The second-order ZD, GD and hybrid systems solving nonlinear equations compared with other dynamics

Solving nonlinear equations has become increasingly significant and indispensable in many disciplines. In the recent decade, two powerful methods, the Zhang dynamics (ZD) method and the gradient dynamics (GD) method have been extensively investigated and implemented in solving nonlinear equations. In addition, some conventional methods, such as the dynamic relaxation method (DRM), redundant manipulators dynamics (RMD), and Langevin dynamics (LD), can also be applied to solve nonlinear equations. In this paper, we propose four novel types of systems based on the ZD method, the GD method and the hybrid dynamics methods to solve nonlinear equations in time-invariant and time-variant situations, respectively. In addition, it is worth pointing out that, by comparison, the four proposed systems depicted in the second-order dynamics are evidently quite different from and more general than some other conventional systems/dynamics for solving nonlinear equations, which all constitute the unified second-order methodology for nonlinear equations solving.