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Multi-delay complexity collapse
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DOI：10.1103/PhysRevResearch.2.033485.png)
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Increasing the number of delays in nonlinear dynamical systems is generally assumed to lead to higher complexity, but distributed delay systems with an infinite number of delays to lesser complexity. This paradox is studied here using the Lang-Kobayashi laser model by first extending a recent method for Lyapunov exponent estimation from single to multiple delays. The Kolmogorov-Sinai entropy, permutation entropy, and time delay signature suppression initially increase with number of delays as the dynamics become more hyperchaotic. At a large number of delays that depends on the feedback strength, this trend reverses, leading to simpler dynamics. The phenomenon is also found in other delay equations, such as the Mackey-Glass system. A similar collapse is uncovered in the distributed delay case with broadening delay kernel.
Keyword:
CHAOTIC SEMICONDUCTOR-LASER
OPTICAL FEEDBACK
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