Periodic Flows in Continuous Systems

Abstract

This chapter will present periodic flows in nonlinear dynamical systems through the discrete implicit mappings. The period-1 flows in nonlinear dynamical systems will be discussed first by the one-step discrete maps, and then, the period-m flows in nonlinear dynamical systems will also be discussed through the one-step discrete maps. Multi-step, implicit discrete maps will be used to discuss the period-1 and period-m motions in nonlinear dynamical systems. Periodic flows in nonlinear time-delay dynamical systems will be discussed with time-delay discrete nodes interpolated by two non-delay discrete nodes. In addition, periodic flows in time-delay nonlinear dynamical systems will be also discussed through the delay nodes determined by integration. Through the discrete nodes in periodic flows, the periodic flows will be approximated by the discrete Fourier series and the frequency space of the periodic flows can be determined through amplitude spectrums.