Abstract
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 λ(0) 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.
Highlights
In the interdisciplinary science of complex systems one often encounters large dynamical systems described as networks of nonlinear units
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
In this paper we extend the investigations on strong and weak chaos presented in Ref. [17] by focusing on the dynamics of semiconductor lasers
Summary
In the interdisciplinary science of complex systems one often encounters large dynamical systems described as networks of nonlinear units. II we complete the discussion of the scaling behavior of the LE for a single chaotic unit with delayed self-feedback in the limit of large delays, which has been sketched in Ref. [17], numerical simulations of the Lang-Kobayashi equations yield the transition from weak to strong chaos and back to weak chaos upon monotonically increasing the coupling strength We extend this result by discussing the scaling just at the transition and the dependence of the scaling on the laser pump current. We report on an experiment on semiconductor lasers that supports the sequence of weak to strong to weak chaos with increasing coupling strength. We present a generalized investigation of networks with several distinct sub-LEs and certain network patterns
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