Generalized zeroing neural dynamics model for online solving time-varying cube roots problem with various external disturbances in different domains

As a basic problem of the nonlinear dynamic model, the online solution of time-varying cube root problem (TVCRP) is widely used in science and engineering. However, the practical system is frequently disturbed by the external factors, which inevitably leads to unknown disturbances in the solution process. Therefore, addressing the TVCRP with high accuracy in non-ideal environment (unknown disturbances) is the basis of solving the nonlinear dynamic model. In this work, a noise-suppression zeroing neural dynamics (NSZND) model is investigated and developed from the control perspective to resolve the time-varying or time-invariant cube root problem with the different disturbances (bounded and unbounded disturbances) in real/complex domain. Moreover, the generalized noise-suppression zeroing neural dynamics model with various activation functions is discussed and designed for eliminating the interference of different disturbances to improve the precision and noise immunity of the NSZND model. The global/exponential convergence of the developed models with various disturbances are proved by theoretical analyses. With unbounded disturbance (linear noise), the solving accuracy of the NSZND model is about 101 and 103 times superior to the gradient neural dynamics model and the zeroing neural dynamics model. Finally, the proposed NSZND model is extended to the tensor cube root problem, and the feasibility of the proposed model is verified in this work. Beyong that, different fractals are generated by using the proposed model to solve the cube root problem in the complex domain, which provides an interesting idea for advertising design and computer graphics.