Chaotic dynamical systems are present in the nature in various forms such as the weather, activities in human brain, variation in stock market, flows and turbulence. In order to get a detailed understanding of a system, the modeling and analysis of the system is to be done in an effective way. A recurrent neural network (RNN) structure has been designed for modeling the dynamical system. The neural network weights are estimated using the Particle Filter algorithm. There are various natural systems, which can be represented by chaotic dynamical systems. But closed form mathematical equations for such systems are not readily available for generating such time series. The North Atlantic oscillations are one such system which is modeled with the selected RNN model structure and Particle Filter algorithm. While the model faithfully reproduces the given time series, the phase plane generated unravels the dynamics of the system. The characterization of the natural chaotic systems is done in the time domain by Embedding Dimension, Phase plots and Lyapunov Exponents.

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Chaotic Systems North Atlantic Oscillation Embedding Dimension Lyapunov Exponent Phase Plots