Constructing bifurcation diagram for a chaotic time-series data through a recurrent neural network model

The Bifurcation Diagram (BD) of a given dynamical system gives the idea of the behaviour of one of the outputs of that system with different values of one of the control input parameters keeping all the other input parameters constant. It also gives the idea of iterative behaviour of the system for the particular input conditions. Plotting the BD through the mathematical models is popular in control/chaos theory domain. In this work, a methodology to construct the BD from the available time-series data using recurrent neural networks (RNN) and chaos theory has been developed. The ability of the developed methodology is first demonstrated on a time-series data from a mathematical dynamical system and then on a real-life complex system (submerged arc furnace). The model developed for the dynamical system has shown a high sensitivity to the training MSE level of RNN rather than to the network architecture and the recurrence level of the model, etc.