Self-similarity in a system with short-time delayed feedback

Abstract

Using the Poincar\'{e} section technique, we study in detail the dynamical behaviors of delay differential system and find a new type of solutions $S_i$ in short-time delay feedback. Our numerical results remind us to deny the opinion that there are no complex phenomena in short-time delay case. Many similarities between foundamental solution and the new type of solutions are found. We demonstrate that the scales of $S_i$ increase with exponential growth via $i$ in the direction of $\mu $, while decrease with exponential decays in the direction of $x$ or delay time $t_R$.