@article{Jiang2024, 
author = {Ziguo Jiang},
title = {Limit cycles in an    m-piecewise discontinuous polynomial differential system},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {2},
pages = {3613-3629},
keywords = {limit cycle, piecewise differential equation, averaging method},
url = {https://www.sciopen.com/article/10.3934/math.2024177},
doi = {10.3934/math.2024177},
abstract = {In this paper, I study a planar    m-piecewise discontinuous polynomial differential system              x      ˙        =  y  ,            y      ˙        =  −  x  −  ε  (  f  (  x  ,  y  )  +      g    m    (  x  ,  y  )  h  (  x  )  ), which has a linear center in each zone partitioned by those switching lines, where    f  (  x  ,  y  )  =      ∑          i      +      j      =      0        n        a          i      j            x    i        y    j  ,    h  (  x  )  =      ∑          j      =      0        l        b    j        x    j    ,      a          i      j        ,      b    j    ∈      R    ,  n  ,  l  ∈      N  , and        g    m    (  x  ,  y  ) with the positive even number    m as the union of    m      /    2 different straight lines passing through the origin of coordinates dividing the plane into sectors of angle    2  π      /    m. Using the averaging theory, I provide the lower bound        L    m    (  n  ,  l  ) for the maximun number of limit cycles, which bifurcates which bifurcating from the annulus of the origin of this system.}
}