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

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