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We show that a discrete dynamical system with delayed arguments that describe the computational performance of a neural network with a loop structure can exhibit the coexistence of huge number of periodic solutions, and we describe the domains of attraction for the stable periodic orbits. This demonstrates a great potential of discrete time delayed neural nets with a loop structure for the purpose of storage and retrieval of periodic patterns.doi:10.1142/s0218127404011090 fatcat:5pm6crn3fzel7lxes26wzqys54