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 and wide-ranging zig-zag parameter networks embedded in chaos in the control space of nonlinear systems. Such networks interconnect shrimplike windows of stable oscillations and are illustrated here for a tunnel diode, for an erbium-doped fiber-ring laser, and for the Hénon map, a proxy of certain CO(2) 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.