For generic non-linear dynamical systems, we develop a theory to show that the exact edge of chaos is between the periodic cycle phase due to Neimark-Sacker bifurcation and the chaotic phase. The asymptotic Jacobian norm determines the location of the edge, and such theoretical result can be extrapolated to simple systems like the logistic map. It further establishes the understanding that the maximal number of periodic states is the reason behind the optimality of the system, such that it can represent the most diverse patterns, and this can be observed in both the logistic map and the neural networks. To verify the theory, our experiments on multilayer perception trained on benchmark dataset Fashion MNIST demonstrate the optimality of the models near the edge of chaos, as well as large periodic cycles associated with it.
