基本信息

更新日期:
版本:
最新版
大小:
1.26 MB
类型:
教育
平台:
Windows
评分:
2
发布日期:
2022-03-13
价格:
免费
开发者:

Attractors应用截图

【图】Attractors(截图1)

Attractors应用简介

Using “Attractors” you may search for new Strange Attractors in the following differential equation system (ODE system):

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 + b₂z³

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

The 60 coefficients correspond to 60 scroll bars in „Attractors“. The solution of the ODE system is shown as trajectories in the phase space. Changing the scroll bars (i. e. the coefficients) is immediately shown as changed trajectories. Found new Strange Attractors may be saved.
If on the computer Matlab is installed, some additional calculations can be executed for the new found attractors, namely their Lyapunov Exponents, Critical Points and Eigen Values. The Lyapunov exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectories. The calculation results are saved in an additional file.

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