Neighboring Stable Equilibrium Points in Spatially-Periodic Nonlinear Dynamical Systems: Theory and Applications

Stability is of fundamental importance to the design and application of control systems, in which stable equilibrium points and the neighboring points can have various interesting physical implications. In the paper, we derive a lower bound and an upper bound on the number of neighboring stable equilibrium points in the spatially-periodic nonlinear dynamical systems. It is shown that, in such an n-dimensional system, there are at least 2n neighboring stable equilibrium points. Meanwhile, an upper bound on the number of neighboring stable equilibrium points is derived. Some applications of these analytical results are illustrated.