Global bifurcation structure of chaotic neural networks and its application to traveling salesman problems

This paper studies global bifurcation structure of the chaotic neural networks applied to solve the traveling salesman problem (TSP). The bifurcation analysis clarifies the dynamical basis of the chaotic neuro-dynamics which itinerates a variety of network states associated with possible solutions of TSP and efficiently ‘searches’ for the optimum or near-optimum solutions. By following the detailed merging process of chaotic attractors via crises, we find that the crisis-induced intermittent switches among the ruins of the previous localized chaotic attractors underly the ‘chaotic search’ for TSP solutions. On the basis of the present study, efficiency of the ‘chaotic search’ to optimization problems is discussed and a guideline is provided for tuning the bifurcation parameter value which gives rise to efficient ‘chaotic search’.