Control on Julia Sets in Switching Complex System

In view of the practical application in engineering, it is noted that switching system is paid much more attention [500–509]. Switching system is composed of a family of subsystems and a rule that governs the switching among them. This section introduces time delay and switch to complex system, and analyze the Julia set of the following system. Consider $$\begin{aligned} z_{n+1}=\frac{z_{n}^{r_{\sigma }+l_{\sigma }}+\alpha _{\sigma }}{z_{n-\tau }^{r_{\sigma }}+\beta _{\sigma }}+\gamma _{\sigma }, \end{aligned}$$ where \(\tau \in N^{+},\sigma \in \mathbb {L}=\{1,2,\ldots ,p\}, l_{\sigma }\ge 2,r_{\sigma }>0,\alpha _{\sigma },\beta _{\sigma },\gamma _{\sigma }\) are complex constant, and \(z_{-\tau }, z_{-\tau +1},\cdots , z_0\) are the initial values of (10.1.1).