Theoretical and numerical approach for quantifying sensitivity to system parameters of nonlinear systems

Abstract Sensitivity evaluation of nonlinear systems to system parameters is critically important in nonlinear dynamics, though current focuses in the field are mainly on the sensitive dependence of nonlinear systems upon initial conditions. The present research intends to develop an approach for quantitatively measuring the sensitivity of nonlinear dynamic systems to system parameters. A single-value sensitivity index is created via a theoretical approach. Numerical simulations are conducted to demonstrate the reliability and applicability of the index in quantifying and analyzing the system parameter-dependent sensitivity for nonlinear systems. With the implementation of the sensitivity index, a diagram illustrating the sensitive and insensitive regions and degree of sensitivity over a large range of system parameters is constructed for a typical nonlinear dynamic system. The sensitivity index developed shows effectiveness and convenience in quantitatively evaluating and analyzing the parameter-dependent sensitivity for nonlinear systems. The results of the research show that chaos and quasi-periodicity of a nonlinear system are sensitive to the system’s parameters, independent of its sensitivities to initial conditions. Based on the proposed method, region diagrams regarding to different parameters are presented, which may help to avoid high sensitivity parameter values such as stiffness, mass and damping values in the design of mechanical systems.