Three-dimensional limit cycles generated from discontinuous piecewise differential systems separated by cylinders

<p>The study of piecewise differential systems appears in various scientific topics and serves as an important tool for modeling many phenomena in contemporary research. Moreover, the existence and maximum number of limit cycles in such systems represent one of the most difficult problems in mathematics. This paper examines the existence and the maximum number of crossing limit cycles for the 3<span class="math inline">\(D\)</span>-discontinuous piecewise differential system formed by a linear differential center and relay system separated by cylinder. Firstly we consider the right circular cylinder <span class="math inline">\(\mathcal{C}_1 =\{(x,y,z)\in \mathbb{R}^3:x^2+y^2=1\}\)</span> as a switching manifold. Secondly we separate the entire space by the parabolic cylinder <span class="math inline">\(\mathcal{C}_2 =\{(x,y,z)\in \mathbb{R}^3:z=y^2\}\)</span>.</p>