Semi-Analytical Closed-Form Solutions for the Rikitake-Type System through the Optimal Homotopy Perturbation Method

The goal of this work is to build semi-analytical solutions the Rikitake-type system by means optimal homotopy perturbation method (OHPM) using only two iterations. chaotic behaviors are excepted. By taking into consideration geometrical properties system, closed-form can be established. obtained have a periodical behavior. These allow reducing initial second-order nonlinear differential equation. latter equation solved analytically OHPM procedure. validation presented for three cases physical parameters. advantages technique, such as small number iterations (the efficiency), convergence control (in sense that approaching exact solution), and writing in an effective form, shown graphically with tables. accuracy results provides good agreement between analytical corresponding numerical results. Other dynamic systems similar could successfully same