The Bifurcating Neuron Network 3 as coloring problem solver and N-ary associative memory

Abstract

The Bifurcating Neuron (BN) is an integrate-and-fire neuron that exhibits crisis-mediated transitions between multiple, symmetrical chaotic attractors. The Bifurcating Neuron Network 3 (BNN-3), a class of BN networks, was reported to be a natural model for solving coloring problems due to the multi-stability of BN. An important question left behind unanswered by the preliminary report was the scalability of BNN-3 as a coloring problem solver. Another question was the possibility of BNN-3 playing an N-ary associative memory as other multi-state neuron network models do. We carried out an extended study and were able to reach positive conclusions for both questions.