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Fractal Dimension and Synchronization of the Controlled Julia Sets of a Reaction–Diffusion System
Author(s) -
Zhang Yongping,
Liu Changchun,
Liu Shutang,
Sun Jie
Publication year - 2017
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1520
Subject(s) - julia set , brusselator , fractal , fractal dimension , reaction–diffusion system , dimension (graph theory) , nonlinear system , mathematics , computer science , perturbation (astronomy) , mandelbrot set , box counting , control theory (sociology) , algorithm , fractal analysis , mathematical analysis , control (management) , artificial intelligence , pure mathematics , physics , quantum mechanics
This paper is concerned with the fractal dynamics of a reaction–diffusion system, – the forced Brusselator model. The Julia set of the discrete version of the model is established. Then, the control of the Julia set is realized by combining the parameter perturbation control method and feedback control method. The box‐counting dimensions of the Julia sets of the controlled system for different control parameters are computed, which is used to describe the complexity and irregularity of the Julia sets. Finally, nonlinear coupling items are designed to make one Julia change to be another. The simulations illustrate the efficacy of these methods.