Artificial Neural Network model design and topology analysis for FPGA implementation of Lorenz chaotic generator

Abstract

This paper presents an Artificial Neural Network (ANN) design for a chaotic generator, and the training performances for a three layer ANN architecture with different number of hidden neurons. Chaotic systems can be synchronized and used for secure communication. Chaotic systems such as Lorenz attractor, Rossler attractor and Chen's system are generally implemented directly based on their definitions represented by a unique group of ordinary differential equations (ODEs). An feed forward ANN can be trained using the output values of a chaotic system. The training process is carried out on a computer and the weights are generated for all neurons in an ANN architecture. These weights are then used for a trained ANN architecture model to generate the expected output for the target chaotic system. The complexity of the ANN architecture defines the implementation cost and speed. Therefore it is beneficial to use less number of hidden neurons to achieve the target training performance. Lorenz attractor has its significance in studying chaotic systems and is used as the design subject in this paper. The 3-layer ANN has one input, one hidden and one output layer. The ANN architecture with 1 to 16 hidden neurons is designed and trained respectively using MATLAB Neural Network Toolbox with three training algorithms: Levenberg-Marquardt, Scaled Conjugate Gradient algorithm and Bayesian Regulation. The optimized ANN architecture can be used to improve the efficiency of the fixed-point implementation on an Field Programmable Gates Array (FPGA) device.