ARTIFICIAL INTELLIGENCE APPLICATION IN STUDYING CHAOTIC BEHAVIOR ON DUFFING OSCILLATOR - Andhita Scantya, Miranti
In this thesis the chaotic behavior in a system that is modelled by Duffing equation is examined. Duffing equation can be used to illustrate a chaotic behavior in a real-world problems such as a weather prediction and economic problems. In an economic system, the Duffing equation can model a movement of stock price. A method is needed to recognize chaotic patterns using non-chaotic data. The study on Duffing equation started by finding numerical solution using Euler, 2nd order Runge-kutta (RK2), 4th order (RK4), and 6th order Runge Kutta method. The purpose of these methods is to determine the comparison of more accurate result. The data that is generated by these methods used to determine the data’s amount for simulating the chaotic condition in the system. In this research the artificial intelligence method that is implemented is Artificial Neural Network (ANN) with backpropagation method. The ability test of ANN in recognizing the chaotic pattern in Duffing equation is done by recognizing the data’s pattern that is never included in ANN training process. The result of this thesis shows the performance of the optimal ANN structure to recognize chaotic behavior of Duffing equation. The correlation of learning parameter and the ANN training duration is obtained, furthermore the correlation between the optimal amount of nodes in hidden layer and the expected MSE value of ANN training. The most optimal amount of nodes in hidden layer shown by the ability of the ANN to reach the stopping criteria and ability to reach minimum error.