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 prac-tical 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 non-linear 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 pre-cision 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, dif-ferent 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 com-puter graphics.

Automated summary

In this study, a noise-suppression zeroing neural dynamics (NSZND) model is developed from the control perspective to solve the time-varying or time-invariant cube root problem with different disturbances. The model achieves superior solving accuracy compared to other models and is extended to solve the tensor cube root problem and generate different fractals in the complex domain.