Contents I. Introduction
Chaotic systems and their phenomena are widespread in nature. Chaos is sensitive to initial value and its signal is random. It is very difficult to predict long-term chaotic behavior. However, in many studies, the regularity of chaos is gradually revealed and applied, such as measurement, coding and confidentiality, sensors, etc. [1]-[4]. As an important research direction, chaos-control has been designed to control chaos since Ott, Grebogi and Yorke proposed the "OGY" chaos control method in the 1990s [5]. Many chaos control methods have been designed to control chaos [6]-[8].The control of chaotic laser has always been an important aspect of people's attention [9]-[11]. Currently, laser control methods include disturbance, photoelectric feedback, double feedback, phase shift modulation and injection light methods, etc. [9]-[11]. Because erbium-doped fiber laser has very important applications in many fields [12], [13], such as optical fiber communication and fiber sensor, the application research of erbium-doped fiber laser has become a very attractive problem. In erbium-doped fiber laser, the laser can transition from continuous working state to self-pulsation or chaotic state due to its metastable life of erbium-doped fiber is 1-10ms and high power density of fiber core. L.uo et al. observed this nonlinear dynamic phenomenon and established a theoretical model of two coupled lasers [12], [13]. The two-ring erbium-doped fiber laser can show more complex dynamics and chaotic behavior. Although there have been reports on the research on chaos of two-ring erbium-doped fiber laser [12], [13], considering its application prospect in the field of control and laser, we feel that further research is needed to discover new physical phenomena, propose new control methods and promote the development of new laser chaos control technology.
