SIMULATION OF THE LOGISTIC MAP USING ARTIFICIAL NEURAL NETWORK

Abstract

The logistic map is one of the oldest mathematical model that exhibit chaos. It was originally used to model population dynamics but has now found applications in many other fields. In this work the logistic map is simulated using artificial neural network while adjusting the value of the Malthusian parameter (r) which represents the ratio of existing population to the maximum population. The result was then compared with that of the theoretical logistic map data using non – linear analyses. The non – linear analyses carried out are Hurst exponent, correlation dimension, approximate entropy and sample entropy. The Hurst exponent and the correlation show that the simulated data is chaotic in nature when r = 0.9. The Approximate Entropy and Sample Entropy revealed that the level of complexity in the simulated data is low. The result obtained in this study compares well with those obtained for the original logistic map data. This research has contributed to the growing number on chaos application. It also makes it possible for the generation of random numbers, reliable cryptobased systems amongst other applications of chaotic data sets.