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Tamari Attractor


TamariAttractor

The Tamari attractor is the attractor of a three-dimensional autonomous system introduced as a model of cyclical economic growth. A commonly plotted form satisfies

x^.=(x-ay)cosz-bysinz
(1)
y^.=(x+cy)sinz+dycosz
(2)
z^.=e+fz+gatan^(-1)((1-u)/(1-i)xy),
(3)

where a, b, c, d, e, f, g, u, and i are parameters. The values a=1.013, b=-0.021, c=0.019, d=0.96, e=0, f=0.01, g=1, and u=i=0.05 produce a bounded aperiodic map orbit with a folded band structure.

The name refers to the particular system rather than to a general class of attractors. As with other numerically displayed strange attractors, the appearance depends on the parameters, initial conditions, integration interval, and projection.


See also

Attractor, Autonomous, Lorenz Attractor, Map Orbit, Strange Attractor

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References

E-Cell Project. "Tamari Attractor." https://ecell4.e-cell.org/examples/example01.html.Zeleny, E. "Tamari Attractor." Wolfram Demonstrations Project. https://demonstrations.wolfram.com/TamariAttractor/.

Cite this as:

Weisstein, Eric W. "Tamari Attractor." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TamariAttractor.html

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