Exact Parametric and Semi-Analytical Solutions for the Rucklidge-Type Dynamical System

The behavior of the Rucklidge-type dynamical system was investigated, providing some semi-analytical solutions, in this paper. This system was analytically investigated by means of the Optimal Auxiliary Functions Method (OAFM) for two cases. An exact parametric solution was obtained. The effect of the physical parameters was investigated on the asymptotic behaviors and damped oscillations of the solutions. Damped oscillations are essential for analyzing and designing various mechanical, biological, and electrical systems. Many of the applications involving these systems represent the main reason of this work. A comparison between the obtained results via the OAFM, the analytical solution obtained with the iterative method, and the corresponding numerical solution was performed. The accuracy of the analytical and corresponding numerical results is illustrated by graphical and tabular representations.