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Many real-world processes tend to be chaotic and also do not lead to satisfactory analytical modelling. It has been shown here that for such chaotic processes represented through short chaotic noisy time-series, a multi-input and multi-output recurrent neural networks model can be built which is capable of capturing the process trends and predicting the future values from any given starting condition. It is further shown that this capability can be achieved by the Recurrent Neural Network model when it is trained to very low value of mean squared error. Such a model can then be used for constructing the Bifurcation Diagram of the process leading to determination of desirable operating conditions. Further, this multi-input and multi-output model makes the process accessible for control using open-loop/closed-loop approaches or bifurcation control etc. All these studies have been carried out using a low dimensional discrete chaotic system of Hénon Map as a representative of some real-world processes.

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 o ( " ) 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 reallife 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.