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Strong and weak chaos in networks of semiconductor lasers with time-delayed couplings

Heiligenthal, Sven; Jüngling, Thomas; D'Huys, Otti; Arroyo-Almanza, Diana A.; Soriano, Miguel C.; Fischer, Ingo; Kanter, Ido; Kinzel, Wolfgang
Physical Review E 88, 012902 (2013)

Nonlinear networks with time-delayed couplings may show strong and weak chaos, depending on the scaling of their Lyapunov exponent with the delay time. We study strong and weak chaos for semiconductor lasers, either with time-delayed self-feedback or for small networks. We examine the dependence on the pump current and consider the question of whether strong and weak chaos can be identified from the shape of the intensity trace, the autocorrelations, and the external cavity modes. The concept of the sub-Lyapunov exponent λ0 is generalized to the case of two time-scale-separated delays in the system. We give experimental evidence of strong and weak chaos in a network of lasers, which supports the sequence of weak to strong to weak chaos upon monotonically increasing the coupling strength. Finally, we discuss strong and weak chaos for networks with several distinct sub-Lyapunov exponents and comment on the dependence of the sub-Lyapunov exponent on the number of a laser's inputs in a network.