12.8 MB

Windows

2022-06-19

### VisualEconomics应用简介

The examples in VISUAL ECONOMICS visualize economic processes by attractors. The processes themselves are described by ordinary nonlinear differential equation systems (ODEs), which have the following general structure:

x’ = fx(x,y,z)
y’ = fy(x,y,z)
z’ = fz(x,y,z)

and in some cases the following special structure

x’ = a₁₀ + a₁₁x + a₁₂y + a₁₃z + a₁₄xy + a₁₅xz + a₁₆yz + a₁₇x² + a₁₈y² + a₁₉z² + b₁₀x³ + b₁₁x²y + b₁₂x²z + b₁₃xy² + b₁₄xyz + b₁₅xz² + b₁₆y³ + b₁₇y²z + b₁₈yz² + b₁₉z³

y’ = a₂₀ + a₂₁x + a₂₂y + a₂₃z + a₂₄xy + a₂₅xz + a₂₆yz + a₂₇x² + a₂₈y² + a₂₉z² + b₂₀x³ + b₂₁x²y + b₂₂x²z + b₂₃xy² + b₂₄xyz + b₂₅xz² + b₂₆y³ + b₂₇y²z + b₂₈yz² + b₂₉z³

z’ = a₃₀ + a₃₁x + a₃₂y + a₃₃z + a₃₄xy + a₃₅xz + a₃₆yz + a₃₇x² + a₃₈y² + a₃₉z² + b₃₀x³ + b₃₁x²y + b₃₂x²z + b₃₃xy² + b₃₄xyz + b₃₅xz² + b₃₆y³ + b₃₇y²z + b₃₈yz² + b₃₉z³

Mathematically an attractor is a value or set of values toward which variables in a dynamical system tend to evolve.
In the examples in VISUAL ECONOMICS you may change the coefficients of the concerning ODE system by using of scrollbars. Meanwhile, it can be observed how the attractor changes. When using scrollbars, you change the coefficients of the ODE system (that is, the parameters of the economic process), and the shape of the attractor changes. The shape and dynamic behavior of the attractor allow conclusions about the stability and characteristics of the economic process.

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