Synchronization of Julia Sets in Three-Dimensional Discrete Financial Models

Abstract

When aiming to achieve consistency in fractal characteristics between different models, it is crucial to consider the synchronization of Julia sets. This paper studies the synchronization of Julia sets in three-dimensional discrete financial models. First, three-dimensional discrete financial models with different model parameters are proposed and their Julia sets are presented. According to the model forms, two kinds of synchronous couplers that can achieve synchronization of Julia sets between different models are designed by changing the synchronization parameters. The proposed synchronization method is theoretically derived and the efficiency of different synchronous couplers are compared. Finally, the effectiveness is verified by Julia sets graphics. This method has reference value for theoretical research into financial models in the field of fractals.