Theory of an m × n apple surface network with special boundary

Abstract

As is well known, any condition change in a network model will affect the research method and result. This paper studies an arbitrary m × n apple surface network with a pair of non-uniform boundary resistors, which is a complex network that has not been solved before. The research process of this paper consists of four strict basic steps according to RT-V theory. With the breakthrough of matrix transformation and eigenvector solution, two exact potential function formulae and two equivalent resistance formulae are derived. A series of applications and special cases are given to help readers understand the results. In particular, we have drawn eight visualized potential function images, which can intuitively understand the changing characteristics of potential function. The establishment of theoretical results provides a new theoretical basis for related interdisciplinary research.