Zig-zag networks of self-excited periodic oscillations in a tunnel diode and a fiber-ring laser

We report numerical evidence showing that periodic oscillations can produce unexpected andwide-ranging zigzag parameter networks embedded in chaos in the control space of nonlinear systems. Such networks interconnect shrimplikewindows of stable oscillations and are illustrated here for a tunnel diode, for an erbium-doped fiber-ring laser, and for the H´enon map, a proxy of certain CO2 lasers. Networks in maps can be studied without the need for solving differential equations. Tuning parameters along zig-zag networks allows one to continuously modify wave patterns without changing their chaotic or periodic nature. In addition, we report convenient parameter ranges where such networks can be detected experimentally