Time series difference approach for evaluating sensitivity of nonlinear dynamic systems
Industrial systems Engineering, University of Regina, Regina, SK, S4S0A2, Canada.
Research Article
World Journal of Advanced Engineering Technology and Sciences, 2022, 07(01), 149–160.
Article DOI: 10.30574/wjaets.2022.7.1.0107
Publication history:
Received on 14 September 2022; revised on 19 October 2022; accepted on 22 October 2022
Abstract:
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.
Keywords:
Sensitivity; Time series difference; Chaos; Quasi-periodicity; System-parameter dependent sensitivity; Initial-condition dependent sensitivity; Nonlinear behavior; Nonlinear dynamic systems; Lyapunov exponents
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