Different discrete-time noise-suppression Z-type models for online solving time-varying and time-invariant cube roots in real and complex domains: Application to fractals

Abstract

Different from the conventional calculation method, the discrete-time noise-suppression zeroing neural dynamic (DTNSZND) model is developed and investigated for online solving the time-varying/time-invariant scalar cube root problem with different disturbances (bounded/unbounded disturbances) from a control perspective in this paper. The solving precision and robustness of different DTNSZND models are generated via various difference rules are discussed and analyzed, and numerical simulations verify that the convergence property of the developed models are closely related to the accuracy of difference rules. The zero-stable, consistent and convergent of different DTNSZND models are demonstrated via theoretical analyses. Furthermore, numerical simulation and comparative results prove that the convergence, robustness and superiority of the presented different DTNSZND models for online solving time-varying/time-invariant cube root problems with different interferences in real domain or complex domain. Finally, different fractals are generated by utilizing the developed DTNSZND model to solve the cube root problem with different noises in complex domain, which are quite different from Newton fractals produced by Newton–Raphson iteration. Therefore, the proposed different DTNSZND models can be considered as a novel iterative algorithm to generate new fractal.