Delayed transiently chaotic neural networks and their application

In this paper, we propose a novel model, a delayed transiently chaotic neural network (DTCNN), and numerically confirm that the model performs better in finding the global minimum for the traveling salesman problem (TSP) than the traditional transiently chaotic neural network. The asymptotic stability and chaotic behavior of the dynamical system with time delay are fully discussed. We not only theoretically prove the existence of Marotto's chaos for the delayed neural network without the cooling schedule by geometrically constructing a transversal homoclinic orbit, but we also discuss the stability of nonautonomous delayed systems using LaSalle's invariance principle. The result of the application to the TSP by the DTCNN might further explain the importance of systems with time delays in the neural system.