| Contents |
| We focus our attention on the existence of periodic orbits for the reversible two-zonal piecewise linear system
\[
\left\{\begin{array}{l}
\dot x= y, \\
\dot y=z,\\
\dot z= 1-y-\lambda(1+\lambda^2)|x|,\\
\end{array}\right.
\]
where the parameter $\lambda$ is strictly positive. This system is formed from two linear systems separated by the plane $x=0$ and can be considered as a continuous piecewise linear version of the Michelson system. Both systems present the well-known noose bifurcation. Indeed, a numerical study of the stability and bifurcations of the periodic orbits involved in the noose curve for the piecewise linear system allows us to assure that they exhibit the same configuration that the Michelson system has.
The orbits that take part in the noose bifurcation for the piecewise linear system have two and four points of intersection with the separation plane and they are arranged in two curves that are connected by a point where the periodic orbit has a crossing tangency with the separation plane. This periodic orbit plays an important rule because the crossing tangency forces a small loop that allows the appearance of the noose structure. |
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