Guaranteed storage and stabilization of desired binary periodic orbits in three-layer dynamic binary neural networks

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This paper presents three-layer dynamic binary neural networks characterized by ternary connection parameters and the signum activation function. The dynamics is described by a difference equation of binary state variables. Depending on the parameters, the network can generate various binary periodic orbits. We give two main theoretical results. First, when a desired periodic orbit is given, we can set the parameters that guarantee storage and local stability of the periodic orbit. The stability is related to error correction of various binary signals in engineering applications. Second, if a part of the connection parameters becomes zero then stability of the periodic orbit becomes very strong. In this case, all the initial states fall directly into the periodic orbit.