On the spatial Julia set generated by fractional Lotka-Volterra system with noise.

• The spatial Julia set of the fractional complex system is obtained, and the dynamical characteristics of the system are studied from the fractal point of view. • The influence of dynamic noise on the fractal characteristics of fractional Lotka-Volterra system is analysed quantificationally and visualized. • Propose the Julia deviation index to characterize and analyze the effect of the noise on the systems Julia sets. The new definition has stronger immanence and wider applicability. This paper investigates the structures and properties of the spatial Julia set generated by a fractional complex Lotka-Volterra system with noise. The influence of several types of dynamic noise upon the system's Julia set is quantitatively analyzed through the Julia deviation index. Then, the symmetry of the Julia set is discussed and the symmetrical structure destruction caused by noise is studied. Numerical simulations are presented to further verify the correctness and effectiveness of the main theoretical results. [ABSTRACT FROM AUTHOR]