This will not simulate non-classical correlations then. You either need to have superdeterminism, retrocausality (i.e. actual information carrying physical interaction moving back in time), nonlocality (actual interaction at a distance), rejection of Reichenbach's principle (specifically the no decorrelating explanation part), rejection of single outcomes or reject the concept of the fundamental dynamics being mathematical (i.e. anti scientific realism). It doesn't matter if the dynamics is chaotic, dissipative and more nonlinear than anything ever conceived, unless one of these things is true Bell's theorem guarantees it will fail to replicate non-classical correlations.