The Duffing map (also called as 'Holmes map') is a discrete-time dynamical system. It is an example of a dynamical system that exhibits chaotic behavior. The Duffing map takes a point (xn, yn) in the plane and maps it to a new point given by

x n 1 = y n {\displaystyle x_{n 1}=y_{n}}
y n 1 = − b x n a y n − y n 3 . {\displaystyle y_{n 1}=-bx_{n} ay_{n}-y_{n}^{3}.}

The map depends on the two constants a and b. These are usually set to a = 2.75 and b = 0.2 to produce chaotic behaviour. It is a discrete version of the Duffing equation.

External links

  • Duffing oscillator on Scholarpedia



Duffing attractor and Poincaré return map for a ¼ 02954 and b ¼ 02875

Bifurcation diagram of the state of the Duffing oscillator given by

The strange attractors of the original and modulated Duffing map

Based on counting iterations of the Duffing map for each pixel. 2nd

Duffing map alogorithm, (a) Time series for chaotic duffing map and (b