Abstract: Nonlinear system is a complex subject in the field of finance, and its complexity change and control methods have always been the key and difficult research points for experts and scholars. Earlier studies of nonlinear systems were based on integer-order nonlinear systems. With the deepening of the research on fractional-order systems, people have gradually realized that the complexity of fractional-order systems is generally higher than that of integer-order systems. Analyzing and studying its complex characteristics is helpful to define system parameters and increase the complexity of the system. This paper takes a fractional Rucklidge system as an example to study its dynamic and complex characteristics. For the fractional-order nonlinear system, a synchronous controller is designed, which can be controlled and simulated synchronously. Simulation results show that the controller can achieve synchronization in a short time.

Key words: Rucklidge system, complexity, finite time synchronization, fractional order, Adomain decomposition method