If we couple two 1D maps of the form x(k+1)=g(x(k)), and get a 2D map like x(k+1)=f(y(k),x(k)); y(k+1)=f(x(k),y(k)), where the function f and its related parameters are the same for both variables, and only the initial conditions of x and y are differently assigned, is it possible to have different attractors for x and y in the new coupled 2D map?
Sajad Jafari
I think you should change your equations to x(k+1) = f(x(k), y(k)), y(k+1) = f(y(k),x(k))
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Christophe Letellier
In fact, there is a single attractor since you have a single system made of the two coupled map. Synchronized or not, there is a unique attractor in the phase space R^2(x,y).
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