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Mackey-Glass Equation

The Mackey-Glass equation is a nonlinear delay differential equation with a constant delay tau>0 and a nonmonotonic feedback term (Mackey and Glass 1977, Glass and Mackey 2010). For nonnegative x(t), one form is

x^'(t)=(betax(t-tau))/(1+[x(t-tau)]^n)-gammax(t),

where x^'(t) is the derivative with respect to time t, beta,gamma>0, and n>1. The constant solution x(t)=0 always exists. There is also a positive constant solution x(t)=(beta/gamma-1)^(1/n) when beta>gamma. Numerical studies show both periodic solutions and chaos as the parameters vary (Glass and Mackey 2010).

See also

Chaos, Delay Differential Equation

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References

Glass, L. and Mackey, M. C. "Mackey-Glass Equation." Scholarpedia 5, 6908, 2010. https://doi.org/10.4249/scholarpedia.6908.Mackey, M. C. and Glass, L. "Oscillation and Chaos in Physiological Control Systems." Science 197, 287-289, 1977. https://doi.org/10.1126/science.267326.

Cite this as:

Weisstein, Eric W. "Mackey-Glass Equation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Mackey-GlassEquation.html

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