As a continuous opinion dynamics model, the information accumulation system (IAS) includes three basic mechanisms of the news, the inheritance and the diffusion as contributing to the information accumulation process of a system. A system is composed of agents who diffuse information through internal interaction, while each of them has incomplete memory or inheritance rate. The news comes from external sources of information, such as mass media. Previously the model IAS was studied only for the small news problems. In this study, a tipping news problem is considered. A key question of the problem is: what is the minimum strength of advertisement that can tip the minority opinion to a majority one? Dynamics of the IAS is briefly revisited with a special interest on nonlinear behavior of the model. In particular, it is shown that a discrete map of the IAS for a single color problem can be transformed into a logistic map, from which the dynamics of the IAS can be better understood. To show the applicability of the IAS model, the result is applied to explain the concept of the critical population size, which claims that there is a minimum population size for a social knowledge system to be continuously inherited without being lost. And critical size of the tipping news is found analytically in terms of IAS parameters. Some of the key results from the present study are compared in detail with the results from the Brownian particle model, which is believed to be the most similar model to the IAS. The concept of tipping news is used to show that a traditional society can tip at an exceptionally low inter-community exposure. Finally, the result was applied to the language competition problem.
