Frequency-truncation fast-slow analysis for parametrically and externally excited systems with two slow incommensurate excitation frequencies.

Highlights • An approximation method is proposed for analyzing fast-slow dynamics in parametrically and externally excited systems with two slow incommensurate excitation frequencies. • The validity of the approach is demonstrated by the Duffing and van der Pol systems, respectively. • The proposed approach explains the generation of complex bursting dynamics related to incommensurate excitation frequencies. Abstract This paper aims to report an approximation method, the frequency-truncation fast-slow analysis, for analyzing fast-slow dynamics in parametrically and externally excited systems with two slow incommensurate excitation frequencies (PEESTSIEFs). We obtain truncated, commensurate excitation frequencies, which are approximations of the incommensurate excitation frequencies. Then, we show numerically that bursting behavior in PEESTSIEFs can be approximated in the same systems but with truncated, commensurate excitation frequencies, and therefore bursting dynamics in PEESTSIEFs can be understood by analyzing the same systems with truncated, commensurate excitation frequencies. Based on this, the approximation method for analyzing bursting dynamics in PEESTSIEFs is proposed. The validity of the approach is demonstrated by the Duffing and van der Pol systems, respectively. [ABSTRACT FROM AUTHOR]