Periodic behavior of a nonlinear dynamical system

Nonlinear dynamical systems, being more of a realistic representation of nature, could exhibit a somewhat complex behavior. Their analysis requires a thorough investigation into the solution of the governing differential equations. In this paper, a class of third order nonlinear differential equations has been analyzed. An attempt has been made to obtain sufficient conditions in order to guarantee the existence of periodic solutions. The results obtained from this analysis are shown to be beneficial when studying the steady-state response of nonlinear dynamical systems. In order to obtain the periodic solutions for any form of third order differential equations, a computer program has been developed on the basis of the fourth order Runge-Kutta method together with the Newton-Raphson algorithm. Results obtained from the computer simulation model confirmed the validity of the mathematical approach presented for these sufficient conditions.