A novel cell-coupling leading to nonlocal interactions

Abstract

ABSTRACT: It is shown that nonlocal interactions and phenomena can be achieved through local considerations, in which the departure of some scalar field from an harmonic one in a point changes as a function of the field itself in such point. After discretizing the equation of motion, it is shown that the shape of the nonlocal interaction function depends deeply on the choice of boundary conditions. As a physical implementation, the found interactions describes the evolution for the inductively coupled nonlinear networks. A qualitative analysis suggests that under such interactions the system self-organizes quite naturally, finally this is evidenced through the numerical solution of the equations of motion in the case of local cubic nonlinearities for two diferent boundary conditions.