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Assume two different communities each of which maintain their respectiveopinions mainly because of the weak interaction between the two communities. Insuch a case, it is an interesting problem to find the necessary strength ofinter-community interaction in order for the two communities to reach aconsensus. In this paper, the Information Accumulation System (IAS) model isapplied to investigate the problem. With the application of the IAS model, theopinion dynamics of the two-community problem is found to belong to a widerclass of two-species problems appearing in population dynamics or incompetition of two languages, for all of which the governing equations can bedescribed in terms of coupled logistic maps. Tipping diffusivity is defined asthe maximal inter-community interaction that the two communities can stay indifferent opinions. For a problem with simple community structure andhomogeneous individuals, the tipping diffusivity is calculated theoretically.As a conclusion of the paper, the convergence of the two communities to thesame value is less possible the more overall interaction, intra-community andinter-community, takes place. This implies, for example, that the increase inthe interaction between individuals caused by the development of moderncommunication tools, such as facebook and twitter, does not necessarily improvethe tendency towards global convergence between different communities. If thenumber of internal links increases by a factor, the number of inter-communitylinks must be increased by an even higher factor, in order for consensus to bethe only stable attractor.

Tipping Diffusivity in Information Accumulation Systems: More Links, Less Consensus