Characterization of 1D Linear Piecewise-Smooth Discontinuous Map

摘要

One-dimensional (1D) linear piecewise-smooth discontinuous (LPSD) map with one jump discontinuity are known to exhibit a rich and complex dynamics ranging from fixed point to periodic orbits and even chaotic orbits. In this paper, we have given a complete characterization of 1D LPSD map. Further, with the help of cobweb plots, the theoretical analysis is validated. We have considered three different quadrants to illustrate behaviour of these maps. Moreover, the summary of analysis of all the results is presented in a table.