Fractals control in particle’s velocity

Julia set, a fractal set of the literature of nonlinear physics, has significance for the engineering applications. For example, the fractal structure characteristics of the generalized M–J set could visually reflect the change rule of particle’s velocity. According to the real world requirement, the system need show various particle’s velocity in some cases. Thus, the control of the nonlinear behavior, i.e., Julia set, has attracted broad attention. In this work, an auxiliary feedback control is introduced to effectively control the Julia set that visually reflects the change rule of particle’s velocity. It satisfies the performance requirement of the real world problems.