Frustrated chaos in neural networks

Abstract

Frustrated chaos is one of the most frequent dynamical regimes encountered in basic neural networks of any size. This chaotic regime results from an intertwining of almost stable attractors and leads to an unpredictable itinerancy among these attractors. Similarities with the classical intermittency and crisis-induced intermittency chaotic regimes are underlined. Original aspects of this chaos are the induction of this regime by a logical frustration of the connectivity structure, the recursive nature of the bifurcation diagram in which new cycles of increasing size appears continuously by increasing the resolution of the diagram, the description of this chaos as a weighted combination of the cycles at both ends of the chaotic window (the importance of each cycle being dependent on the distance to the critical points). The problematic of learning should draw some benefits from a better understanding of the bifurcations occurring by varying the connection values.