The Modeling of the Rucklidge Chaotic System with Artificial Neural Networks

Abstract

Chaotic systems are systems that show sensitive dependence on initial conditions, and an immeasurably small change in initial value causes an immeasurably large change in the future state of the system. Besides, there is no randomness in chaotic systems and they have an order within themselves. Researchers use chaotic systems in many areas such as mixer systems that can make more homogeneous mixtures, encryption systems that can be used with high security, and artificial neural networks by taking the advantage of the order in this disorder. Differential equations in which chaotic systems are expressed mathematically are solved by numerical solution methods such as Heun, Euler, ODE45, RK4, RK5-Butcher and Dormand-Prince in the literature. In this research, Feed Forward Neural Network (FFNN), Layer Recurrent Neural Network (LRNN) and Cascade Forward Backpropogation Neural Network (CFNN) structures were used to model the Rucklidge chaotic system by making use of the MATLAB R2021A program Neural Network (NN) Toolbox. By comparing the results of different activation functions used in the modeling, the ANN structure that can best model the Rucklidge chaotic system has been determined. The training of the compared Artificial Neural Networks (ANNs) was carried out with the values obtained from the Euler numerical solution method, which can get satisfactory and fast results.

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“…• Multiscroll: System described by a monoparametric family (Figure 1a,b), used to model diffusion processes [28,29]. • Rucklidge: This system models double convection processes where the motion is confined to coils resembling convection in an applied vertical magnetic field and a slightly rotating fluid layer [30] (see Figure 1c,d).…”

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