Analysis of New 4D Hyperchaotic Systems MACM and Implementation Using Runge-kutta

Abstract

In general, hyperchaotic system is defined as a chaotic system with more than one positive Lyapunov exponent, this implies that its chaotic dynamics extend in several different directions simultaneously. The discovery of reliable and effective methods for solving hyperchaotic systems is carried out extensively. The aim of this research is to implement nonlinear hyperchaotic using runge-kutta. The NHS system is built by inspecting, modifying and adding one state to the MACM chaotic system. In this study, we use the same initial conditions x_0=y_0=z_0=w_0=1 and the parameters a = 2,b = 2,c = 0.5, and d = 14.5. At first we experiments modified approaches, namely Classic Runge-Kutta Method 3 Order, Runge-Kutta Method Based On Arithmetic Mean, Metode Runge-Kutta Method Based On Geometric Mean, Modified Runge-Kutta Geometric Mean Based Method-1, RKLCM Approaches Instead of RKGM using MAPLE software as a calculation tool. In this work, we observe that the Runge-Kutta Method Based on Arithmetic Mean has the smallest error value with an average variable x of 0.000606953, variable y of 0.009280181, variable z of 0.000378639 and variable w of 0.60781585. Then also in RKLCM Approaches Instead of RKGM it has the largest error value with an average variable x of 0.483789793, variable y of 0.620803849, variable z of 0.92097139, and variable w of 0.596137549.