Abstract
This paper gives the definition of Mandelbrot set in a coupled map lattice (CML Mandelbrot set), and studies its control and synchronization. A proper mathematical transform is used to achieve the scaling, with regards to size, of the CML Mandelbrot set without changing its structure properties. Furthermore, two different methods, gradient control and optimal control, are separately applied to realize the synchronization of different CML Mandelbrot sets, that making one CML Mandelbrot set change into another. Numerical simulations show the effectiveness of these controls and the feasibility of achieving synchronization using the two different methods.
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