Time series difference approach for evaluating sensitivity of nonlinear dynamic systems

This research is aimed to establish a novel approach for assessing sensitivities of nonlinear systems to initial conditions and system parameters via an evaluation of Time Series Difference. An evaluation method is proposed for measuring the differences of two trajectories representing the solutions of nonlinear systems, in responding to different initial conditions and/or system parameters. Recurrence relations are established for numerically evaluating the time series differences. Various nonlinear responses are evaluated with the approach proposed. A typical nonlinear dynamic system the Duffing system are considered for demonstrating the application of the approach in numerically and graphically assessing the sensitivities. The approach shown effectiveness in the assessment and can a useful tool for scientists and engineers in evaluating the initial-condition and system-parameter dependent sensitivities.