Chaos is a seeming random behavior in a nonlinear dynamic system with determinateexpression. It is well known that chaotic phenomena always occur comprehensively in nature.Of them, the chaos system and hyperchaos system of single-ring erbium fiber laser and thedouble-ring erbium fiber laser are of important application in many fields, including opticsand communication. Therefore, the deep investigation of theory and application aboutdynamic characteristics of chaos, chaos control and chaos synchronization have tremendousscience significance and applied value.The main works in the thesis are as following.(1) The definition and basic characteristics of chaos are introduced briefly. The historyand current status of chaos investigation, especially hyperchaos investigation, are summarized,including the development of theory and experiment research about chaos control, chaossynchronization, spot diagram and secure communication based on chaos systems.(2) The chaos and hyperchaos characteristics of single-ring erbium fiber laser and thedouble-ring erbium fiber laser are analyzed. N2-single-ring erbium fiber lasers are used toconstruct an N×N laser array and boundary conditions are periodic change. The patterns andevolvement with time of spot diagram of the laser array are discussed based on the theory oftwo-dimension coupled map lattice. The change of patterns is further analyzed throughadjusting different coupling coefficients, the number of lattice and periods.(3) Two hyperchaos systems of double-ring erbium fiber lasers are selected as transmitterand acceptor of secure information, respectively. At the same time, the multi-channel securesignals are loaded at the parameters of hyperchaos in the transmitter. The optimal controller ofdeformation synchronization and the signal update rules are designed based on the Lyapunovprinciple of stability. The multi-channel secure information is ensured to demodulated andrecognized without distortion at acceptor.(4) Finally, the works in the thesis are summed up and summarized briefly. At the sametime, the direction and goal of further investigation about optics chaos are prospected. |