# How to plot the basin of attraction of a time delayed duffing oscillator

I have the following time delayed duffing oscillator equation.

u''[t] + h u'[t] + \[CapitalOmega]^2 u[t] + k u[t]^3 =  q u[t - \[Tau]]

h = 0.05; \[Tau] = 2; \[CapitalOmega] = 1.225; k = 0.5; q = 0.5;


How can I plot the basin of attraction of this time delayed equation.

• To solve delayed ode Mathematica NDSolve needs some information about the time history , something like u[ t /; t <= 0] == f[t]. Before doing this you should correct your ode u^3[t] -> u[t]^3 – Ulrich Neumann Dec 26 '17 at 21:50
• There are many questions relating to basins of attraction, including three for the Duffing equation. Please search Mathematica.StackExchange. – bbgodfrey Dec 26 '17 at 23:07
• I haven't worked with delay differential equations, so maybe this is an ignorant question, but doesn't the dynamics depend on the past history, not just the initial point? If so, how would you plot this in 2D? Do you have an example of such a plot from the literature that you want to reproduce? – Chris K Dec 31 '17 at 16:02