The Performance Analysis of Artificial Neural Network Based Shimizu-Morioka Chaotic System with Respect to Sample Numbers

Abstract

In this paper, Shimizu-Morioka Chaotic System (SMCS) is modelled using Feed Forward Artificial Neural Network. In the realized network model, Log-Sigmoid and Purelin transfer functions have been used for hidden and output layer, respectively. 3-10-3 network structure is created using MATLAB. The model inputs are the state variables of SMCS. Outputs represent not only the outputs of SMCS but also iterative versions of these inputs. For the equations' numeric solutions of describing SMCS, Runge Kutta 5 Butcher (RK-5-B) algorithm which is one of the differential equation solution methods, is used. Samples in the structure of described network, the created different numbers of samples using RK-5-B have been used as input data and performance analysis have been performed for these data. As a result, the paper shows that when the sample data numbers increase, network modeling performance gives more successful results.

A novel high speed Artificial Neural Network–based chaotic True Random Number Generator on Field Programmable Gate Array

“…Besides, chaos has become a widespread subject that has been studied nearly in every disciplines like astronomy, biology, physics, chemistry, engineering sciences, geology, mathematics, medicine, meteorology, and even social sciences . There are many methods to investigate if a dynamic system exhibits chaotic feature or not.…”

“…7,19,20 Besides, chaos has become a widespread subject that has been studied nearly in every disciplines like astronomy, biology, physics, chemistry, engineering sciences, geology, mathematics, medicine, meteorology, and even social sciences. [21][22][23][24][25][26][27][28][29] There are many methods to investigate if a dynamic system exhibits chaotic feature or not. Three of the most frequently used analysis methods in nonlinear dynamic systems are Lyapunov exponents, Lyapunov dimension, and Lyapunov exponents spectrum.…”