Contents 1. INTRODUCTION
Chaos characterizes sensitivity to its initial condition while produced infinite dense phase trajectory leads to a chaotic attractor. Chaos becomes of disorder, complication and pseudorandom. Currently, a chaotic laser is used to apply in secure communication and radar[1],[2]. An erbium-doped fiber laser is widely used in optics communication and optics sensor while it shows some unique physical characterizations. The lifetime of erbium ion at the metastable state is found to exist about 10ms. So the laser leads to a continuous transition to result in chaos and other nonlinear optics [3]. And an erbium-doped fiber laser can produce chaos via an additional operation of the laser[3]-[6]. We present a method of two degrees of freedom modulation of the laser to produce nonlinear optical dynamics behavior. And we are attracted to chaos and other nonlinear optics of a short cavity single-mode erbium-doped fiber laser [5]. We focus on a path to chaos after one-cycle while the chaotic region is discussed via varying the modulation frequency and modulation depth respectively.
