Equations of Motion for the Socio-Configuration

It has been explained in Sect. 3.1, that the motions of the socio-configuration and the situation vector are coupled. Nevertheless it is reasonable in a first approximation to treat the equations for the socio-configuration n (t) separately. The justification for this is that the motion of n (f) is due to collective psychological processes which in general are much more flexible than the material situation y(t). This implies that n(t) often (but not always) changes much more quickly than y (t). In these cases y (t) can be regarded as quasi-constant and the couphng of its dynamics with n (t) need not be considered. This is the approximation adopted in the models of Chapters 2, 4. 

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Equations of Motion for the Socio-Configuration 63 is introduced and normalized to... 

The equations of motion for the socio-configuration do not yet reflect the full complexity of the dynamics of a socio-system. Nevertheless they describe the motion of collective psychological and political processes (namely the changes... 

At such a point quantitative argumentation can be applied The qualities and their intensities are translated into grossvariables of the socio-configuration and of the material situation. Finally, a dynamic model in terms of equations of motion for the grossvariables is tailored which takes the qualitative model mentioned above into account. 

Turning to the equations of motion for the six primary gross variables Pi, P2, E2, Qi and Q2 it is convenient to begin with the variables Pj of political psychology in In the simplest non-trivial case the socio-configuration (6.1) would consist of members of the society disposing of one dovish (a = 1) and one hawkish (a = - 1) attitude only ... 

Inserting (6.13) into the mean value equations of motion for the components ria of the socio-configuration,... 

Of course, the assumption of one dovish and one hawkish attitude only is an oversimplification. Returning to the general case described by (6.1-3) it can be shown that there exists a plausible choice of individual transition probabilities between the elements of a set of gradually varying attitudes leading to exactly the same equation of motion (6.12) for the collective variable Pj, even though the socio-configuration considered is much more complicated. 

So far, the discussion of the equation of motion (6.28) and of the potentials formally corresponds with that of the equations (2.48) and (2.124) for the opinion formation model in Sect. 2.4. In the presently discussed model, however, Pj is a collective variable of a complex socio-configuration and, more important, the trend parameters <5y, JCy depend on further dynamic grossvariables. Hence the shape of the potentials (6.29) will vary during the motion of all grossvariables. The equations (6.28) then describe the motion of Pj in terms of time dependent potentials, whose shape is determined by the other equations of motion not yet discussed. Thus the form of the dependence of the trend parameters (5y, Kj on the other grossvariables should now be considered. 

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