Diffusion-Localization Transition Point of Gravity Type Transport Model on Regular Ring Lattices and Bethe Lattices

Abstract Focusing on the diffusion-localization transition, we theoretically analyzed a nonlinear gravity-type transport model defined networks called regular ring lattices, which have an intermediate structure between complete graph and simple ring. Exact eigenvalues were derived around steady states, values of transition points evaluated for control parameter characterizing nonlinearity. We also case Bethe lattice (or Cayley tree) found that point is 1/2, lowest value ever reported.