Verhulst–Lotka–Volterra (VLV) model of ideological struggle

A model for ideological struggles is formulated. The underlying set is a closed one, like a country but in which the population size is variable in time. The dynamics of the struggle is described by model equations of Verhulst–Lotka–Volterra kind. Several “ideologies” compete to increase their number of adepts. Such followers can be either converted from one ideology to another or become followers of an ideology though being previously ideologically-free. A reverse process is also allowed. Two kinds of conversions are considered: unitary conversion, e.g. by means of mass communication tools, or binary conversion, e.g. by means of interactions between people. It is found that the steady state, when it exists, depends on the number of ideologies. Moreover when the number of ideologies increases some tension arises between them. This tension can change in the course of time. We propose to measure the ideology tensions through an appropriately defined scale index. Finally it is shown that a slight change in the conditions of the environment can prevent the extinction of some ideology; after almost collapsing the ideology can spread again and can affect a significant part of the country’s population. Two kinds of such resurrection effects are described as phoenix effects.