SOCIAL PEACE deals with a problem from the field of sociology. The problem itself is described by a system of ordinary nonlinear differential equation systems (ODEs) or by discrete-time dynamic systems (MAPs) and visualized by attractors. The system of equations has the following general structure:
x' = a₁y + b₁z + c₁yz
y' = a₂x + b₂z + c₂xz
z' = a₃x + b₃y + c₃xy
or
x' = ay + bz + cyz + dy² + ez²
y' = az + bx + czx + dz² + ex²
z' = ax + by + cxy + dx² + ey²
The variables x,y,z mean:
Freedom
Prosperity
Contentment
These three sociological categories are interrelated in such a way that each depends on the other two. For social peace, it is essential that these categories behave in a reasonable relationship to one another. If this is not the case, social peace is disturbed. This would also be reflected in the shape of the attractors. Due to the symmetry of the equation approach, the specific assignment of the variables x, y, z to the categories of freedom, prosperity and Contentment is initially uninteresting.
Mathematically speaking, an attractor is a value or a series of values to which variables in a dynamic system tend to develop. In the individual parameter sets in SOCIAL PEACE, you can change the coefficients of the relevant ODE/MAP system using scroll bars. You can now observe how the attractor changes. If you use scroll bars, you change the coefficients of the ODE system (i.e. the parameters of the sociological process) and the shape of the attractor changes. The shape and dynamic behavior of the attractor allow conclusions to be drawn about the stability and characteristics of the process.
