The present research intends to investigate the characteristics of the periodicity ratio and its implementation in analyzing the nonlinear behavior of dynamic systems governed by second-order differential equations. Numerical analyses on the nonlinear dynamic systems with employment of the periodicity ratio for diagnosing chaotic, regular, and irregular behaviors of dynamic systems are performed. To characterize the approach with periodicity ratio in distinguishing different behaviors of the nonlinear dynamic systems, a comparison of periodicity ratio with the widely used Lyapunov exponent in numerically assessing the responses of nonlinear dynamic systems is presented.
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