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The two-dimensional predator–prey Lotka–Volterra model is discussed from the point of fractal theory. Julia set of the discrete version of the model is introduced. Then, the linear feedback control is taken to control the Julia set. By controlling the Julia set, the attractive domain of the attractive fixed point is controlled indirectly. To associate two different Julia sets of the model with different parameters, nonlinear coupling items are designed to make one Julia set change to be another. The simulations illustrate the efficacy of these methods. [ABSTRACT FROM PUBLISHER]

The forced Brusselator model is investigated from the fractal viewpoint. A Julia set of the discrete version of the Brusselator model is introduced and control of the Julia set is presented by using feedback control. In order to discuss the relations of two different Julia sets, a coupled item is designed to realize the synchronization of two Julia sets with different parameters, which provides a method to discuss the relation and the changing of two different Julia sets, one Julia set can be changed to be the other. Numerical simulations are used to verify the effectiveness of these methods. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, control of Julia set of the complex standard family is studied by adding the dissipative feedback control item to the system in two different ways. One is added to the complex system directly and the other is added to the imaginary part of the complex system. For this control method, both the system and the fixed point can be controlled at the same time even the unstable periodic orbits or the fixed points are unknown. Synchronization of two different Julia sets of this system with different system parameters is discussed by two methods, which makes one Julia set change to be another one. [Copyright &y& Elsevier]

The Julia set is one of the most important sets in fractal theory. The previous studies on Julia sets mainly focused on the properties and graph of a single Julia set. In this paper, activated by the consensus of multi-agent systems, the consensus of Julia sets is introduced. Moreover, two types of the consensus of Julia sets are proposed: one is with a leader and the other is with no leaders. Then, controllers are designed to achieve the consensus of Julia sets. The consensus of Julia sets allows multiple different Julia sets to be coupled. In practical applications, the consensus of Julia sets provides a tool to study the consensus of group behaviors depicted by a Julia set. The simulations illustrate the efficacy of these methods. [ABSTRACT FROM AUTHOR]