Fractal control and synchronization of population competition model based on the T–S fuzzy model

Abstract

It is of great significance to study the law of population change in species protection, resource utilization, ecological stability, and so on. The fractal behavior of the population competition model is discussed from the fractal viewpoint. By using the sector nonlinear method, the Takagi–Sugeno (T–S) fuzzy model of the population competition model is established, and the Julia set of the population competition model based on the T–S fuzzy model is introduced. The parallel distributed compensation (PDC) is used to design the corresponding fuzzy controller, and sufficient conditions for the stability of the system are given in the form of linear matrix inequalities (LMIs). The parameters of controller gain are obtained by solving LMIs, and the control of the Julia set of the population competition model based on the T–S fuzzy model is carried out. Using the exact linearization technique, the synchronization of the Julia sets of the population competition models is realized based on the T–S fuzzy model by the linear control method, and the Julia set diagram of the corresponding population competition model is analyzed.