Algorithmic complexity in chaotic lasers with extreme events

KOVALSKY, MARCELO G.; ALEJANDRO A. HNILO; MÓNICA B. AGÜERO

Punta del Este

Congreso; DYNAMICS DAYS Latin America and the Caribbean; 2018

Determining whether a "noisy" signal is random or chaotic from experimental time series is a fundamental problem.Chaos is deterministic and, to some extent, predictable and controllable. Random signal, on the other hand, is not predictable and therefore uncontrollable.Proving that a system is chaotic implies finding the underlying attractor and positive Lyapunov exponents. This task is, in general, complicated in addition to requiring a huge amount of experimental data. In the 1960s, Kolmogorov developed the concept of algorithmic complexity. It basically tries to answer the question: What is a random object? The Kolmogorov complexity of an object x is the length of the shortest description of x. In this way the only possibledescription of a random object is the explicit enumeration of each of its components, and it has maximum complexity. A periodic signal, at the other end, will have minimal complexity, while chaotic signals have intermediate complexity.In this poster we present the results of the computation of the algorithmic complexity or Kolmogorov complexity through the Lempel - Ziv algorithm, fromexperimental time series of three different lasers, all with chaotic behaviors with extreme events but of different etiology. It is shown that in all cases theKolmogorov complexity adequately describes chaotic behaviors with and without extreme events. Given its simplicity of calculation, it becomes an effective tool for diagnosing chaotic behaviors that can also be easily incorporated into real-time chaos control schemes.