Time delays widely exist in the complex dynamical systems. In this paper, time-delay complex dynamical systems are studied by analyzing the properties of corresponding Julia sets. Experimental results show that the stability of complex dynamical system changes greatly due to the influence of time delay. The variations in time-delay Julia sets are studied. In addition, the conditions holding the dynamical systems stable are found. Time delay affects the stability of complex dynamical systems, and the existence of the fixed and periodic points is also discussed.
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