Reconstrucción de la Dinámica no Lineal de Sistemas Caóticos con Retraso Mediante Redes Neuronales

Resumo

In the last years there has been an intense research in chaos-based communications. Chaotic waveforms provide an additional layer or level of privacy beyond any conventional software-based cryptography that can be simultaneously part of the communication protocol. However, the analysis of the security of different chaotic communication systems is still a question that has to be addressed for practical applications in the field. In this thesis, we particularly focus on optical communication systems with delayed feedback. Optical communication systems are very interesting because they offer the possibility of high transmission rates (range of Gbits). Moreover, semiconductor lasers subject to feedback provide simple ways of generating chaotic signals with high dimensional attractors. Higher dimensional systems, especially those involving hyperchaotic dynamics, are likely to provide improved security. It is computationally difficult to reconstruct the nonlinear dynamics of these systems with time-series analysis techniques based on the standard embedding approach. However, it is possible to reconstruct the nonlinear dynamic of a single-variable time-delay system by using an embedding-like approach. This method works with a special embedding space that includes both short time and feedback time delayed values of the system variable. This thesis focuses on the reconstruction of the nonlinear dynamic of time-delay systems applying this special embedding. We use a new type of modular neural network based on the structure of time-delay systems. We also carefully investigate the time delay identification from the time series, a crucial parameter to construct the special embedding vector. Finally we use the reconstructed models to show the vulnerability of the chaos-based communication system based on time-delay systems and to study the predictability of these systems. Although we mainly focus on electro-optical feedback system, the techniques investigated in this thesis have a general applicability to scalar time-delay systems.