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This paper presents two contributions: (i) a new type of neural network the dynamic wave expansion neural network, for path generation in a dynamic environment for both mobile robots and robotic manipulators, and (ii) the simulative comparisons to known discrete-time neural network models - the classical resistive grid model, and the Hopfield-type neural network, proposed by Glasius et al. The network has discrete-time dynamics, is locally connected, highly parallel, and hence, computationally efficient. The model does not require any a-priory information about the environment. The path is generated according to a neural-activity landscape, which forms a dynamically updating scalar potential field over a distributed representation of the configuration space of a robot. The simulations reveal that the proposed model yields dominantly shorter paths, especially in highly-dynamic environments.