Abstract
Hostility between two populations n and m is described in terms of a first-order differential equation system for the population sizes n(t) and m(t) over time t. Each population is subdivided into two subpopulations 'Doves' and 'Hawks'. Hawks represent the strategy aggression against the other population. The number of hawks which actually exert aggression depends on the overall frustration within their population. Conversely, aggression causes the conversion from doves to hawks in the attacked population. Thus, a system of flows among the subpopulation is established. The actual behaviour of n(t) and m(t) over time t depends on the coefficients chosen for the differential system and in particular on the temporal development of the frustration parameters. No calculation or simulation of actual population sizes is intended. The only goal of the paper is to establish a model which describes an never ending conflict between both populations caused by internal frustrations.
Highlights
Consider two human populations n and m
Smn is expressed by a differential term depending on n(t) in the differential equation for the growth dm(t)/dt of m(t) with time t
Sociophysics covers a lot of topics, see for example [1] for a review
Summary
Consider two human populations n and m. Our only goal is to introduce contentedness/frustration as a mechanism which subdivides a population into irenic and aggressive subpopulations. In terms of the model, this perception leads to a flow from the irenic subpopulation of n to the aggressive subpopulation of n This flow is the stronger the stronger the frustration (1-un(t)) is. Consider a population n with n(t) members at time t. Smn is expressed by a differential term depending on n(t) in the differential equation for the growth dm(t)/dt of m(t) with time t. Similar equations apply to the aggressive subpopulation nH, nH(t) = nHl(t)+nHh(t). Internal growth appears among two subpopulations of a given population. The factor (1 − un(t)) restricts the transition to members of nDH(t) = (1 − un(t)) nD(t), since in our model only highly frustrated individuals change from non-aggressive to aggressive behaviour.
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