@Article{JNMA-6-3,
author = {Ghermoul, Bilal and Llibre, Jaume},
title = {Limit Cycles for a Class of Continuous-Discontinuous Piecewise Differential Systems},
journal = {Journal of Nonlinear Modeling and Analysis},
year = {2024},
volume = {6},
number = {3},
pages = {669--682},
abstract = {<p style="text-align: justify;">During this century, an increasing interest appeared in studying
the planar piecewise differential systems. This is due to their numerous applications for modelling many natural phenomena. For understanding the
dynamics of the planar differential systems we must control the existence or
non-existence of periodic orbits and limit cycles. So many papers have been
published studying the existence or non-existence of periodic orbits and limit
cycles for continuous or discontinuous piecewise differential systems. But until now very few papers have studied the periodic orbits and limit cycles of
piecewise differential systems where two differential systems of the piecewise
differential system are continuous and discontinuous respectively. We study
the periodic orbits and limit cycles of the planar continuous–discontinuous
piecewise differential systems separated by two parallel straight lines, such
that either in one of these straight lines the piecewise differential system is
continuous and in the other one discontinuous. In two pieces of these piecewise differential systems there are arbitrary Hamiltonian systems of degree
two and in the third piece there is an arbitrary Hamiltonian system of degree
one forming the continuous-discontinuous piecewise differential systems. We
determine the limit cycles of these piecewise differential systems by considering two cases. In the first the Hamiltonian system of degree one can be in
the middle of the three zones, and in the second it is on one side of the three
zones.</p>},
issn = {2562-2862},
doi = {https://doi.org/10.12150/jnma.2024.669},
url = {https://global-sci.com/article/91174/limit-cycles-for-a-class-of-continuous-discontinuous-piecewise-differential-systems}
}