Fractal features and synchronization of a class of generalized Logistic map
HU Chang-quan
LIU Shu-tang
Abstract：In this paper,Julia and Mandelbrot sets of a class of two-dimensional generalized real Logistic map are discussed.Firstly,the fractal dimension of Julia set of the real map is obtained by box-counting method,then the control of Julia sets of the real map is accomplished via using the linear feedback control.Secondly,we introduce the concept of synchronization of Julia sets between different systems and achieve the synchronization of Julia sets of two real maps with different parameters using the nonlinear coupling control.Finally,the Mandelbrot set of the real map is constructed by introducing real parameters,and gradient control is taken to realizing the synchronization of Mandelbrot sets of two real maps which have different parameters.Simulation results show the effectiveness of the control method and the synchronization method.
Keywords：generalized real Logistic mapJulia setMandelbrot setfeedback controlsynchronization
Publication Date：2017-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：9( 215-223 )