous piecewise
differential systems, we prove that five is the maximum number of limit cycles
that can bifurcate from the discontinuous piecewise differential systems formed
by an arbitrary linear focus or center and an arbitrary cubic uniform
isochronous center separated by a straight line.
Mathematics Subject Classification: 34C05, 34A34
Key words and phrases: Cubic uniform isochronous center, linear center, limit cycle, averaging theory