Hidden multi-scroll and coexisting self-excited attractors in optical injection semiconductor laser system: Its electronic control

In this paper, we investigate hidden and coexisting self-excited multi-scroll attractors by using a modified rate equations model of semiconductor lasers (REM-SCLs) subjected to optical injection by exploring various quantifying analytical and numerical methods. The multi-leveled dynamics sticks out the existence of several sets of equilibria that asymptotically attract trajectories originating outside of them. Chaos topology based on the impact of equilibria allows the describing of the so-called stable or unstable multi-scroll chaotic attractors. Shaping of the new coexisting self-excited multi-scroll attractor, whose source is from coupling of equilibria, is analyzed, as well as its structural dynamics along with the dynamical emergence of the hidden multi-scroll attractor in the restricted interval, defined by an additional decisive parameter. Additionally, specific 3D plots with embedded contour plots obtained by harnessing two-parameter bifurcation analysis clarify structural dynamics of such a multi-scroll attractor and accurately circumscribe stretching of its fractal-like basin of attraction. Strange metamorphoses undergone by the fractal-like basin of attraction of the studied multi-scroll attractor are stepwisely parsed in the map of two-codimension bifurcation as its scroll number evolves. At last, an electronic circuit of equivalent REM-SCLs is designed and simulated in the PSpice environment alongside a tailored electronic controller. The achieved results align with the ones of numerical analysis; besides, temporal controlling of optical waves pertaining thereto is also fulfilled.